# This is the main file of the program. 

# Global variables are:
# MPL_CTYPE, MPLf, MPLft, MPLb, COMPATIBILITY_GRAPH, MPL_CoefflnZeroList, MPLGlobalCoordinates, MPLnumberofvar, MPLvariable, MPLArnoldEq, MPLLowestArnoldEquations

#==========================================
# Changes since version 1.0:
# Version 1.1: 
# - A slight change in the procedure MPLPrimitive: The maximal length of
#   words in the integrand is now determined automatically. Therefore the third argument 
#   of the procedure is removed.
#
#==========================================



MPLVersionNumber:=proc()
return "1.1":
end proc:


# Print the name of the program:
printf(cat("MPL Version ",MPLVersionNumber()));
printf("");

# All additional Maple-packages are read here:
with(difforms):
with(linalg):
with(LinearAlgebra):
with(SolveTools):
with(ListTools):
with(FileTools):
with(combinat):
#with(Threads):

# Basic definitions:
define(bar,'multilinear', bar(1)=1, bar(1,1)=1, bar(ONE)=ONE, bar(0)=0):
define(barlog,'multilinear', barlog(1)=1, barlog(1,1)=1, barlog(ONE)=ONE, barlog(0)=0):
define(base,'multilinear', base(1)=1, base(1,1)=1, base(ONE)=ONE, base(0)=0):
define(tens,'multilinear', 
tens(a::anything, 1) = a, 
tens(1, a::anything) = a,
tens(a::anything) = a,
tens(a::anything, tens(b::anything, ONE)) = conc(a,b), 
tens(a::anything, tens(b::anything, c::anything)) = tens(conc(a,b),c)):
define(conc,'multilinear', 'flat', 
 conc(ONE)=1,
 conc(1)=1,
 conc(a::algfun)=a,
 conc(c::anything*tens(a::anything, b::anything))=c*conc(a,b),
 
  
 conc(a::anything, 1) = a,
 conc(a::anything, ONE) = a,
 conc(ONE, b::anything) = b,
 conc(a::function, b::function) = bar(unbar(a), unbar(b))):
define(expansion, 
expansion(va::anything, u::integer, ONE) = 1,
expansion(va::anything, u::integer, tens(a::anything, ONE)) = EXPAND(va, u, a), 
expansion(va::anything, u::integer, tens(bar(a::anything), b::anything)) = integr(conc(bar(a),b), va, u, EXPAND(va, u, a)*expansion(va, u, unconc(b))) ): 
define(multipl,'multilinear',
multipl(tens(ONE, a::anything))=a,
multipl(tens(a::anything,ONE))=a,
multipl(tens(a::anything,b::anything))=a*b,
multipl(tens(a::anything,b::anything)*c::anything)=a*b*c,
multipl(a::const)=a,
multipl(bar(a::anything))=bar(a),
multipl(ONE)=1):

unbar:=proc(expr1)
return op(expr1):
end proc:


MPL_CTYPE:=2:





####################################################################
####################################################################
#
#   BASIC OPERATIONS
#
####################################################################
####################################################################



# The following creates the list of all coordinates of the type 'ctype' 
# (e.g. ctype=1 produces simplicial coordinates, ctype=2 cubical coordinates ...)

GetCoordinates:=proc(variablename::symbol, n::integer, ctype::integer)
local i, output;
output:=[]:
defform(variablename=0):
# simplicial coordinates t:
# construct the sequence [0, t[1], t[2], ..., t[n], 1]
if ctype=1 then 
 for i from 0 to n+1 do
  if i=0 then output:=[op(output), 0]:
  elif i=n+1 then output:=[op(output), 1]:
  else output:=[op(output), variablename[i]]:
  end if:
 end do:
# cubical coordinates x:
elif ctype=2 then 
 for i from 1 to n+1 do
  output:=[op(output),variablename[i]]:
 end do:
# For the purpose of testing other parts of the program, we introduce test-coordinates v[0], v[1], ..., v[n+1]:
elif ctype=50 then
 defform(variablename=0, e=1, b=1, f=1):
 for i from 0 to n+1 do
  output:=[op(output), variablename[i]]:
 end do:
#here further types of coordinates can be included 
else output:=[]:
end if:
return output:
end proc:



# For some purposes, the coordinates have to be available as a global list:

SetGlobalCoordinates:=proc(va, howmany)
local i:
global MPLGlobalCoordinates:
defform(va=0):
MPLGlobalCoordinates:=[]:
for i from 1 to howmany do
 MPLGlobalCoordinates:=[op(MPLGlobalCoordinates),va[i]]:
end do:
end proc:



# Procedure for deriving all Arnold relations for cubical coordinates and a given n.
# It uses ArnoldCubical and may be called by MPLInitialize.

CreateArnoldCubical:=proc()
global MPLArnoldEq, MPLLowestArnoldEquations:
local i, j, output, NewRhs:
# For MPLnumberofvar<13 the equations are read from a list which is stored in MPL.txt.
# For MPLnumberofvar>12 the equations are derived using ArnoldCubical. This may be the reason for long computation times.
if MPLnumberofvar<13 then 
 MPLArnoldEq:=MPLLowestArnoldEquations[MPLnumberofvar+1]:
else
 output:=[]:
 for j from 2 to MPLnumberofvar+2 do
  for i from 1 to j-1 do
   NewRhs:=ArnoldCubical(MPLft[j], MPLft[i]):
   output:=[op(output), NewRhs]:
  end do:
 end do:
 MPLArnoldEq:=output:
end if:
end proc:



# MPLCoordinates is the user-friendly wrap around MPLInitialize.

MPLCoordinates:=proc(variablename::symbol, n::integer)
return MPLInitialize(variablename, n-1):
end proc:



# The following declares the coordinates due to choices by the user.
# The option to use other than cubical coordinates is still kept here from
# previous versions, but not supported by most of MPL. 
# The default value MPL_CTYPE=2 selects the cubical coordinates.

MPLInitialize:=proc(variablename::symbol, n::integer)
local ctypeword: 
global MPL_COORDINATES, MPLnumberofvar, MPL_CTYPE, MPLvariable:
MPL_COORDINATES:=GetCoordinates(variablename, n, MPL_CTYPE):
MPLnumberofvar:=n:
MPLvariable:=variablename:
if MPL_CTYPE=1 then ctypeword:="simplicial":
elif MPL_CTYPE=2 then ctypeword:="cubical":
 if nargs>3 then 
  if args[4]=true then CreateArnoldCubical():
  end if:
  else CreateArnoldCubical():
 end if:
elif ctype=50 then ctypeword:="symbolical":
else ctypeword:="undefined":
end if:
if nargs>2 then 
 if args[3]=true then 
  printf("%s\n",cat("You are using ", cat(ctypeword, cat(" coordinates: ", convert(MPL_COORDINATES, string)))));
 end if:
end if:
end proc:



# List of differential 1-forms in the basis of the total space:

MPLFormsTotal:=proc()
local i, j, output, counter, newterm;
userinfo(1, 'basic', "(n, ctype): Creates the list of basic forms of the total space Omega_E;"):
output:=[]:
# simplicial coordinates:
if MPL_CTYPE=1 then 
 for i from 1 to n+1 do
  for j from 0 to i-1 do
   newterm:=(d(MPL_COORDINATES[i+1])-d(MPL_COORDINATES[j+1]))/(MPL_COORDINATES[i+1]-MPL_COORDINATES[j+1]):
   output:=[op(output), newterm]:
  end do:
 end do:
# cubical coordinates x:
 elif MPL_CTYPE=2 then
 output:=[op(MPLFormsBase()), op(MPLFormsFiber(true))]: 
# test-coordinates v[i]:
elif MPL_CTYPE=50 then
defform(e=1, b=1, f=1):
counter:=1:
for i from 1 to MPLnumberofvar+1 do
  for j from 0 to i-1 do
   newterm:=e[counter]:
   output:=[op(output), newterm]:
   counter:=counter+1:
  end do:
 end do:
# further coordinates ...
else output:=[]:
end if:
return output:
end proc:
 


# List of differential 1-forms in the basis of the base:

MPLFormsBase:=proc()
local i, j, k, output, counter, newterm, newproduct;
output:=[]:
# simplicial coordinates:
if MPL_CTYPE=1 then 
 for i from 1 to MPLnumberofvar+1 do
  for j from 0 to i-1 do
   newterm:=(d(MPL_COORDINATES[i+1])-d(MPL_COORDINATES[j+1]))/(MPL_COORDINATES[i+1]-MPL_COORDINATES[j+1]):
   if (not(i=MPLnumberofvar) and not(j=MPLnumberofvar)) then
    output:=[op(output), newterm]:
   end if:
  end do:
 end do:
# cubical coordinates x:
elif MPL_CTYPE=2 then 
 for j from 1 to MPLnumberofvar do
  for i from 0 to j do
   newproduct:=1:
   if i=0 then newterm:=d(MPL_COORDINATES[j])/MPL_COORDINATES[j]:
   else 
    for k from i to j do
     newproduct:=newproduct*MPL_COORDINATES[k]:
    end do:
    newterm:=d(newproduct)/(1-newproduct):
   end if:
   output:=[op(output),newterm]:
  end do:
 end do:
# test-coordinates v[i]:
elif MPL_CTYPE=50 then 
defform(e=1, b=1, f=1):
counter:=1:
 for i from 1 to MPLnumberofvar+1 do
  for j from 0 to i-1 do
   newterm:=MPLb[counter]:
   if (not(i=MPLnumberofvar) and not(j=MPLnumberofvar)) then
    output:=[op(output), newterm]:
    counter:= counter+1:
   end if:
  end do:
 end do:
# further coordinates ...
else output:=[]:
end if:
return output:
end proc:


# List of differential 1-forms in the basis of the fiber.
# The boolean argument fixes, whether it is the lifted fiber or not.

MPLFormsFiber:=proc(tilde::boolean)
local i, j, k, output, counter, newproduct, newterm, tildeterm, BasicForms;
output:=[]:
# simplicial coordinates:
if MPL_CTYPE=1 then 
 for i from 0 to MPLnumberofvar+1 do
  if (not(i=MPLnumberofvar)) then 
   if tilde then tildeterm:=d(MPL_COORDINATES[i+1]):
   else tildeterm:=0:
   end if:
   newterm:=(d(MPL_COORDINATES[MPLnumberofvar+1])-tildeterm)/(MPL_COORDINATES[MPLnumberofvar+1]-MPL_COORDINATES[i+1]):
   output:=[op(output), newterm]:
  end if:
 end do:
# cubical coordinates x:
elif MPL_CTYPE=2 then 
 for i from 0 to MPLnumberofvar+1 do
  newproduct:=1:
  if i=0 then newterm:=d(MPL_COORDINATES[MPLnumberofvar+1])/MPL_COORDINATES[MPLnumberofvar+1]:
  elif i=MPLnumberofvar+1 then newterm:=d(MPL_COORDINATES[MPLnumberofvar+1])/(1-MPL_COORDINATES[MPLnumberofvar+1]):
  else 
   for k from i to MPLnumberofvar do
    newproduct:=newproduct*MPL_COORDINATES[k]:
   end do:
   if tilde then newterm:=d(newproduct*MPL_COORDINATES[MPLnumberofvar+1])/(1-newproduct*MPL_COORDINATES[MPLnumberofvar+1]):
   else newterm:=newproduct*d(MPL_COORDINATES[MPLnumberofvar+1])/(1-newproduct*MPL_COORDINATES[MPLnumberofvar+1]):
   end if:
  end if:
  output:=[op(output),newterm]:
 end do:
# test-coordinates v[i]:
elif MPL_CTYPE=50 then 
defform(e=1, b=1, f=1):
counter:=1:
 for i from 0 to MPLnumberofvar+1 do
  if (not(i=MPLnumberofvar)) then 
   if tilde then newterm:=MPLft[counter]:
   else newterm:=MPLf[counter]:
   end if:
   output:=[op(output), newterm]:
   counter:=counter+1:
  end if:
 end do:
# further coordinates ...
else output:=[]:
end if:
return output:
end proc:


# The following creates a list of words, where in each new word two of the neighbour-entries are paired.

PairNeighbours:=proc(word::list)
local i, j, output, newword;
userinfo(1, 'basic', "(word): creates a list of words, where in each new word two of the neighbour-entries are paired."):
output:=[]:
for i from 1 to nops(word)-1 do
 newword:=[]:
 # As the pairs stand for wegde-products, no word is added in this case of a pair of two equal neighbours.
 if not(op(i,word)=op(i+1,word)) then
  for j from 1 to nops(word) do
   if i=j then newword:=[op(newword), [op(j,word), op(j+1,word)]]:
   elif not(j=i+1) then newword:=[op(newword),op(j,word)]:
   end if:
  end do:
  output:=[op(output),newword]:
 end if:
end do:
return output:
end proc:


# Wedge products are given a canonical order:

OrderWedge:=proc(term)
local i, j, output:
output:=term:
for i from 1 to nops(MPL_COORDINATES) do
 for j from 1 to i do
  output:=subs(d(MPL_COORDINATES[i]) &^ d(MPL_COORDINATES[j]) = - d(MPL_COORDINATES[j]) &^ d(MPL_COORDINATES[i]),output):
 end do:
end do:
return output:
end proc:


# Creates a list of words, where in each new word two of the neighbour-entries are wedge-multiplied.

WedgeNeighbours:=proc(word::list)
local i, j, k, output, newword, OmegaE;
userinfo(1, 'basic', "(word): creates a list of words, where in each new word two of the neighbour-entries are wedge-multiplied."):
output:=[]:
OmegaE:=MPLFormsTotal():
for i from 1 to nops(word)-1 do
 newword:=[]:
 # No word is added in this case of a pair of two equal neighbours.
 if not(op(i,word)=op(i+1,word)) and not(simplify(op(i,word) &^ op(i+1,word))=0) then
  for j from 1 to nops(word) do
   if i=j then 
    newword:=[op(newword), OrderWedge(simplify(op(j,word) &^ op(j+1,word)))]:
   elif not(j=i+1) then newword:=[op(newword),op(j,word)]:
   end if:
  end do:
  output:=[op(output),newword]:
 end if:
end do:
return output:
end proc:



# For a word of elements in the fiber, each element is lifted to the total space.

Lift:=proc(word::list)
local i, j, OmegaF, OmegaFtilde, output, newword:
userinfo(1, 'basic', "(word, n, ctype): For a word of elements in the fiber, each element is lifted to the total space."):
output:=[]:
OmegaF:=MPLFormsFiber(false):
OmegaFtilde:=MPLFormsFiber(true):
# We assume that the elements of word are in OmegaF. We lift it to OmegaFtilde:
for i from 1 to nops(word) do
 newword:=word[i]:
 for j from 1 to nops(OmegaF) do
  newword:=subs([OmegaF[j]=OmegaFtilde[j],MPLf[j]=MPLft[j], normal(-OmegaF[j])=normal(-OmegaFtilde[j]),-MPLf[j]=-MPLft[j]],newword):
  #if word[i]=OmegaF[j] then output:=[op(output),OmegaFtilde[j]]:
  #end if:
 end do:
 output:=[op(output),newword]:
end do:
return output:
end proc:


# For a word of elements in the total space (Omega_F_tilde), each element is 'lowered' to the fiber.

Lower:=proc(word::list)
local i, j, OmegaF, OmegaFtilde, output, newword:
userinfo(1, 'basic', "(word, n, ctype): For a word of elements in the total space (Omega_F_tilde), each element is 'lowered' to the fiber."):
output:=[]:
OmegaF:=MPLFormsFiber(false):
OmegaFtilde:=MPLFormsFiber(true):
# We assume that the elements of word are in OmegaFtilde. We lower it to OmegaF:
for i from 1 to nops(word) do
 newword:=word[i]:
 for j from 1 to nops(OmegaFtilde) do
  newword:=subs([OmegaFtilde[j]=OmegaF[j],MPLft[j]=MPLf[j], normal(-OmegaFtilde[j])=normal(-OmegaF[j]),-MPLft[j]=-MPLf[j]],newword):
  #if word[i]=OmegaFtilde[j] then output:=[op(output),OmegaF[j]]:
  #end if:
 end do:
 output:=[op(output),newword]:
end do:
return output:
end proc:


# ZMatrix is an auxiliary matrix of coefficients of Arnold relations. 

ZMatrix:=proc(rows,columns)
local i, j, newrow, output:
output:=[]:
for i from 1 to rows do
 newrow:=[]:
 for j from 1 to columns do
  newrow:=[op(newrow),0]:
 end do:
 output:=[op(output),newrow]:
end do:
return output:
end proc:


# MPLshuffle(word1, word2) creates the list of all shuffles of word1 and word2.
# We use the name 'MPLshuffle' because 'Shuffle' already exists in Maple (and gives only one random shuffle).
# MPLshuffle has no userinfo, because it is called recursively and would print the info-text with each call.

MPLshuffle:=proc(word1::list, word2::list)
local i, j, a, b, w1, w2, part1, part2, output;
output:=[]:
#Cases with empty words: 
if (word1=[] and word2=[]) then output:=[[]]:
elif (not(word1=[]) and word2=[]) then output:=[op(output),word1]:
elif (word1=[] and not(word2=[])) then output:=[op(output),word2]:
elif (word1=[1] and word2=[1]) then output:=[[1]]:
elif (not(word1=[1]) and word2=[1]) then output:=[op(output),word1]:
elif (word1=[1] and not(word2=[])) then output:=[op(output),word2]:
else
 #For nonempty words we write word1=[a, w1], word2=[b, w2].
 a:=op(1,word1):
 w1:=subsop(1=NULL,word1):
 b:=op(1,word2):
 w2:=subsop(1=NULL,word2):
 part1:=MPLshuffle(w1,word2):
 part2:=MPLshuffle(word1,w2):
 for i from 1 to nops(part1) do
  part1[i]:=[a,op(part1[i])]:
 end do:
 for j from 1 to nops(part2) do
  part2[j]:=[b,op(part2[j])]:
 end do:
output:= [op(part1),op(part2)]:
end if:
return output:
end proc:


# MPLShuffleProduct is intended to be applied by the user for shuffle multiplication of combinations of bar-terms.

MPLShuffleProduct:=proc(term1, term2)
local i, j, k, term1list, term2list, coefflist1, coefflist2, wordlist1, wordlist2, newcoeffs, newwords, shuffleresult, position:
# First we check if term1 and term2 are lists. If not, we apply BarToLists.
if type(term1,list) then term1list:=term1:
else term1list:=BarToLists(term1):
end if:
if type(term2,list) then term2list:=term2:
else term2list:=BarToLists(term2):
end if:
coefflist1:=term1list[1]:
coefflist2:=term2list[1]:
wordlist1:=term1list[2]:
wordlist2:=term2list[2]:
newcoeffs:=[]:
newwords:=[]:
for i from 1 to nops(coefflist1) do
 for j from 1 to nops(coefflist2) do
  shuffleresult:=MPLshuffle(wordlist1[i],wordlist2[j]):
  for k from 1 to nops(shuffleresult) do
   newcoeffs:=[op(newcoeffs), coefflist1[i]*coefflist2[j]]:
  end do:
  newwords:=[op(newwords), op(shuffleresult)]:
 end do:
end do:
return ListsToBar([newcoeffs, newwords]):
end proc:



# The following few procedures serve for the translation of 
# differential 1-forms to internal symbolic notation:

FiberToSymbols:=proc(word)
local i, newword, OmegaF:
newword:=normal(word):
OmegaF:=MPLFormsFiber(false):
for i from 1 to nops(OmegaF) do
 newword:=subs(OmegaF[i]=MPLf[i], newword):
 newword:=subs(normal(-OmegaF[i])=-MPLf[i], newword):
end do:
return eval(newword):
end proc:


SymbolsToTotal:=proc(word)
local i, j, newword, OmegaFtilde, OmegaB:
newword:=word:
OmegaFtilde:=MPLFormsFiber(true):
OmegaB:=MPLFormsBase():
for i from 1 to nops(OmegaFtilde) do
 newword:=subs(MPLft[i]=OmegaFtilde[i], newword):
 newword:=subs(-MPLft[i]=-OmegaFtilde[i], newword):
end do:
for j from 1 to nops(OmegaB) do
 newword:=subs(MPLb[j]=OmegaB[j], newword):
 newword:=subs(-MPLb[j]=-OmegaB[j], newword):
end do:
return newword:
end proc:


TotalToSymbols:=proc(word)
local i, newword, OmegaFtilde, OmegaB:
newword:=normal(word):
OmegaFtilde:=MPLFormsFiber(true):
for i from 1 to nops(OmegaFtilde) do
 newword:=subs(OmegaFtilde[i]=MPLft[i], newword):
 newword:=subs(normal(-OmegaFtilde[i])=-MPLft[i], newword):
end do:
OmegaB:=MPLFormsBase():
for i from 1 to nops(OmegaB) do
 newword:=subs(OmegaB[i]=MPLb[i], newword):
 newword:=subs(normal(-OmegaB[i])=-MPLb[i], newword):
end do:
return eval(newword):
end proc:



# The coproduct of bar(a,b,...) is
# tens(bar(ONE), bar(a,b,...)) + tens(bar(a),bar(b,...)) + ... + tens(bar(a,b,...),bar(ONE))
# where bar(ONE) acts as the empty word.

MPLCoproduct:=proc(inp)
local i, j, preloutput, oneelement, output, newtens, BarTable:
if not(has(inp, bar)) then return 0:
end if:
BarTable:=table():
BarToTable(inp,BarTable):
output:=0:
for j in indices(BarTable,'nolist') do
 if j=[1] then
  output:=output:
 else
  newtens:=tens(bar(ONE),bar(op(j))):
  preloutput:=newtens:
  for i from 1 to nops(bar(op(j)))-1 do
   newtens:=tens(op(1,newtens), unconc(op(2,newtens))):
   if nargs<2 then 
    preloutput:=preloutput+eval(newtens):
   elif args[2]=i then 
    oneelement:=eval(newtens):
   end if:
  end do:
  if nargs>1 then 
   if args[2]=nops(bar(op(j))) then
    oneelement:=tens(bar(op(j)),bar(ONE)):
   elif args[2]=0 then 
    oneelement:=tens(bar(ONE),bar(op(j))):
   elif args[2]>nops(bar(op(j))) then
    oneelement:=0:
   end if: 
  end if:
   preloutput:=preloutput+tens(bar(op(j)),bar(ONE)):
  if nargs<2 then 
   output:=output+BarTable[j]*preloutput:
  else 
   output:=output+BarTable[j]*oneelement:
  end if:
 end if:
end do:
return output:
end proc:


# Older version using lists:

Coproduct:=proc(inp)
local i, j, preloutput, oneelement, output, newtens, BarLists:
if not(has(inp, bar)) then return 0:
end if:
BarLists:=BarToLists(inp):
output:=0:
for j from 1 to nops(BarLists[1]) do
 if op(BarLists[2][j])=1 then
  output:=output:
 else
  newtens:=tens(bar(ONE),bar(op(BarLists[2][j]))):
  preloutput:=newtens:
  for i from 1 to nops(bar(op(BarLists[2][j])))-1 do
   newtens:=tens(op(1,newtens), unconc(op(2,newtens))):
   if nargs<2 then 
    preloutput:=preloutput+eval(newtens):
   elif args[2]=i then 
    oneelement:=eval(newtens):
   end if:
  end do:
  if nargs>1 then 
   if args[2]=nops(bar(op(BarLists[2][j]))) then
    oneelement:=tens(bar(op(BarLists[2][j])),bar(ONE)):
   elif args[2]=0 then 
    oneelement:=tens(bar(ONE),bar(op(BarLists[2][j]))):
   elif args[2]>nops(bar(op(BarLists[2][j]))) then
    oneelement:=0:
   end if: 
  end if:
   preloutput:=preloutput+tens(bar(op(BarLists[2][j])),bar(ONE)):
  if nargs<2 then 
   output:=output+BarLists[1][j]*preloutput:
  else 
   output:=output+BarLists[1][j]*oneelement:
  end if:
 end if:
end do:
return output:
end proc:



# An auxiliary procedure for the separation of lists in a list of lists:

PullListsApart:=proc(ListOfLists)
local i, j, Coeffsa, Coeffsb, Factors1a, Factors1b, Factors2a, Factors2b:
Coeffsa:=[]:
Factors1a:=[]:
Factors2a:=[]:
Coeffsb:=[]:
Factors1b:=[]:
Factors2b:=[]:
for i from 1 to nops(ListOfLists[1]) do
 if type(ListOfLists[2][i], `+`) then 
  for j from 1 to nops(ListOfLists[2][i]) do
   Coeffsa:=[ op(Coeffsa), ListOfLists[1][i] ]:
   Factors1a:=[ op(Factors1a), op(j, ListOfLists[2][i]) ]:
   Factors2a:=[ op(Factors2a), ListOfLists[3][i] ]:
  end do:
 else
   Coeffsa:=[ op(Coeffsa), ListOfLists[1][i] ]:
   Factors1a:=[ op(Factors1a), ListOfLists[2][i] ]:
   Factors2a:=[ op(Factors2a), ListOfLists[3][i] ]:
 end if:
end do:
for i from 1 to nops(Coeffsa) do
 if type(Factors2a[i], `+`) then 
  for j from 1 to nops(Factors2a[i]) do
   Coeffsb:=[ op(Coeffsb), Coeffsa[i] ]:
   Factors1b:=[ op(Factors1b), Factors1a[i] ]:
   Factors2b:=[ op(Factors2b), op(j, Factors2a[i]) ]:
  end do:
 else 
  Coeffsb:=[ op(Coeffsb), Coeffsa[i] ]:
  Factors1b:=[ op(Factors1b), Factors1a[i] ]:
  Factors2b:=[ op(Factors2b), Factors2a[i] ]:
 end if:
end do:
return [Coeffsb, Factors1b, Factors2b]:
end proc:



# For a linear combination of bar-terms, the following procedure returns a list, where the terms of the input 
# are sorted by the length of the words.

SortByLength:=proc(inp)
local i, j, outp, inpArray, maxlength, newTerm, outpLengths, outpTerms:
outpLengths:=Array([]):
outpTerms:=Array([]):
inpArray:=BarToArrayCollected(inp):
maxlength:=0:
for i from 1 to ArrayNumElems(inpArray(1)) do
 if nops(inpArray(2)(i))>maxlength then
  maxlength:=nops(inpArray(2)(i)):
 end if:
end do:
newTerm:=0:
for i from 1 to ArrayNumElems(inpArray(1)) do
 if (inpArray(2)(i)=[1]) then 
  newTerm:=newTerm+inpArray(1)(i):
 end if:
end do:
if not(newTerm=0) then
 outpLengths(1):=0:
 outpTerms(1):=newTerm:
end if:
for j from 1 to maxlength do
 newTerm:=0:
 for i from 1 to ArrayNumElems(inpArray(1)) do
  if (nops(inpArray(2)(i))=j and not(inpArray(2)(i)=[1])) then 
   newTerm:=newTerm+inpArray(1)(i)*bar(op(inpArray(2)(i))):
  end if:
 end do:
 if not(newTerm=0) then
  outpLengths(ArrayNumElems(outpLengths)+1):=j:
  outpTerms(ArrayNumElems(outpTerms)+1):=newTerm:
 end if:
end do:
outp:=Array([]):
outp(1):=outpLengths:
outp(2):=outpTerms:
return outp:
end proc:


# The same purpose as the previous procedure, using tables:

SortByLengthTable:=proc(inp)
local i, j, outp, inpTable, maxlength, newTerm, outpLengths, outpTerms:
outpLengths:=[]:
outpTerms:=[]:
inpTable:=table():
BarToTable(inp, inpTable):
maxlength:=0:
for i in indices(inpTable,'nolist') do
 if nops(i)>maxlength then
  maxlength:=nops(i):
 end if:
end do:
newTerm:=0:
for i in indices(inpTable,'nolist') do
 if (i=[1]) then 
  newTerm:=newTerm+inpTable[i]:
 end if:
end do:
if not(newTerm=0) then
 outp[0]:=newTerm:
end if:
for j from 1 to maxlength do
 newTerm:=0:
 for i in indices(inpTable,'nolist') do
  if (nops(i)=j and not(i=[1])) then 
   newTerm:=newTerm+inpTable[i]*bar(op(i)):
  end if:
 end do:
 if not(newTerm=0) then
  outp[j]:=newTerm:
 end if:
end do:
return outp:
end proc:






####################################################################
####################################################################
#
#   ARNOLD RELATIONS
#
####################################################################
####################################################################


# The following few procedures serve for the construction of Arnold equations.

BasePosition:=proc(Indexi, Indexj)
return (((Indexi-1)^2-Indexi+1)/2)+Indexj:
end proc:


BuildBaseReplacements:=proc(vars, varc)
local i, j, k, RepForm, output, AuxProd:
output:=[]:
for j from 1 to MPLnumberofvar do
 RepForm:=0:
 AuxProd:=1:
 for k from 1 to j do
  RepForm:=RepForm+d(varc[k])/varc[k]:
  AuxProd:=AuxProd*varc[k]:
 end do:
 output:=[op(output), d(vars[j])/vars[j] = RepForm]:
 output:=[op(output), d(vars[j])/(vars[j]-1) = d(AuxProd)/(AuxProd-1), d(vars[j])/(1-vars[j]) = -d(AuxProd)/(AuxProd-1)]:
end do:
for j from 1 to MPLnumberofvar do
 for i from 1 to j-1 do
  RepForm:=0:
  AuxProd:=1:
  for k from 1 to i do
   RepForm:=RepForm+d(varc[k])/varc[k]:
  end do:
  for k from i+1 to j do
   AuxProd:=AuxProd*varc[k]:
  end do:
  output:=[op(output), (d(vars[j])-d(vars[i]))/(vars[j]-vars[i]) = RepForm+d(AuxProd)/(AuxProd-1),
(d(vars[j])-d(vars[i]))/(vars[i]-vars[j]) = -RepForm-d(AuxProd)/(AuxProd-1)]:
 end do:
end do:
return output:
end proc:


BuildFiberReplacements:=proc(vars, varc)
local i, j, k, RepForm, output, AuxProd:
AuxProd:=1:
for i from 1 to MPLnumberofvar+1 do
 AuxProd:=AuxProd*varc[i]:
end do:
output:=[d(vars[MPLnumberofvar+1])/vars[MPLnumberofvar+1]=d(varc[MPLnumberofvar+1])/varc[MPLnumberofvar+1], d(vars[MPLnumberofvar+1])/(vars[MPLnumberofvar+1]-1)=d(AuxProd)/(AuxProd-1), 
d(vars[MPLnumberofvar+1])/(-vars[MPLnumberofvar+1]+1)=d(AuxProd)/(-AuxProd+1)]:
for j from 1 to MPLnumberofvar do
 AuxProd:=1:
 for i from j+1 to MPLnumberofvar+1 do
  AuxProd:=AuxProd*varc[i]:
 end do:
 output:=[op(output), (d(vars[MPLnumberofvar+1])-d(vars[j]))/(vars[MPLnumberofvar+1]-vars[j])=d(AuxProd)/(AuxProd-1)]:
end do:
return output:
end proc:


ArnoldCubical:=proc(Form1, Form2)
global MPL_CTYPE:
local iInd, jInd, SymbForm1, SymbForm2, bs, fs, GSign, RhsCoeff, RhsBase, RhsFiber, Auxform, nVar, BaseRep, FiberRep, varc, OldAndNewExpansionOrder, ctype, OldMPL_CTYPE:
if Form1=Form2 then return 0:
end if:
varc:=MPLvariable:
nVar:=MPLnumberofvar+1:
SymbForm1:=TotalToSymbols(Form1):
SymbForm2:=TotalToSymbols(Form2):
GSign:=1:
# If SymbForm1 is not greater than SymbForm2 in the order of
# Omega_F_true then switch places.
if op(SymbForm1)<op(SymbForm2) then
 Auxform:=SymbForm1:
 SymbForm1:=SymbForm2:
 SymbForm2:=AuxForm:
 GSign:=-1:
end if:
# The right hand side of the Arnold relation of the form 'Base wedge Fiber'
# will be stored as three lists, one for the prefactors, one for forms in the base and one for the fiber.
# Case a: MPLft[2] wedge MPLft[1]
if SymbForm1=MPLft[2] and SymbForm2=MPLft[1] then
 GSign:=-GSign;
 RhsCoeff:=[-GSign, GSign, GSign]:
 RhsBase:=[ MPLb[BasePosition(nVar+1, 1)], MPLb[BasePosition(nVar+1, 1)], MPLb[BasePosition(nVar-1, nVar-2)+1] ]:
 RhsFiber:=[ MPLft[nVar+1], MPLft[1], MPLft[nVar+1] ]:
# Case b: MPLft[j] wedge MPLft[1], j>2
elif op(SymbForm1)>2 and SymbForm2=MPLft[1] then
 GSign:=-GSign;
 jInd:=op(SymbForm1):
 RhsCoeff:=[-GSign, GSign, -GSign, GSign]:
 RhsBase:=[ MPLb[BasePosition(jInd-1, 1)], MPLb[BasePosition(jInd-1, 1)], MPLb[BasePosition(jInd-2, jInd-3)+1], 
 MPLb[BasePosition(nVar-1, nVar-2)+1] ]:
 RhsFiber:=[ MPLft[jInd-1], MPLft[1], MPLft[1], MPLft[jInd-1] ]:
# Case c: MPLft[j] wedge MPLft[2], j>2
elif op(SymbForm1)>2 and SymbForm2=MPLft[2] then
 jInd:=op(SymbForm1):
 RhsCoeff:=[GSign, -GSign, -GSign]:
 RhsBase:=[ MPLb[BasePosition(nVar+1, jInd-1)], MPLb[BasePosition(nVar+1, jInd-1)], MPLb[BasePosition(jInd-2, jInd-3)+1] ]:
 RhsFiber:=[ MPLft[nVar+1], MPLft[jInd-1], MPLft[nVar+1] ]:
# Case d: MPLft[j] wedge MPLft[i], j>i>2
elif op(SymbForm1)>3 and op(SymbForm2)>2 then
 jInd:=op(SymbForm1):
 iInd:=op(SymbForm2):
 RhsCoeff:=[-GSign, GSign, GSign, -GSign]:
 RhsBase:=[ MPLb[BasePosition(jInd-1, iInd-1)], MPLb[BasePosition(jInd-1, iInd-1)], MPLb[BasePosition(iInd-2, iInd-3)+1], 
 MPLb[BasePosition(jInd-2, jInd-3)+1] ]:
 RhsFiber:=[ MPLft[jInd-1], MPLft[iInd-1], MPLft[jInd-1], MPLft[iInd-1] ]:
end if:
# Translate back from symbolic notation to actual forms.
BaseRep:=BuildBaseReplacements(vars, varc):
OldAndNewExpansionOrder:=MPLExpansionOrder:
OldMPL_CTYPE:=MPL_CTYPE:
MPL_CTYPE:=1:
MPLInitialize(vars, MPLnumberofvar+1, false, false):
RhsBase:=SymbolsToTotal(RhsBase):
RhsBase:=subs(BaseRep, RhsBase):
RhsFiber:=SymbolsToTotal(RhsFiber):
MPL_CTYPE:=2:
MPLInitialize(varc, MPLnumberofvar-1, false, false):
FiberRep:=BuildFiberReplacements(vars, varc):
RhsFiber:=subs(FiberRep, RhsFiber):
MPL_CTYPE:=OldMPL_CTYPE:
return TotalToSymbols(PullListsApart([RhsCoeff, RhsBase, RhsFiber])):
end proc:


GetArnoldRhsCubical:=proc(Form1, Form2, outputexpr, symbolic)
local i, NewEq, EqNumber, SymbForm1, SymbForm2, Auxform, GSign, SignS1, SignS2, SymbForm1Abs, SymbForm2Abs, outputList, output:
if Form1=Form2 then return 0:
end if:
SymbForm1:=TotalToSymbols(Form1):
SymbForm2:=TotalToSymbols(Form2):
SignS1:=sign(SymbForm1):
SignS2:=sign(SymbForm2):
SymbForm1Abs:=SignS1*SymbForm1:
SymbForm2Abs:=SignS2*SymbForm2:
GSign:=SignS1*SignS2:
# If SymbForm1Abs is not greater than SymbForm2Abs in the order of
# Omega_F_true then switch places.
if op(SymbForm1Abs)<op(SymbForm2Abs) then
 Auxform:=SymbForm1Abs:
 SymbForm1Abs:=SymbForm2Abs:
 SymbForm2Abs:=Auxform:
 GSign:=-GSign:
end if:
EqNumber:=BasePosition(op(SymbForm1Abs), op(SymbForm2Abs)):
NewEq:=MPLArnoldEq[EqNumber]:
if symbolic then outputList:=[GSign*op(1, NewEq), op(2, NewEq), op(3, NewEq)]:
else outputList:=SymbolsToTotal([GSign*op(1, NewEq), op(2, NewEq), op(3, NewEq)]):
end if:
if outputexpr then 
 output:=0:
 for i from 1 to nops(outputList[1]) do
  output:=output+outputList[1][i]*outputList[2][i] &^ outputList[3][i]:
 end do:
 return output:
else
 return outputList:
end if:
end proc:


GetArnoldCoefficients:=proc(LHS)
local i, j, k, h, g, AuxSym, OmegaB, OmegaFtilde, Coordinates, RHSList, NewLHS, RHSArray:
userinfo(2,'arnold',"(LHS, n, ctype):  The coefficients of the right-hand side for the particular Arnold-relation, given by the left-hand side (LHS).");
OmegaB:=MPLFormsBase():
OmegaFtilde:=MPLFormsFiber(true):
NewLHS:=LHS:
# Generate the list RHSList of all wedge-products of one element of OmegaB and one of OmegaF.
# These are the possible terms on the right-hand-side of an Arnold-relation.
RHSList:=[]:
for i from 1 to nops(OmegaB) do
 for j from 1 to nops(OmegaFtilde) do
  RHSList:=[op(RHSList),expand(OmegaB[i] &^OmegaFtilde[j])]:
 end do:
end do:
RHSArray:=convert(RHSList,Array);
# In LHS and RHSArray we now have to replace all wedge-products of forms by 
# products of auxiliary sympols AuxSym. 
for k from 1 to ArrayNumElems(RHSArray) do 
 for i from 1 to nops(MPL_COORDINATES) do
  for j from 1 to nops(MPL_COORDINATES) do
    if i<j then RHSArray[k]:=subs(d(MPL_COORDINATES[i]) &^ d(MPL_COORDINATES[j])=AuxSym[i]*AuxSym[j],RHSArray[k]):
   else RHSArray[k]:=subs(d(MPL_COORDINATES[i]) &^ d(MPL_COORDINATES[j])=-AuxSym[i]*AuxSym[j],RHSArray[k]):
   end if:
  end do:
 end do:
end do:
RHSList:=convert(RHSArray,list);
for h from 1 to nops(MPL_COORDINATES) do
 for g from 1 to nops(MPL_COORDINATES) do
  if h<g then NewLHS:=subs(d(MPL_COORDINATES[h]) &^ d(MPL_COORDINATES[g])=AuxSym[h]*AuxSym[g],NewLHS):
  else NewLHS:=subs(d(MPL_COORDINATES[h]) &^ d(MPL_COORDINATES[g])=-AuxSym[h]*AuxSym[g],NewLHS):
  end if:
 end do:
end do:
# Now that all differential forms are replaced by symbols, we can apply the Maple-command
# RationalCoefficients to find a solution for the coefficients on the right-hand-side.
return RationalCoefficients(NewLHS,RHSList):
end proc: 



# GetArnoldMatrices creates a list of matrices, where each matrix contains the scalar coefficients of the right-hand-side of a particular Arnold relation.
# Let the left-hand side of an Arnold relation be f_i &^ f_j, where f_i and f_j are the i-th and j-th element in Omega_F_tilde, according to the
# ordering obtained from MPLFormsFiber. Furthermore let i > j. Then the corresponding Arnold-matrix is the one at position ((i - 1)^2 - i + 1)/2 + j in the
# list of matrices. 

GetArnoldMatrices:=proc()
local i, j, k, h, counteri, counterj, counter, output, newmatrix, Coordinates, OmegaB, OmegaFtilde, GenericRHS, SolutionList, LHS, ArnoldEQ, NumberOfMatrices;
userinfo(2,'arnold',"(n, ctype):  The list of all 'Arnold-matrices' for given n and type of coordinates. There is one matrix for each possible wedge-product of two elements in Omega_F_tilde, and the matrix-elements are the coefficients in the right-hand-side of the Arnold-relations."); 
output:=[]:
OmegaB:=MPLFormsBase():
OmegaFtilde:=MPLFormsFiber(true):
NumberOfMatrices:=binomial(nops(OmegaFtilde),2):
# simplicial coordinates: ----------------------------------------------------
if MPL_CTYPE=1 then 
counter:=0:
for i from 1 to nops(MPL_COORDINATES)-1 do
 for j from 0 to i-1 do
  if not(i=MPLnumberofvar) and not(j=MPLnumberofvar) then 
   # create a new matrix with all entries zero:
   newmatrix:=ZMatrix(nops(OmegaB),nops(OmegaFtilde)):
   # change two of the matrix-elements appropriately, according the Arnold relation in simplicial coordinates:
   if i>MPLnumberofvar then counteri:=i-1:
    else counteri:=i:
   end if:
   if j>MPLnumberofvar then counterj:=j-1:
    else counterj:=j:
   end if:
   newmatrix[counter+1,counteri+1]:=-1:
   newmatrix[counter+1,counterj+1]:=1:
   # add the new matrix to the list:
   output:=[op(output),newmatrix]:
   counter:=counter+1:
  end if:
 end do:
end do:
# cubical coordinates: ----------------------------------------------------
elif MPL_CTYPE=2 then 
if MPLnumberofvar>3 then print("The computation will take more than just a few minutes."):
end if:
print(cat("Of ", convert(NumberOfMatrices,string), " matrices the program already generated: " ) ): 
GenericRHS:=0:
SolutionList:=[]:
for k from 2 to nops(OmegaFtilde) do
 for h from 1 to k-1 do
  newmatrix:=ZMatrix(nops(OmegaB),nops(OmegaFtilde)):
  LHS:=OmegaFtilde[k] &^ OmegaFtilde[h]:
  # The Arnold-relations are obtained using the procedure GetArnoldCoefficients.
  if LHS=0 then  output:=[op(output), newmatrix]:
  else
   SolutionList:=GetArnoldCoefficients(LHS):
   if not(SolutionList=[]) then 
    counter:=1:
    for i from 1 to nops(OmegaB) do
     for j from 1 to nops(OmegaFtilde) do
      newmatrix[i,j]:=SolutionList[counter]:
      counter:=counter+1:
     end do:
    end do:
   # We expect everything to work, but for the case that the Maple-procedure RationalCoefficients 
   # fails at some point, there is an error-message:
   else print("Error: Not all Arnold-matrices could be generated by 'GetArnoldMatrices'."):
   print("The problem occurs for the left-hand side:"):
   print(LHS):
   end if:
   output:=[op(output), newmatrix]:
  end if:
  print(cat(" ",convert(nops(output),string)) ): 
 end do:
end do:
# symbolic coordinates (for testing-purposes):-----------------------------------
elif MPL_CTYPE=50 then
counter:=1:
for i from 1 to nops(MPL_COORDINATES)-1 do
 for j from 0 to i-1 do
  if not(i=MPLnumberofvar) and not(j=MPLnumberofvar) then 
   # create matrix with all entries zero:
   newmatrix:=ZMatrix( nops(OmegaB),nops(OmegaFtilde)):
   # for some values of n we invent fantasy-matrices for testing purposes:
   # n=2:
   if MPLnumberofvar=2 then
    if counter=1 then
     newmatrix[1,1]:=a[1]:
     newmatrix[1,2]:=a[2]:
    elif counter=2 then
     newmatrix[1,2]:=a[3]:
     newmatrix[2,2]:=a[4]:
    elif counter=3 then
     newmatrix[2,3]:=a[5]:
    end if:
   # n=4:
   elif MPLnumberofvar=4 then
    if counter=1 then 
     newmatrix[1,1]:=a[1]:
     newmatrix[1,4]:=a[2]:
     newmatrix[3,5]:=a[3]:
    elif counter=2 then
     newmatrix[2,4]:=a[3]:
     newmatrix[2,5]:=a[4]:
     newmatrix[3,3]:=a[5]:
     newmatrix[3,4]:=a[6]:
    elif counter=3 then
     newmatrix[2,2]:=a[1]: 
     newmatrix[2,4]:=a[2]:
     newmatrix[3,1]:=a[3]:
     newmatrix[3,3]:=a[4]:
    elif counter=4 then
     newmatrix[1,1]:=a[1]:
     newmatrix[1,2]:=a[2]:   
     newmatrix[1,3]:=a[3]:
     newmatrix[1,4]:=a[4]:
     newmatrix[1,5]:=a[5]:
     newmatrix[3,3]:=a[3]:
    elif counter=5 then
     newmatrix[2,1]:=a[1]:
     newmatrix[2,2]:=a[2]:
     newmatrix[2,4]:=a[3]:
     newmatrix[3,5]:=a[5]:
    elif counter=6 then
     newmatrix[1,4]:=a[4]:
     newmatrix[1,5]:=a[5]:
    elif counter=8 then
     newmatrix[1,2]:=a[5]:
     newmatrix[2,2]:=a[3]:
     newmatrix[3,2]:=a[4]:
    elif counter=9 then
     newmatrix[1,1]:=a[5]:
     newmatrix[2,2]:=a[4]:
    elif counter=10 then
     newmatrix[2,4]:=a[1]:
    end if:  
   end if:
   output:=[op(output),newmatrix]:
   counter:=counter+1:
  end if:
 end do:
end do:
# further coordinates ...
else output:=[]:
end if:
return output:
end proc:
 


# The Arnold matrices for the given weight and coordinate-type are generated and written to a file.

StoreArnoldMatrices:=proc()
local ActiveFile, OpenedFile, newstring:
userinfo(1,'arnold'," The Arnold matrices for the given weight and coordinate-type are generated and written to a file."):
if MPL_CTYPE=1 then ActiveFile:="MatricesSimplicial.txt":
elif MPL_CTYPE=2 then ActiveFile:="MatricesCubical.txt":
elif MPL_CTYPE=50 then ActiveFile:="MatricesTestcoordinates1.txt":
else return "There is no file for the chosen type of coordinates yet.":
end if:
# If the chosen file does not exist yet, it is created now.
if not(Exists(ActiveFile)) then 
 fopen(ActiveFile,WRITE):
 fclose(ActiveFile):
 fopen(ActiveFile,READ):
 fclose(ActiveFile):
end if:
# If n is smaller or equal the number of lines in the file, these matrices have already been
# stored and can not be added again. 
if (MPLnumberofvar <= FileTools[Text][CountLines](ActiveFile)) then 
 print("These matrices are already stored."):
elif (MPLnumberofvar > (FileTools[Text][CountLines](ActiveFile)+1)) then 
 print("You first have to store the matrices of this coordinate-type for lower weights."):
else 
 fclose(ActiveFile):
 OpenedFile:=fopen(ActiveFile, APPEND):
 newstring:=convert(GetArnoldMatrices(),string):
 writeline(OpenedFile, newstring):
 fclose(ActiveFile):
 print(cat("The matrices were generated and stored in file: ",ActiveFile)):
end if:
end proc:


# The Arnold matrices for the given weight and coordinate-type are read from a file.

ReadArnoldMatrices:=proc()
local i, ActiveFile, OpenedFile, newstring, output:
userinfo(1,'arnold',"(n::integer, ctype::integer): The Arnold matrices for the given weight and coordinate-type are read from a file."):
output:=[]:
if MPL_CTYPE=1 then ActiveFile:="MatricesSimplicial.txt":
elif MPL_CTYPE=2 then ActiveFile:="MatricesCubical.txt":
elif MPL_CTYPE=50 then ActiveFile:="MatricesTestcoordinates1.txt":
else return "There is no file for the chosen type of coordinates yet.":
end if:
# If the chosen file does not exist yet, an error message in shown.
if not(Exists(ActiveFile)) then print("Error: The program tried to open a file that does not exist."):
else
 # If the matrices are not contained in the file yet, an error message is shown.
 if MPLnumberofvar>FileTools[Text][CountLines](ActiveFile) then
  print("Error: The program tried to access matrices which were not generated yet."):
 else
  fclose(ActiveFile):
  OpenedFile:=fopen(ActiveFile,READ):
  # Go to the n-th line by successive calls of readline.
  for i from 1 to MPLnumberofvar-1 do readline(OpenedFile):
  end do:
  # Read the n-th line.
  output:=readline(OpenedFile):
  fclose(OpenedFile):
  return output:
 end if:
end if:
end proc:



# GetArnoldRHS(form1, form2, expr, symbolic): Derives the right-hand-side of the Arnold-relation, where the left-hand-side is form1^form2. 
# The Arnold-matrices are obtained from files, previously generated with StoreArnoldMatrices.
# The boolean variable expr fixes whether the output is given as three lists of factors (expr=false) or as one expression where 
# the wedge-products are written explicitely.
# The expression has the form of a sum over terms c_i * b_i ^ f_i  where the c_i are scalar coefficients
# (i.e. entries of the Arnold-matrices, possibly times a sign), the b_i are elements of Omega_B and the f_i
# are elements of Omega_F_tilde. For expr=false, the the three lists contain the c_i in a first, the f_i in a second and the b_i in a third list.

GetArnoldRHS:=proc(form1, form2, outputexpr::boolean, symbolic::boolean)
local k, i, counter, counterF, counterB, signfactor, matrixnumber, output, OmegaB, OmegaFtilde,
ArnoldMatrices, ArnoldMatrix::Matrix, found1, found2, foundmax, foundmin, outputcoeff, outputF, outputB;
userinfo(1,'arnold',"(form1, form2, n, ctype, expr): Right-hand-side of the Arnold-relation, where the left-hand-side is form1^form2. For expr=true the output has the form of an expression. For expr=false the factors are sorted in lists."):
if MPL_CTYPE=2 then return GetArnoldRhsCubical(form1, form2, outputexpr, symbolic):
end if:
output:=[]:
OmegaB:=MPLFormsBase():
OmegaFtilde:=MPLFormsFiber(true):
ArnoldMatrices:=parse(ReadArnoldMatrices()):
# There will only be a non-empty output if form1 and form2 belong to OmegaFtilde.
# The variables found1 and found2 are the positions in OmegaFtilde where form1 and form2 are found.
# They are zero if the forms are not found. 
found1:=0:
found2:=0:
for k from 1 to nops(OmegaFtilde) do
 if (not(symbolic) and OmegaFtilde[k]=form1) or (symbolic and MPLft[k]=form1) then found1:=k:
 end if:
 if (not(symbolic) and OmegaFtilde[k]=form2) or (symbolic and MPLft[k]=form2) then found2:=k:
 end if:
end do:
if found1=found2 then return 0:
elif found1+found2<2 then return []:
else
  #The left-hand side of the Arnold relation is form1 wedge form2.
  #If form1 appears earlier in OmegaFtilde than form2, we obtain an additional sign.
  if found1<found2 then signfactor:=-1:
  else signfactor:=1:
  end if:
  foundmax:=max(found1,found2):
  foundmin:=min(found1,found2):
  #According to the counting in GetArnoldMatrices, the number of the appropriate Arnold matrix is:
  matrixnumber:=(((foundmax-1)^2-foundmax+1)/2)+foundmin:
  ArnoldMatrix:=Matrix(ArnoldMatrices[matrixnumber]):
  #The output is at first organized in three lists: 
  #one for the coefficients, i.e. the matrix-elements, one for the elements of OmegaFtilde, one for the 
  #elements of OmegaB. The above signfactor is taken into account in the first list.
  outputcoeff:=[]:
  outputF:=[]:
  outputB:=[]:
  for counterF from 1 to nops(OmegaFtilde) do
   for counterB from 1 to nops(OmegaB) do
    if not(ArnoldMatrix(counterB,counterF)=0) then 
     if symbolic then 
      outputcoeff:=[op(outputcoeff),signfactor*ArnoldMatrix(counterB,counterF)]:
      outputB:=[op(outputB),MPLb[counterB]]:
      outputF:=[op(outputF),MPLft[counterF]]:
     else
      outputcoeff:=[op(outputcoeff),signfactor*ArnoldMatrix(counterB,counterF)]:
      outputB:=[op(outputB),OmegaB[counterB]]:
      outputF:=[op(outputF),OmegaFtilde[counterF]]:
     end if:
    end if:
   end do:
  end do:
  #If outputexpr was chosen to be false, the output is simply a collection of the three above lists.
  #If it is chosen to be true, the output is written as a single expression using wedge products.
  if outputexpr=false then output:=[outputcoeff,outputB,outputF]:
  else 
   output:=0:
   for i from 1 to nops(outputcoeff) do
    output:= output + outputcoeff[i] * outputB[i] &^ outputF[i]:
   end do:
  end if:
end if:
return output:
end proc:


# For the user, the following wrapping function provides the right-hand sides of
# Arnold relations.

MPLArnoldEquation:=proc(form1, form2)
return GetArnoldRHS(form1, form2, true, false):
end proc:



# A procedure to automatically test Arnold matrices:

TestArnoldMatrices:=proc()
local i, j, counter, OmegaFtilde, LHS, RHS, DIFF, foundmistake:
userinfo(1,'arnold',"(n, ctype): All generated Arnold relations of given weight and coordinate-type are checked."):
foundmistake:=false:
counter:=1:
OmegaFtilde:=MPLFormsFiber(true):
for i from 2 to nops(OmegaFtilde) do
 for j from 1 to i-1 do
  LHS:=OmegaFtilde[i] &^ OmegaFtilde[j]:
  RHS:=GetArnoldRHS(OmegaFtilde[i], OmegaFtilde[j], true, false):
  DIFF:=simplify(simpform(LHS-RHS)):
  if not(DIFF=0) then 
   foundmistake:=true:
   print(cat("A problem ocurred at equation ", convert(counter, string))):
  else
   print(cat(cat("Equation ", convert(counter, string)), " is ok.")):
  end if:
  counter:=counter+1:
 end do:
end do:
if not(foundmistake) then print("All matrices for the given weight and coordinate type are ok."):
end if:
return not(foundmistake):
end proc:






####################################################################
####################################################################
#
#   DIFFERENTIATION AND INTEGRABLE WORDS
#
####################################################################
####################################################################



# The procedue BarDiff constructs the standard (Gauss-Manin) connection which the total differentiation
# is based on. It uses the Arnold equations.

BarDiff:=proc(word::list, exprtype::boolean, symbolic::boolean)
##option remember:
local i, j, k, h, output, prefactors, elementij, form1, form2, listC, listB, newwordlist, WNwords, ArnoldRHS, newword:
output:=[]:
listC:=[]:
listB:=[]:
if not(nops(word)=0) then
 newwordlist:=[];
 # At first, the nearest neighbours are wedge-multiplied. WNwords is the resulting list of words:
 WNwords:=PairNeighbours(word):
 for i from 1 to nops(WNwords) do
  for j from 1 to nops(WNwords[i]) do 
   # Call the j-th letter of the i-th word elementij.
   elementij:=WNwords[i][j]:
   # If elementij is a list, we assume it is two-element list standing for the wedge-product of two forms and extract them:
   if type(elementij,list) then
    form1:=op(1,elementij):
    form2:=op(2,elementij):
    # With these forms we compute the Arnold relation in the form of lists:
    ArnoldRHS:=GetArnoldRHS(form1, form2, false, symbolic):
    # For each term of ArnoldRHS replace the wedgeproduct with the element of Omega_F_tilde: 
    for k from 1 to nops(ArnoldRHS[3]) do
     newword:=WNwords[i]:
     newword[j]:=ArnoldRHS[3][k]:
     # Collect the new word and the prefactors in lists:
     newwordlist:=[op(newwordlist), newword]:
     listC:=[op(listC), ArnoldRHS[1][k]]:
     listB:=[op(listB), ArnoldRHS[2][k]]:
    end do:
   end if:
  end do:
 end do:
end if:
# Depending on the value of exprtype, the output is given as one expression or a collection of lists:
if exprtype then 
 output:=0:
 for h from 1 to nops(newwordlist) do
  output:=output+listC[h]*listB[h]*newwordlist[h]:
 end do:
else output:=[listC, listB, newwordlist]:
end if:
return output:
end proc:



# The only difference between the following two procedures is:
# MPLd de-concatenates the leftmost 1-form,
# MPLdInternal writes this 1-form also in the argument of a bar(...)

MPLd:=proc(inp)
##option remember:
local output:
# In a first step we cut off the first letter of bar(...) and replace it by the auxiliary place-holder ONE.
output:=eval(evalindets(inp, 'specfunc(anything, bar)', proc (h) options operator, arrow; tens(op(Lift([op(1,h)])),subsop(1 = ONE,h)) end proc)):
# After bar(ONE)=ONE we erase all remaining ONE in bar(...).
return evalindets(output, 'specfunc(anything, bar)', proc (h) options operator, arrow; subs(ONE=NULL, h) end proc):
end proc:


MPLdInternal:=proc(inp)
##option remember:
local output:
# In a first step we cut off the first letter of bar(...) and replace it by the auxiliary place-holder ONE.
output:=eval(evalindets(inp, 'specfunc(anything, bar)', proc (h) options operator, arrow; tens(bar(op(Lift([op(1,h)]))),subsop(1 = ONE,h)) end proc)):
# After bar(ONE)=ONE we erase all remaining ONE in bar(...).
return evalindets(output, 'specfunc(anything, bar)', proc (h) options operator, arrow; subs(ONE=NULL, h) end proc):
end proc:



# PartialDiff computes the partial differentiation of a bar-term with respect to one chosen variable va.
# It takes MPLdInternal and then the coefficient of d(va).
PartialDiff:=proc(va, inp)
local i, BarLists, dTerm, output:
BarLists:=BarToLists(inp):
output:=0:
for i from 1 to nops(BarLists[1]) do
 if BarLists[2][i]=[1] then dTerm:=0:
 else dTerm:=MPLdInternal(bar(op(BarLists[2][i]))):
 dTerm:=evalindets(dTerm, 'specfunc(anything, tens)', proc (h) options operator, arrow; coeff(op(op(1,h)),d(va))*eval(op(2,h),      ONE=1) end proc):
 end if:
 output:=output+diff(BarLists[1][i],va)*bar(op(BarLists[2][i]))+BarLists[1][i]*dTerm:
end do:
return output:
end proc:



# The following cuts off the first letter of a word, without lifting it.
unconc:=proc(inp)
##option remember:
local output:
# In a first step we cut off the first letter of bar(...) and replace it by the auxiliary place-holder ONE.
output:=eval(evalindets(inp, 'specfunc(anything, bar)', proc (h) options operator, arrow; tens(bar(op(1,h)),subsop(1 = ONE,h)) end proc)):
return evalindets(output, 'specfunc(anything, bar)', proc (h) options operator, arrow; subs(ONE=NULL, h) end proc):
end proc:



# Remark: The input for BarDiff is a word from OmegaFtilde, but the input of
# TotalDiff and IntegrableWords is a word from OmegaF. Here we internally use the procedures
# Lift and Lower to obtain one from the other, as needed.

# For a linear combination of bar(...) such as a*bar(word1)+b*bar(word2)+...
# the procedure BarToLists returns the list of coefficients and the list of 
# words: [[a,b,...],[word1,word2,...]].


# ListsToBar does the reverse of BarToLists. Its input is assumed to be 
# of the form [[a,b,...],[word1,word2,...]] and the procedure 
# returns a*bar(word1)+b*bar(word2)+...

ListsToBar:=proc(list1)
local i, output:
userinfo(1,'bar',"(list1): Converts two lists containing the scalar coefficients and words to the corresponding linear combination, using the notation bar(...)."):
# If the input is not a list, nothing is done.
if not(type(list1,list)) then output:=list1:
# Otherwise the input is assumed to be a list of two lists,
# the first one containing scalar coefficients and the second one words,
# i.e. the arguments of bar(...).
else
 output:=0:
 for i from 1 to nops(list1[1]) do
  output:=output+list1[1][i]*bar(op(list1[2][i])):
 end do:
end if:
return output:
end proc:


BarToLists:=proc(expr1)
local i, j, k, output, barlist, coefflist, wordlist, remainder:
userinfo(1,'bar',"(expr1): Converts a linear combination of bar(...)-terms to two lists containing the scalar coefficients and the arguments of bar(...)."):
coefflist:=[]:
wordlist:=[]:
# If the input is already of type list, nothing is done.
if type(expr1, list) then output:=expr1:
else
 # barlist is the list of a terms bar(...) in the expression.
 # The otput is going to be the list of coefficients of these terms and the list
 # of arguments of bar(...), i.e. the words.
 barlist:=[op(selectfun(expr1, bar))]:
 for i from 1 to nops(barlist) do
  if type(coeff(expr1,barlist[i]),`+`) then 
   for j from 1 to nops(coeff(expr1,barlist[i])) do
    coefflist:=[op(coefflist), op(j, coeff(expr1,barlist[i]))]:
    wordlist:=[op(wordlist), [op(barlist[i])]]:
   end do:
  else
   coefflist:=[op(coefflist), coeff(expr1,barlist[i])]:
   wordlist:=[op(wordlist), [op(barlist[i])]]:
  end if:
 end do:
 output:=[coefflist, wordlist]:
 # We still have to catch the remainder which has no bar-terms.
 remainder:=simplify(expr1-ListsToBar(output)):
 if not(remainder=0) then
  if type(remainder,`+`) then 
   for k from 1 to nops(remainder) do
    coefflist:=[op(coefflist), op(k, remainder)]:
    wordlist:=[op(wordlist), [1]]:
   end do: 
   output:=[coefflist, wordlist]:
  else
   output:=[[op(coefflist),remainder], [op(wordlist),[1]]]:
  end if:
 end if:
end if:
return output:
end proc:


# Bar terms are collected while conversion to the list:

BarToListsCollected:=proc(expr1)
local i, newexpr, coefflist, wordlist, exprlist:
if type(expr1, list) then return expr1:
else
 coefflist:=[]:
 wordlist:=[]:
 newexpr:=collect(expr1, bar, `distributed`):
 if type(newexpr, `+`) then 
  exprlist:=convert(newexpr, list):
 else
  exprlist:=[newexpr]:
 end if:
 map(proc(x) 
     local j, word:
     if has(x, bar) then
      word:=[op(op(selectfun(x, bar)))]: 
     else word:=[1]:
     end if:
     if member(word, wordlist) then 
      for j from 1 to nops(wordlist) do
       if wordlist[j]=word then
        coefflist[j]:=coefflist[j]+eval(x, bar=1):
       end if:
      end do:
     else
      wordlist:=[op(wordlist), word]:
      coefflist:=[op(coefflist), eval(x, bar=1)]:
     end if:  
     end proc, exprlist):
end if:
return [coefflist, wordlist]:
end proc:


# Conversion to arrays:

BarToArrayCollected:=proc(expr1)
local i, j, newexpr, coefflist, wordlist, exprlist, word:
if type(expr1, Array) then return expr1:
else
 coefflist:=Array([]):
 wordlist:=Array([]):
 newexpr:=expand(expr1):
 if type(newexpr, `+`) then 
  for i from 1 to nops(newexpr) do
   if has(op(i, newexpr), bar) then
    word:=[op(op(selectfun(op(i, newexpr), bar)))]: 
   else 
    word:=[1]:
   end if:
   if member(word, wordlist) then 
    for j from 1 to ArrayNumElems(wordlist) do
     if wordlist(j)=word then
      coefflist(j):=coefflist(j)+eval(op(i, newexpr), bar=1):
     end if:
    end do:
   else
    wordlist(ArrayNumElems(wordlist)+1):=word:
    coefflist(ArrayNumElems(coefflist)+1):=eval(op(i, newexpr), bar=1):
   end if:      
  end do:
 else
  if has(newexpr, bar) then
   word:=[op(op(selectfun(newexpr, bar)))]: 
  else 
   word:=[1]:
  end if:
  wordlist(ArrayNumElems(wordlist)+1):=word:
  coefflist(ArrayNumElems(coefflist)+1):=eval(newexpr, bar=1):
 end if:
end if:
return Array([coefflist, wordlist]):
end proc:


# To tables:

BarToTable:=proc(expr1, outp)
local i, j, newexpr, coefflist, wordlist, exprlist, word:
if type(expr1, table) then return expr1:
else
 newexpr:=collect(expr1, bar,`distributed`):
 if type(newexpr, `+`) then 
  for i from 1 to nops(newexpr) do
   if has(op(i, newexpr), bar) then
    word:=[op(op(selectfun(op(i, newexpr), bar)))]: 
   else 
    word:=[1]:
   end if:
   if assigned(outp[word]) then 
    outp[word]:=outp[word]+eval(op(i, newexpr), bar=1)
   else
    outp[word]:=eval(op(i, newexpr), bar=1):
   end if:      
  end do:
 else
  if has(newexpr, bar) then
   word:=[op(op(selectfun(newexpr, bar)))]: 
  else 
   word:=[1]:
  end if:
  if assigned(outp[word]) then 
    outp[word]:=outp[word]+eval(newexpr, bar=1)
   else
    outp[word]:=eval(newexpr, bar=1):
   end if:
 end if:
end if:
end proc:



TableToBar:=proc(inp)
local i, outp:
outp:=0:
for i in indices(inp,'nolist') do
 outp:=outp+inp[i]*bar(op(i)):
end do:
return outp:
end proc:



AppendToArray:=proc(inp, bararray)
local i, j, newinp, word:
newinp:=expand(inp):
for i from 1 to nops(newinp) do
 if has(op(i, newinp), bar) then
  word:=[op(op(selectfun(op(i, newinp), bar)))]: 
 else 
  word:=[1]:
 end if:
 if member(word, bararray(2)) then 
  for j from 1 to ArrayNumElems(bararray(2)) do
   if bararray(2)(j)=word then
    bararray(1)(j):=bararray(1)(j)+eval(op(i, newinp), bar=1):
   end if:
  end do:
 else
  bararray(2)(ArrayNumElems(bararray(2))+1):=word:
  bararray(1)(ArrayNumElems(bararray(1))+1):=eval(op(i, newinp), bar=1):
 end if:      
end do:
return bararray:
end proc:



ArrayToBar:=proc(bararray)
local i, outp:
outp:=0:
for i from 1 to ArrayNumElems(bararray(1)) do
 outp:=outp+bararray(1)(i)*bar(op(bararray(2)(i))):
end do:
return eval(outp):
end proc:


# For some puposes it is useful to have taylored commands for the simplification 
# of bar-terms. Some of the following have been useful.

SimplifyBarExpression:=proc(inp)
local collectedinp, output, firsttime, secondtime:
#####output:=collect(inp, bar,`distributed`, normal):
collectedinp:=collect(inp, bar, `distributed`):
if type(inp, `+`) then 
 output:=map(proc(x) normal(x) end proc, inp):
else
 output:=normal(inp):
end if:
return output:
end proc:

SimplifyBarExpressionFactor:=proc(inp)
local collectedinp, output, firsttime, secondtime:
#####output:=collect(inp, bar,`distributed`, normal):
collectedinp:=collect(inp, bar, `distributed`):
if type(inp, `+`) then 
 output:=map(proc(x) factor(x) end proc, inp):
else
 output:=factor(inp):
end if:
return output:
end proc:


SimplifyTable:=proc(inp)
local i, outp:
outp:=table():
for i in indices(inp, 'nolist') do
 outp[i]:=factor(inp[i]):
 if outp[i]=0 then 
  outp[i]:=evaln(outp[i]):
 end if:
end do:
return outp:
end proc:


# Conversion between combination of tens-terms and lists:

ListsToTens:=proc(list1)
local i, output:
userinfo(1,'bar',"(list1): Converts three lists containing the scalar coefficients and bar-expressions to the corresponding linear combination of tensor products, using the notation tens(...)."):
# If the input is not a list, nothing is done.
if not(type(list1,list)) then output:=list1:
# Otherwise the input is assumed to be a list of three lists,
# the first one containing scalar coefficients and the other ones bar-expressions,
# being the left and right part of a tensor product.
else
 output:=0:
 for i from 1 to nops(list1[1]) do
  output:=output+list1[1][i]*tens(list1[2][i], list1[3][i]):
 end do:
end if:
return output:
end proc:


TensToLists:=proc(inp)
local i, j, output, coefflist, exprlist1, exprlist2, tenslist, remainder, expr1:
userinfo(1,'bar',"(expr1): Converts a linear combination of tens(...)-terms to three lists containing the scalar coefficients, the left and the right argument of tens(...)."):
expr1:=expand(inp):
coefflist:=[]:
exprlist1:=[]:
exprlist2:=[]:
# If the input is already of type list, nothing is done.
if type(expr1, list) then output:=expr1:
else
 # tenslist is the list of a terms tens(...) in the expression.
 # The otput is going to be the list of coefficients of these terms and the lists
 # of arguments of tens(...), i.e. the words.
 tenslist:=[op(selectfun(expr1, tens))]:
 for i from 1 to nops(tenslist) do
  coefflist:=[op(coefflist), coeff(expr1,tenslist[i])]:
  exprlist1:=[op(exprlist1),op(1,tenslist[i])]:
  exprlist2:=[op(exprlist2),op(2,tenslist[i])]:
 end do:
 output:=[coefflist, exprlist1, exprlist2]:
 # We still have to catch the remainder which has no tens-terms.
 remainder:=normal(expr1-ListsToTens(output)):
 if not(remainder=0) then
  output:=[[op(coefflist),remainder], [op(exprlist1),1], [op(exprlist2),1]]:
 end if:
end if:
return output:
end proc:


# ... and between tens-terms and tables:

TensToTable:=proc(expr1, outp)
local i, j, newexpr, coefflist, wordlist, exprlist, doublelist:
if type(expr1, table) then return expr1:
else
 newexpr:=collect(expr1, tens,`distributed`):
 if type(newexpr, `+`) then 
  for i from 1 to nops(newexpr) do
   if has(op(i, newexpr), tens) then
    doublelist:=[op(1,op(selectfun(op(i, newexpr), tens))), op(2,op(selectfun(op(i, newexpr), tens)))]:
   else 
    doublelist:=[1]:
   end if:
   if assigned(outp[doublelist]) then 
    outp[doublelist]:=outp[doublelist]+eval(op(i, newexpr), tens=1)
   else
    outp[doublelist]:=eval(op(i, newexpr), tens=1):
   end if:      
  end do:
 else
  if has(newexpr, tens) then
   doublelist:=[op(1,selectfun(op(newexpr), tens)), op(2,selectfun(op(newexpr), tens))]: 
  else 
   doublelist:=[1]:
  end if:
  if assigned(outp[doublelist]) then 
    outp[doublelist]:=outp[doublelist]+eval(newexpr, tens=1)
   else
    outp[doublelist]:=eval(newexpr, tens=1):
   end if:
 end if:
end if:
end proc:


# Concatenation of the words of two bar-terms:

MPLconcatenate:=proc(expr1,expr2)
local concatenation:
concatenation:=conc(expr1,expr2):
return evalindets(concatenation, 'specfunc(anything, conc)', proc (h) options operator, arrow; bar(op(op(1,h)),op(op(2,h))) end proc):
end proc:


# User-friendly wrapping procedure for the total differentiation:

MPLTotalConnection:=proc(inp)
return TotalDiffWithoutBar(inp, false):
end proc:


TotalDiffWithoutBar:=proc(inputterm, symbolic::boolean)
##option remember:
local i, j, k, m, output, inputlists, firstpartlists, inputcoeffs, inputwords, outputcoeffs, outputwords, wordcutfirst, BarLists, newword, loweredword, IntW1, IntW2: 
userinfo(1,'bar',"(word, n::integer, ctype::integer, expr::boolean): The integrable words, derived from an input word in the forms on the fiber."):
# The inputterm is assumed to be a linear combination of words. We transform it into a list of lists.
inputlists:=BarToLists(inputterm):
inputcoeffs:=inputlists[1]:
inputwords:=inputlists[2]:
output:=0:
if nops(inputcoeffs)=0 then return output:
else
 # First part of psi:
 output:= output + MPLd(inputterm): 
 # Second part of psi:
 for i from 1 to nops(inputcoeffs) do
  newword:=inputwords[i]:
  if nops(newword)>1 then  
   BarLists:=BarDiff(SymbolsToTotal(Lift(newword)), false, symbolic):
   for k from 1 to nops(BarLists[1]) do 
    output:=output + (-1)*inputcoeffs[i]*BarLists[1][k]* tens(BarLists[2][k], bar(op(Lower(BarLists[3][k])))):
   end do:
  end if:
 end do: 
end if:
return output:
end proc:


TotalDiff:=proc(inputterm, symbolic::boolean)
##option remember:
local i, j, k, m, output, inputlists, firstpartlists, inputcoeffs, inputwords, outputcoeffs, outputwords, wordcutfirst, BarLists, newword, loweredword, IntW1, IntW2: 
userinfo(1,'bar',"(word, n::integer, ctype::integer, expr::boolean): The integrable words, derived from an input word in the forms on the fiber."):
# The inputterm is assumed to be a linear combination of words. We transform it into a list of lists.
inputlists:=BarToLists(inputterm):
inputcoeffs:=inputlists[1]:
inputwords:=inputlists[2]:
output:=0:
if nops(inputcoeffs)=0 then return output:
else
 # First part of psi:
 output:= output + MPLdInternal(inputterm): 
 # Second part of psi:
 for i from 1 to nops(inputcoeffs) do
  newword:=inputwords[i]:
  if nops(newword)>1 then  
   BarLists:=BarDiff(SymbolsToTotal(Lift(newword)), false, symbolic):
   for k from 1 to nops(BarLists[1]) do 
    output:=output + (-1)*inputcoeffs[i]*BarLists[1][k]* tens(bar(BarLists[2][k]), bar(op(Lower(BarLists[3][k])))):
   end do:
  end if:
 end do: 
end if:
return output:
end proc:


# User-friendly symbol map:

MPLSymbolMap:=proc(inp)
return SymbolsToTotal(IntWordsRecursive(inp)):
end proc: 


# Actual symbol map in symbolic notation:

IntWordsRecursive:=proc(inp)
##option remember:
local output, TDterm, inputterm:
inputterm:=FiberToSymbols(inp):
TDterm:=TotalDiff(inputterm, true):
output:=conc(expand(evalindets(TDterm, 'specfunc(anything, tens)', proc (h) options operator, arrow; subsop(2 = IntWordsRecursive(op(2,h),true),h) end proc))):
return output:
end proc:


# ... returning a table:

IntWordsRecursiveTable:=proc(inp)
##option remember:
local i, output, TDterm, inputterm, prefactor:
output:=table():
for i in indices(inp, nolist) do
 prefactor:=inp[i]:
 inputterm:=FiberToSymbols(bar(op(i))):
 TDterm:=TotalDiff(inputterm, true):
 BarToTable(prefactor*normal(SymbolsToTotal(conc(expand(evalindets(TDterm, 'specfunc(anything, tens)', proc (h) options operator, arrow; subsop(2 =  IntWordsRecursive(op(2,h),true),h) end proc))))), output):
end do:
return output:
end proc:


# The unshuffle map:

MPLUnshuffle:=proc(inp, va)
local i, j, k, SortedInput, outp, inpList, maxlength, fn1, fn1List, fTens1, oldxi, xi, fTensList, Co, fTensNext:
outp:=0:
# Sort the input by the length of the words.
SortedInput:=SortByLength(inp):
for k from 1 to ArrayNumElems(SortedInput(1)) do
 if SortedInput(1)(k)=0 then
  outp:=outp+SortedInput(2)(k):
 else
  # Initial step of the iteration:
  fn1:=restrictF(SortedInput(2)(k), va, 0):
  fn1List:=BarToLists(fn1):
  fTens1:=0:
  for i from 1 to nops(fn1List[1]) do
   fTens1:=fTens1+fn1List[1][i]*tens(ONE, bar(op(fn1List[2][i]))):
  end do: 
  outp:=outp+fTens1:
  ###if SortedInput(1)(k)>0 then
   # Iteration:
   oldxi:=SortedInput(2)(k)-SymbolsToTotal(IntWordsRecursive(fn1)):
   fTensList:=TensToList(fTens1):
   for j from 1 to SortedInput(1)(k) do
    Co:=TensToLists(Coproduct(oldxi, j)):
    fTensNext:=0:
    xi:=oldxi:
    for i from 1 to nops(op(3,Co)) do
     fTensNext:=fTensNext+Co[1][i]*tens(Co[2][i], restrictF(Co[3][i], va, 0)):
     xi:=xi-Co[1][i]*MPLShuffleProduct(Co[2][i], SymbolsToTotal(IntWordsRecursive(restrictF(Co[3][i], va, 0)))):
    end do:
    oldxi:=xi:
    outp:=outp+fTensNext:
   end do:
  ###end if:
 end if:
end do:
return outp:
end proc:



# For a given tensor-product of bar-terms, the following procedure takes the integrable words of the right part 
# and shuffles with the left part. This can be used to check the MPLUnshuffle procedure as it is it's inverse.

MPLSymbolAndShuffle:=proc(inp)
local i, j, outp, TensList:
outp:=0:
TensList:=TensToLists(inp):
for i from 1 to nops(TensList[1]) do
 outp:=outp+TensList[1][i]*eval(MPLShuffleProduct(TensList[2][i], SymbolsToTotal(IntWordsRecursive(TensList[3][i]))), ONE=1):
end do:
return outp:
end proc:


# The following are auxiliary procedures to check the integability condition.
# (not entirely reliable but also not used by other parts of the program)

IsBarWedgeZero:=proc(inp)
local i, j, auxexp, BarLists, testpoly, newterm:
BarLists:=BarToListsCollected(inp):
testpoly:=0:
for i from 1 to nops(BarLists[1]) do
 newterm:=1:
 for j from 1 to nops(BarLists[2][i]) do
  if has(BarLists[2][i][j], `&^`) then
   testpoly:=testpoly+BarLists[1][i]*BarLists[2][i][j]*auxexp[j]:
  else
   testpoly:=testpoly+BarLists[1][i]*denom(BarLists[2][i][j])*auxexp[j]:
  end if:
 end do:
end do:
return simpform(normal(testpoly)):
end proc:



CheckIntegrability:=proc(inp)
local i, j, BarLists, dList, WedgeList, testterm:
testterm:=0:
BarLists:=BarToListsCollected(inp):
for i from 1 to nops(BarLists[1]) do
 if BarLists[2][i]=[1] then
  testterm:=testterm + BarLists[1][i]:
 else
  dList:=BarLists[1][i]:
  for j from 1 to nops(BarLists[2][i]) do
   dList:=BarLists[2][i]:
   dList[j]:=d(BarLists[2][i][j]):
   testterm:=testterm + BarLists[1][i]*bar(op(dList)):
  end do:
  WedgeList:=WedgeNeighbours(BarLists[2][i]):
  for j from 1 to nops(WedgeList) do
   testterm:=eval(testterm+BarLists[1][i]*bar(op(WedgeList[j]))):
  end do:
 end if:
end do:
return IsBarWedgeZero(testterm):
end proc:






####################################################################
####################################################################
#
#   CONSTRUCTION OF A BASIS
#
####################################################################
####################################################################


# Computes the basis of words in the lifted fiber of length 'weight'.
# Auxiliary procedure for MPLBasis.

MPLBasisLiftedFiber:=proc(var, nvar, weight)
local i, j, k, fiberforms, setchoices, setperm, barterm, listsymbols, newsymbol, newfiberforms, vbasis:
MPLInitialize(var,nvar-1):
fiberforms:=MPLFormsFiber(false):
newfiberforms:=fiberforms:
vbasis:=[]:
for k from 1 to weight do 
 for i from 2 to k do
  newfiberforms:=[op(newfiberforms),op(fiberforms)]:
 end do:
 setchoices:=choose(newfiberforms,k):
 listsymbols:=[]:
 for i from 1 to nops(setchoices) do
  setperm:=permute(setchoices[i]):
  for j from 1 to nops(setperm) do
   barterm:=bar(op(setperm[j])):
   newsymbol:=MPLSymbolMap(barterm):
   if not(member(newsymbol,listsymbols)) then
    listsymbols:=[op(listsymbols), newsymbol]:
   end if:
  end do:
 end do:
 vbasis:=[op(vbasis),listsymbols]:
end do:
return vbasis:
end proc:



# Computes all shuffle-products of elements of two vectorspaces.
# Auxiliary procedure for MPLBasis.

MPLShuffleVectorspaces:=proc(space1, space2, maxweight)
local i, j, k, h, set1, set2, Shufflespace, newproduct, outp:
outp:=[]:
if maxweight>nops(space1) or maxweight>nops(space2) then
 print("The desired weight is higher than the maximal weight in (one of) the given vectorspaces. Therefore, the full vectorspace of shuffle products up to this weight cannot be computed."):
 return:
end if:
for i from 0 to maxweight do
 Shufflespace:=[]:
 for j from 0 to i do
  if j=0 then
   set1:=[1]:
  else
   set1:=space1[j]:
  end if:
  if i-j=0 then
   set2:=[1]:
  else
   set2:=space2[i-j]:
  end if:
  for k from 1 to nops(set1) do
   for h from 1 to nops(set2) do
    newproduct:=MPLShuffleProduct(set1[k],set2[h]):
    if not(member(newproduct,Shufflespace)) then
     Shufflespace:=[op(Shufflespace),newproduct]:
    end if:
   end do:
  end do:
 end do:
 if i>0 then
  outp:=[op(outp), Shufflespace]:
 end if:
end do:
return outp:
end proc: 



# Constructs a basis of the vectorspace of integrable words in letters with 
# nvar variables up to a lenght given by the argument 'weight'.

MPLBasis:=proc(var, nvar, weight)
local i, initialset:
if nvar=1 then
 return MPLBasisLiftedFiber(var,nvar,weight):
else
 return MPLShuffleVectorspaces(MPLBasis(var,nvar-1,weight),MPLBasisLiftedFiber(var,nvar,weight),weight);
end if:
end proc:





####################################################################
####################################################################
#
#   SERIES EXPANSION
#
####################################################################
####################################################################



# For a chosen variable va, restrictR sets d(va)=0, va=u.
restrictR:=proc(inp, va, u)
local output:
if has(va, MPL_COORDINATES) then 
 output:= subs(d(va)=0,inp):
 output:=subs(va=u,output):
else output:=inp:
end if:
return eval(output):
end proc:


# For a chosen variable va, restrictF sets all other coordinates x=0 and d(x)=0.
restrictF:=proc(inp, va, u)
local i, j, DelCoordinates, output, ReplaceCoords, ZetaTerm:
output:=inp:
ReplaceCoords:=[op(MPL_COORDINATES), op(GlobalCoordinates)]: 
if has(va, ReplaceCoords) then 
 DelCoordinates:=subs(va=NULL,ReplaceCoords):
 for i from 1 to nops(DelCoordinates) do
  output:=subs(d(DelCoordinates[i])=0, output):
  ####output:=subs(DelCoordinates[i]=0, output):
 end do:
end if:
ZetaTerm:=0:
if u=1 then
 for j from 1 to nops(ReplaceCoords) do
  if not(ReplaceCoords[j]=va) and not(inp=ONE) then
   ZetaTerm:=ZetaTerm+RegularizedZeta(inp, ReplaceCoords[j]);
  end if:
 end do:
end if:
return eval(output + ZetaTerm):
end proc:


# The following procedure adapts the order to which a series expansion has to 
# be computed automatically to the problem. It is used internally as extension of
# the standard series command.

betterSeries := proc (expr, place, orderNeeded) 
local compOrder, expansion: 
for compOrder from orderNeeded to orderNeeded+20 do 
 expansion := series(expr, place, compOrder):
 if orderNeeded <= order(expansion) then 
  return expansion 
 end if: 
end do: 
error "Could not expand %1 to order %2 at %3", expr, orderNeeded, place 
end proc:



# The following procedure series-expands combinations of bar-terms at 0 or 1:

MPLexp:=proc(inp, va, u::integer, ExpansionOrder::integer:=1)
global inpexp:
local i, collectedinp, output, symbolicexp, LogTerm, integr, pref, word, seriesterm:
output:=0:
inpexp:=inp:
if not has(inp, va) then 
 return inp:
end if:
# Error-message if u is not 0 or 1:
if not(u=0 or u=1) then print("Error: Limits and expansions have to be evaluated at 0 or 1."):
 return:
end if:
collectedinp:=collect(inp, bar,`distributed`, normal):
if type(collectedinp, `+`) then 
 output:= map(proc(x)
         if has(x, bar) then
          pref:=eval(x, bar=1):
          word:=[op(op(selectfun(x, bar)))]: 
         else 
          pref:=x:
          word:=[1]:
         end if:
         # If bar-term is a logarithm:
         if ((nops(word) = 1) and  (denom(op(word))=va or denom(op(word))=1-va 
           or denom(op(word))=va-1)) then 
          seriesterm:=convert(betterSeries(pref,va=u, ExpansionOrder), polynom):
          output:=seriesterm*ExpLog(va, u, bar(op(word)), ExpansionOrder-ldegree(seriesterm,va-u)):
         # If there is no bar-term or if there is a bar-term, but it doesn't depend on va:
         elif not(has(word,va)) then 
          output:=convert(betterSeries(pref,va=u, ExpansionOrder), polynom)*bar(op(word));
         # All other cases:
         else
          output:=convert(betterSeries(pref,va=u, ExpansionOrder), polynom):
          symbolicexp:=integr(bar(op(word)), va, u, MPLexp(PartialDiff(va, bar(op(word))), va, u,  ExpansionOrder-ldegree(output,va-u) )):
          output := output*eval(subs(integr=IntegrExpl, symbolicexp)):
         end if:
         end proc,
         collectedinp):
else
 if has(collectedinp, bar) then
  pref:=eval(collectedinp, bar=1):
  word:=[op(op(selectfun(collectedinp, bar)))]: 
 else 
  pref:=collectedinp:
  word:=[1]:
 end if:
 # If bar-term is a logarithm:
 if ((nops(word) = 1) and  (denom(op(word))=va or denom(op(word))=1-va 
  or denom(op(word))=va-1)) then 
  seriesterm:=convert(betterSeries(pref,va=u, ExpansionOrder), polynom):
  output:=seriesterm*ExpLog(va, u, bar(op(word)), ExpansionOrder-ldegree(seriesterm,va-u) ):
 # If there is no bar-term or if there is a bar-term, but it doesn't depend on va:
 elif not(has(word,va)) then 
  output:=convert(betterSeries(pref,va=u, ExpansionOrder), polynom)*bar(op(word));
 # All other cases:
 else
#  symbolicexp:=integr(bar(op(word)), va, u, MPLexp(PartialDiff(va, bar(op(word))), va, u )):
#  output:=convert(series(pref,va=u, MPLExpansionOrder), polynom)*eval(subs(integr=IntegrExpl, symbolicexp)):
  output := convert(betterSeries(pref,va=u, ExpansionOrder),polynom):
  symbolicexp:=integr(bar(op(word)), va, u, MPLexp(PartialDiff(va, bar(op(word))), va, u, ExpansionOrder-ldegree(output,va-u))):
  output := output*eval(subs(integr=IntegrExpl, symbolicexp)): 
 end if:
end if:
return output:
end proc:


# Regularisation by wrapping the expansion and eliminatin logarithms:

MPLExpand:=proc(inp, va, u::integer, ExpansionOrder::integer:=1)
local output:
if not has(inp, va) then 
 return inp:
end if:
output:=MPLexp(inp, va, u, ExpansionOrder):
output:=evalindets(output, 'specfunc(anything, ln)', proc (h) options operator, arrow; RegLog(op(1,h), va, u) end proc);
if u=1 then 
 output:=normal(subs([ln(epsilon)=0, bar(d(epsilon)/epsilon)=0], output)):
else
 output:=normal(subs([ln(epsilon)=0, bar(d(epsilon)/epsilon)=0], output)):
end if:
return output:
end proc:


# Expansion of logarithms:

ExpLog:=proc(va, u::integer, inp, ExpansionOrder::integer:=1)
local i, BarLists, FirstFactor, SecondFactor, output, s:
output:=0:
BarLists:=BarToLists(normal(inp)):
for i from 1 to nops(BarLists[1]) do
 FirstFactor:=betterSeries(BarLists[1][i], va=u, ExpansionOrder):
 if u=0 then
  if match(denom(op(BarLists[2][i]))=va, va, 's') then
   SecondFactor:=ln(va):
  elif match(denom(op(BarLists[2][i]))=va-1, va, 's') then
   SecondFactor:=-betterSeries(-ln(1-va), va=0, ExpansionOrder):
  elif match(denom(op(BarLists[2][i]))=va*B-1, va, 's') then
   SecondFactor:=-betterSeries(-ln(-denom(op(BarLists[2][i]))), va=0, ExpansionOrder):
  else SecondFactor:=betterSeries(op(BarLists[2][i]), va=0, ExpansionOrder):
  end if:
 elif u=1 then
  if match(denom(op(BarLists[2][i]))=va, va, 's') then
   SecondFactor:=betterSeries(ln(va), va=1, ExpansionOrder):
  elif match(denom(op(BarLists[2][i]))=va-1, va, 's') then
   SecondFactor:=ln(va-1):
  elif match(denom(op(BarLists[2][i]))=va*B-1, va, 's') then
   SecondFactor:=betterSeries(ln(denom(op(BarLists[2][i]))), va=1, ExpansionOrder):
  else SecondFactor:=betterSeries(op(BarLists[2][i]), va=1, ExpansionOrder):
  end if:
 else print("Expansions are only supported at 0 and 1"):
 end if:
 output:= convert(FirstFactor, polynom) * convert(SecondFactor, polynom); 
end do:
return factor(output):
end proc:




# regularized loragithm:
RegLog:=proc(z, va, u)
if z=0 or z=Var0 then return ln(epsilon):
elif u=1 and z=va-1 then return ln(epsilon):
elif u=1 and z=1-va then return -ln(epsilon):
elif u=0 and z=va then return ln(epsilon):
else return bar(d(z)/z):
end if:
end proc:


# Explicit computation of the integrals which appear in the algorithm for the series expansion:

IntegrExpl:=proc(word, va, u::integer, inp)
local output, input, R, N, IndefInt, LimitTerm, auxvar, TestInput, returnvalue:
input:=inp:
# If the integrand has the form (1/y)*ln(y)^N the output is (1/N)*ln(y)^(N+1).
# Else the procedure integrates from zero to y.
if u=0 then 
 TestInput:=eval(inp, va=epsilon):
 if match(TestInput = R*(1/epsilon)*ln(epsilon)^N, epsilon, 'returnvalue') then
  IndefInt:=eval((R/(N+1))*ln(epsilon)^(N+1), [op(returnvalue)]):
 else
  IndefInt:=int(input, va):
 end if:
elif u=1 then 
input:=eval(inp, va=auxvar+1):
 if match(input = R*(1/auxvar)*ln(auxvar)^N, auxvar, 'returnvalue') then
  IndefInt:=eval(eval((R/(N+1))*ln(auxvar)^(N+1), [op(returnvalue)]), auxvar=va-1):
 else
  IndefInt:=eval(int(input, auxvar),auxvar=va-1):
 end if:
end if:
output:=IndefInt + u*Reg(word, va):
return  output:
end proc:









####################################################################
####################################################################
#
#   LIMITS
#
####################################################################
####################################################################




# RegValue computes the regularized value at 0 or 1, 
# using MPLexp and RegLog.

RegValue:=proc(va, u::integer, inp)
local seriesexp, output:
# If inp is not a bar-term, the usual limit at u is taken.
if has(inp,bar)=false then return limit(inp, va=u):
end if:
# Compute the expansion with MPLexp.
seriesexp:=factor(eval(MPLexp(inp, va, u),csgn=0)):
# Introduce RegLog for ln and evaluate at u.
output:=eval(subs(ln='RegLog', simplify(seriesexp)), va=u):
return output:
end proc:



# For two integers r and k, rPartitions returns all possible sequences [i1, i2, ..., ir] with i1+i2+...+ir = k.
# Here all i are greater or equal zero.

rPartitions:=proc(r::integer, k::integer)
local i, j, partitionlist, output, newpart, oldpart:
partitionlist:=partition(k+r):
output:=[]:
for i from 1 to nops(partitionlist) do
 if nops(partitionlist[i])=r then 
  oldpart:=partitionlist[i]:
  newpart:=[]:
  for j from 1 to nops(oldpart) do
   newpart:=[op(newpart), oldpart[j]-1]:
  end do:
  output:=[op(output),op(permute(newpart))]:
 end if:
end do:
return output:
end proc:


# For a sequence with one or many zeroes at the right end, (cases treated with equation R2) aTOn returns a sequence,
# where the first number is the number of zeroes at the right end, corresponding to the number k in eq. R2, and all other numbers correspond to n1, n2, ...,nr.

aTOn:=proc(inp)
local i, counter, zerocounter, stopcounting, output:
if inp[nops(inp)]=0 then 
 # At first we count the number of zeros at the end of the sequence.
 zerocounter:=1:
 stopcounting:=false:
 for i from 1 to nops(inp)-1 do
  if inp[nops(inp)-i]=0 then zerocounter:=zerocounter+1:
  else  
   if not(stopcounting) then 
    output:=[zerocounter]:
    stopcounting:=true: 
   end if:
  end if:
 end do:
 # Now we collect all n.
 counter:=0:
 for i from 1 to nops(inp)-output[1] do
  if op(i,inp)=0 then
   counter:=counter+1:
  elif op(i,inp)=1 then 
   output:=[op(output),counter+1]:
   counter:=0:
  end if:
 end do:
end if:
return output:
end proc:
 

# For a sequence of numbers giving the n-notation, i.e. the notation obtained from aTOn,
# the following gives back the sequence of zeroes and ones.

nTOa:=proc(inp)
local i, j, output:
output:=[]:
for i from 1 to nops(inp) do 
 output:=[1, op(output)]:
 for j from 1 to inp[nops(inp)-i+1]-1 do
  output:=[0, op(output)]:
 end do:
end do:
return output:
end proc:


# Similar to restrictF above:

restrictFZero:=proc(inp, va)
local i, j, DelCoordinates, output, ReplaceCoords, ZetaTerm:
output:=inp:
ReplaceCoords:=[op(MPL_COORDINATES), op(GlobalCoordinates)]: 
if has(va, ReplaceCoords) then 
 DelCoordinates:=subs(va=NULL,ReplaceCoords):
 for i from 1 to nops(DelCoordinates) do
  output:=subs(d(DelCoordinates[i])=0, output):
  output:=subs(DelCoordinates[i]=0, output):
 end do:
end if:
ZetaTerm:=0:
if u=1 then
 for j from 1 to nops(ReplaceCoords) do
  if not(ReplaceCoords[j]=va) and not(inp=ONE) then
   ZetaTerm:=ZetaTerm+RegularizedZeta(inp, ReplaceCoords[j]);
  end if:
 end do:
end if:
return eval(output + ZetaTerm):
end proc:


# Regularization:

Reg:=proc(inp, va)
local Copr, output, word, pref, collectedinp:
if not(has(inp,va)) then return inp:
end if:
output:=0:
collectedinp:=collect(inp, bar,`distributed`):
if type(collectedinp, `+`) then 
 output:= map(proc(x)
         if has(x, bar) then
          pref:=eval(x, bar=1):
          word:=[op(op(selectfun(x, bar)))]: 
         else 
          pref:=x:
          word:=[1]:
         end if:
         Copr:=Coproduct(bar(op(word))): 
         output:=eval(evalindets(Copr, 'specfunc(anything, tens)', proc (h) options operator, arrow; pref*restrictR(op(1,h), va, 1)          *RegularizedZeta(restrictFZero(op(2,   h), va), va) end proc), ONE=1):
         end proc,
         collectedinp):
else
 if has(collectedinp, bar) then
  pref:=eval(collectedinp, bar=1):
  word:=[op(op(selectfun(collectedinp, bar)))]: 
 else 
  pref:=collectedinp:
  word:=[1]:
 end if:
 Copr:=Coproduct(bar(op(word))): 
 output:=eval(evalindets(Copr, 'specfunc(anything, tens)', proc (h) options operator, arrow; pref*restrictR(op(1,h), va, 1)*   RegularizedZeta(restrictFZero(op(2,   h), va), va) end proc), ONE=1):
 end if:
return output:
end proc:



# RegularizeZeta applies the equations R0, R1, R2 and R4 to any sequence of zeroes and ones to get the regularized multiple zeta value.

RegularizedZeta:=proc(barinp, va)
local counter1, l, m, i, j, h, k, r, summation, inp, output, binomialfactor, aTOnSequence, Partitionlist, newn, newinp, newbarinp, prefactor, firstprefac, BarSeq:
if barinp=ONE then return 1:
end if:
for i from 1 to nops(barinp) do
 if (has(barinp, bar) and not(op(i, barinp)=d(va)/va or op(i, barinp)=d(va)/(1-va) or op(i, barinp)=d(va)/(va-1)))
 then return 0:
 end if:
end do:



# Transferring the bar-input to a sequence of zeroes and ones:

BarSeq:=BarToSequence(va, barinp);
firstprefac:=op(1, BarSeq):
inp:=op(2, BarSeq):
# We consider four cases and apply equations R0, R1, R2 and R4 as in 
# F. Brown: On the decomposition of motivic multiple zeta values.
#
# Case 1: if all numbers in inp are equal, the result is zero (R0) 
# We find such cases by summing over all elements and checking if the sum is zero or nops(inp).
summation:=0:
for l from 1 to nops(inp) do
 summation:= summation + inp[l]:
end do:
if summation=0 or summation=nops(inp) then 
 output:=0:
#
# Case 2: sequence of the form 0,...,1; directly apply R1 to get a multiple zeta value
elif inp[1]=0 and inp[nops(inp)]=1 then 
 output:=SequenceToZeta(inp): 
#
# In all other cases we apply R2, but in the case 1,...,1 we first apply R4:
else
 prefactor:=1:
 newinp:=inp:
 #
 # Case 3: sequence of the form 1,...,1; apply R4 to get to the form 0,...,0
 if inp[1]=1 and inp[nops(inp)]=1 then 
  prefactor:=1:#######(-1)^nops(inp):
  newinp:=[]:
  for m from 1 to nops(inp) do
   newinp:=[op(newinp), 1-inp[nops(inp)-m+1]]:
  end do:
 end if:
 #
 # Case 4: sequence of the form 0,...,0 or 1,...,0; apply R2 to get the form 0,...,1.
 if newinp[nops(newinp)]=0 then 
  # We determine the numbers k, r and all partitions i1+i2+...+ir=k.
  aTOnSequence:=aTOn(newinp):
  k:=aTOnSequence[1]:
  r:=nops(aTOnSequence)-1:
  Partitionlist:=rPartitions(r, k):
  prefactor:=prefactor*(-1)^k:
  output:=0:
  for i from 1 to nops(Partitionlist) do
   binomialfactor:=1:
   for j from 1 to r do
    binomialfactor:=binomialfactor*binomial(aTOnSequence[j+1]+Partitionlist[i][j]-1, Partitionlist[i][j]):
   end do:
   newn:=[]:
   for h from 1 to nops(aTOnSequence)-1 do
    newn:=[op(newn), aTOnSequence[h+1]+Partitionlist[i][h]]:
   end do:
   # It may be that the output now corresponds to a sequence 1,...,1, requiring the use of R4.
   # So we call RegularizedZeta recursively to cover these cases.
   output:=output + binomialfactor * RegularizedZeta(nTOa(newn), va):
  end do:
  # From case 3 there may be a prefactor.
  output:=prefactor * output:
 end if:
end if:
return firstprefac*output;
end proc:



# The following transforms a word with letter d(y)/y and d(y)/(1-y) to the 
# corresponding sequence of 0 and 1. 

BarToSequence:=proc(va, inp)
local i, prefac, outputlist:
# If the input has no bar, we assume that it already is the desired sequence of zeroes and ones
# and just return it:
if not(has(inp, bar)) then return [1, inp]:
end if:
# Else:
prefac:=1:
outputlist:=[]:
for i from 1 to nops(inp) do
 if op(i,inp)=d(va)/va then outputlist:=[op(outputlist), 0]:
 elif op(i,inp)=d(va)/(1-va) then outputlist:=[op(outputlist), 1]:
  elif op(i,inp)=d(va)/(va-1) then outputlist:=[op(outputlist), 1]:
  prefac:=prefac*(-1):
 end if:
end do:
return [prefac, outputlist]:
end proc:



# To a given sequence of numbers 0 and 1 the following procedure associates a symbolic
# function zeta(...), representing the multiple zeta value.

SequenceToZeta:=proc(inp)
local i, counter, word:
counter:=0:
word:=[]:
if op(nops(inp),inp)=1 then 
 for i from 1 to nops(inp) do
  if op(i,inp)=0 then
   counter:=counter+1:
  elif op(i,inp)=1 then 
   word:=[op(word),counter+1]:
   counter:=0:
  end if:
 end do:
end if:
return zeta(op(word)):
end proc:



# By the following procedure, if the set of zeroes and ones contains more ones, the set is 'swapped' such that 
# we obtain an MZV with more zeroes. The procedure is used to simplify results of RegularizedZeta.

SwapZeta:=proc(inpzeta)
local i, j, inpsequence, numberones, prefactor, newseq:
# Assuming the input is zeta(n1, n2, ...), get the corresponding sequence of zeroes and ones.
inpsequence:=nTOa([op(inpzeta)]):
# Count the number of ones in inpsequence:
numberones:=0:
for i from 1 to nops(inpsequence) do
 numberones:=numberones+inpsequence[i]:
end do:
# If there are more ones than zeroes then swap:
if (numberones>nops(inpsequence)-numberones) then 
 prefactor:=(-1)^nops(inpsequence):
 newseq:=[]:
 for j from 1 to nops(inpsequence) do
  newseq:=[op(newseq),1-inpsequence[nops(inpsequence)-j+1]]:
 end do:
else return subs(SymbolicZeta=zeta, inpzeta):
end if:
return prefactor*subs(SymbolicZeta=zeta, SequenceToZeta(newseq)):
end proc:



# Cancellation of logarithms of zero or spurious poles
# (assuming they are not allowed to occur or cancel):

ReturnFinite:=proc(inp)
global MPL_CoefflnZeroList, MPLepsUp, MPLepsLow:
local i, CoefflnZero, newinp, EpsSeries, newCoeff, lowdegree, oldOrder, TestSeries, OrderOfExpansion,  OrderZeroTerm:
oldOrder:=Order:
newinp:=subs({ln(epsilon)=0, bar(d(epsilon)/epsilon)=0}, inp):
########newinp:=subs({ln(epsilon)=lnZero, bar(d(epsilon)/epsilon)=lnZero}, inp):
OrderOfExpansion:=1:
# To determine the required orders of the expansion:
TestSeries:=convert(series(newinp, epsilon=0),polynom):
if ldegree(TestSeries,epsilon)<0 then 
 OrderOfExpansion:=-ldegree(TestSeries,epsilon)+1:
end if:
EpsSeries:=convert(series(newinp, epsilon=0, OrderOfExpansion),polynom):
if EpsSeries=0 then 
 lowdegree:=0:
else
 lowdegree:=ldegree(EpsSeries,epsilon):
end if:
# Extraction of the pole-terms in epsilon:
if lowdegree<0 then 
 for i from 1 to -lowdegree do
  newCoeff:=normal(coeff(EpsSeries, epsilon^(-i))):
  if not(newCoeff=0) then 
   MPL_CoefflnZeroList:=[op(MPL_CoefflnZeroList), newCoeff*epsilon^(-i)]:
  end if:
 end do:
end if:
OrderZeroTerm:=coeff(epsilon*EpsSeries, epsilon):
CoefflnZero:=normal(coeff(OrderZeroTerm, lnZero)):
if not(CoefflnZero=0) then 
 MPL_CoefflnZeroList:=[op(MPL_CoefflnZeroList), CoefflnZero*lnZero]:
end if:
Order:=oldOrder:
return OrderZeroTerm:
end proc:



# Wrapping procedure for ReturnFinite:

EvalBar:=proc(inp)
local i, TestTerm, EvalBarTerm, BarLists, newinp, output, newoutput:
output:=0:
newoutput:=ReturnFinite(inp):
return eval(newoutput, lnZero=0):
end proc:



# The user-friendly procedure taking limits at u=0 or u=1 of an arbitrary bar-term.

MPLLimit:=proc(inp, va, u)
global MPLepsUp, MPLepsLow:
local i, TestTerm, TheExpansion, output, vasymbol, vaN, TermLimitInf, BarLists:
output:=0:
if u=0 then 
 TheExpansion:=subs(va=epsilon, MPLExpand(inp, va, u)):
elif u=1 then 
 TheExpansion:=subs(va=-epsilon+1, MPLExpand(inp, va, u)):
elif u=infinity then
 vasymbol:=op(0,va):
 vaN:=op(1,va):
 TermLimitInf:=VarChangeInfinity(inp, vasymbol, vaN):
 TheExpansion:=subs(va=-epsilon+1, MPLExpand(TermLimitInf, va, 1)): 
else
 print("Limits can only be computed at zero or one."):
 return:
end if:
output:=eval(EvalBar(TheExpansion)):
return output:
end proc:







####################################################################
####################################################################
#
#  Primitives
#
####################################################################
####################################################################



# starN(N, barterm, ...) takes the wedge-product of the N-th and (N+1)-st letter of barterm
# and computes the right-hand-side of the corresponding Arnold relation. From there, the 
# base- and fiber-part are inserted as new letters in barterm.

starN:=proc(N::integer, barterm)
local i, j, output, BarLists, RHSLists, newword:
output:=0:
BarLists:=BarToLists(barterm):
for i from 1 to nops(BarLists[1]) do
 if N=1 and nops(BarLists[2][i])=1 then 
 # If the word has only one letter, it is only lifted for taking the primitive, which means starN has nothing to do.
  output:= 0:
 elif N < nops(BarLists[2][i]) then
  # If the second letter is in the base, the letters are just swapped.
  if not(has(BarLists[2][i][N+1],MPLft)) then
    newword:=BarLists[2][i]:
    newword[N]:=BarLists[2][i][N+1]:
    newword[N+1]:=BarLists[2][i][N]:
    output:= output + BarLists[1][i] * bar(op(newword)):
  # if the letters are equal, nothing is added to the output.
  # Else:
  elif not(BarLists[2][i][N]=BarLists[2][i][N+1]) then
   RHSLists:=GetArnoldRHS(BarLists[2][i][N],BarLists[2][i][N+1], false, true):
   for j from 1 to nops(RHSLists[1]) do
    newword:=BarLists[2][i]:
    newword[N]:=RHSLists[2][j]:
    newword[N+1]:=RHSLists[3][j]:
    output:= output + (-1)*BarLists[1][i]*RHSLists[1][j] * bar(op(newword)):
   end do:
  end if:
 end if:
end do:
return output:
end proc:



# star uses starN as building block to build up the primitive, in the sense:
# star(w) = starN(1,w) + starN(2,starN(1,w)) + ...
# where w is the concatenation of the arguments fiberform and barterm.

star:=proc(fiberform, barterm, maxlength::integer)
local i, output, oldterm, newterm:
oldterm:=TotalToSymbols(conc(bar(fiberform),barterm)):
output:=oldterm:
for i from 1 to maxlength do
 newterm:=starN(i, oldterm):
 output:= output + newterm: 
 oldterm:=newterm:
end do:
return output:
end proc:


# User-friendly wrapping function for the computation of primitives:

MPLPrimitive:=proc(fiberform, barterm)
local maxlength:
maxlength:=max(indices(SortByLengthTable(barterm),nolist)):
return SymbolsToTotal(ComputePrimitive(fiberform, barterm, maxlength+1)):
end proc:



# Actual primitive computation:

ComputePrimitive:=proc(fiberform, barterm, maxlength::integer)
local i, LiftedBar, LiftedForm, output:
LiftedForm:=Lift([fiberform]);
#LiftedBar:=IntWordsRecursive(barterm):
LiftedBar:=barterm:
output:=star(op(LiftedForm), LiftedBar, maxlength):
return output:
end proc:


# The following procedures test the primitive procedure automatically.  

ComputePrimitiveTest1:=proc(form1, inp)
local psiB, LHS, RHS, concatword:
concatword:=conc(bar(form1), inp):
psiB:=SymbolsToTotal(IntWordsRecursive(inp)):
LHS:=SymbolsToTotal(ComputePrimitive(form1, psiB,  nops(concatword))):
RHS:=SymbolsToTotal(IntWordsRecursive(concatword)):
return normal(LHS-RHS):
end proc:

ComputePrimitiveTest2:=proc(form1, inp)
local LHS, RHS, basebar:
basebar:=bar(a,b):
LHS:=SymbolsToTotal(ComputePrimitive(form1, MPLShuffleProduct(basebar, inp),  nops(inp)+nops(basebar)+1)):
RHS:=MPLShuffleProduct(basebar, SymbolsToTotal(ComputePrimitive(form1,inp,nops(inp)+1))):
return normal(LHS-RHS):
end proc:







####################################################################
####################################################################
#
#   INTEGRATION
#
####################################################################
####################################################################




# ParFrac computes the partial fraction decomposition of prefactors of bar-terms.
# It decomposes the output as two lists, the first list, containing the resulting 
# prefactors and the second the corresponding bar-terms.

ParFrac:=proc(va, inp)
local i, j, BarLists, Prefac, outputcoeffs, outputbars:
outputcoeffs:=[]:
outputbars:=[]:
BarLists:=BarToLists(inp):
for i from 1 to nops(BarLists[1]) do
 # partial fraction decomposition of the prefactors:
 Prefac:=convert(BarLists[1][i], parfrac, va);
 if type(Prefac, `+`) then 
 for j from 1 to nops(Prefac) do
  outputcoeffs:=[op(outputcoeffs), op(j,Prefac)]:
  outputbars:=[op(outputbars), bar(op(BarLists[2][i]))]:
 end do:
 else
  outputcoeffs:=[op(outputcoeffs), Prefac]:
  outputbars:=[op(outputbars), bar(op(BarLists[2][i]))]:
 end if:
end do:
return [outputcoeffs, outputbars]:
end proc:




FindForm:=proc(deninp, forms)
local i, j, k, output, newdeninp, NewPoly, PolyFactors:
output:=[]:
if type(deninp, `^`) then newdeninp:=op(1, deninp):
else newdeninp:=deninp:
end if:
if type(newdeninp, `*`) then 
 for i from 1 to nops(newdeninp) do
  if type(op(i,newdeninp), `^`) then NewPoly:=op(1, op(i,newdeninp)):
  else NewPoly:=op(i,newdeninp):
  end if:
  for j from 1 to nops(forms) do
   if NewPoly=denom(forms[j]) then output:=forms[j]:
   end if:
  end do:
 end do:
else
PolyFactors:=factors(newdeninp):
 for j from 1 to nops(forms) do
  for k from 1 to nops(PolyFactors[2]) do
   if op(1, PolyFactors[2][k])=denom(forms[j]) then output:=forms[j]:
   end if:
  end do:
 end do:
end if:
return output:
end proc:




# recognize is a procedure to select terms, which are in a certain form, amenable for the iterated use of 
# partial fraction decomposition and partial integration:
# The output of recognize are terms of the form f*bar(...) where the denominator of f is equal to
# the denominator of a form in the fiber to some arbitrary power a and times some term b.
# The output consists of three lists: The prefactors, the recognized fiber-forms and the power b.

recognize:=proc(inp, forms, va)
local i, j, prefactor, DenDegree, output, auxsymbol, FoundForm:
output:=[]:
if not(has(denom(inp), va)) then 
 output:=[inp,d(va),0]:
else 
 FoundForm:=FindForm(denom(inp), forms):
 DenDegree:=degree(factor(denom(inp)*auxsymbol),denom(FoundForm)):
 prefactor:=simplify(inp/(FoundForm/d(va))^DenDegree):
 if not(has(prefactor,va)) then
  output:=[prefactor,FoundForm,DenDegree]:
 end if:
end if:
return output:
end proc:




# PrepareIntegrand manipulates a linear combination of bar-terms with rational prefactors by iterated
# partial fraction decomposition and partial integration until it can be integrated.
# PrepareIntegrand manipulates a linear combination of bar-terms with rational prefactors by iterated
# partial fraction decomposition and partial integration until it can be integrated.

PrepareIntegrand:=proc(va, inp)
global MPLepsUp, MPLepsLow:
local i, j, h, RecList, inpLists, OmegaF, formF, coeffF, PrefacComputePrimitive, NotReady, Prefac, PrefacList, degreeF, convinp, output, auxresult, AssumingList, newterm, IndefInt:
if inp=0 then return 0:
end if:
output:=0:
NotReady:=0:
OmegaF:=MPLFormsFiber(false):
inpLists:=ParFrac(va, inp);
for i from 1 to nops(inpLists[1]) do
 Prefac:=inpLists[1][i]:
 formF:=0:
 # If a term does not depend on the variable, it remains unchanged.
  if (not(has(Prefac, va)) and not(has(inpLists[2][i], va))) then 
   output:=output + Prefac*bar(op(inpLists[2][i])):
 # If the term has no bar and no denominator depending on va, just integrate.
  elif not(has(denom(Prefac), va)) and inpLists[2][i]=1 then 
   output:=output + int(Prefac, va=0..1):
  else
  # For all other terms, select terms to which partial integration can be applied:
  RecList:=recognize(inpLists[1][i], OmegaF, va):
  if not(RecList=[]) then 
   coeffF:=RecList[1]:
   formF:=RecList[2]/d(va):
   degreeF:=RecList[3]:
   # If a form of the fiber appears in the prefactor to power one,
   # the term is ready for integration. 
   if degreeF=1 then
    output:=output+Prefac*bar(op(inpLists[2][i])):
   # If the term has no bar or a bar-term independent of va and has furthermore a 
   # denominator as in OmegaF, to a power higher than one,
   # then just integrate.
   # We use auxiliary variables and introduce assumptions auxvar>0, auxvar<1 to make automatic
   # integration with Maple's "int(...)" possible.
   elif (not(formF=1/(va) or formF=1/(1-va) or formF=1/(va-1)) and (degreeF>1 and not(has(inpLists[2][i], va)))) then
    AssumingList:=[]:
    for h from 1 to nops(MPL_COORDINATES) do
     AssumingList:=[op(AssumingList), MPL_COORDINATES[h]>0, MPL_COORDINATES[h]<1]:
    end do:
    auxresult:=int(inpLists[1][i], va=0..1) assuming op(AssumingList):
    output:=output+normal(auxresult)*bar(op(inpLists[2][i])):
   # If the term has no bar and a denominator as in OmegaF to the power higher than one, 
   # continue partial integration. 
   elif (((formF=1/(va) or formF=1/(1-va) or formF=1/(va-1)) and degreeF>1 and op(inpLists[2][i])=1)) then
 IndefInt:=int(Prefac, va):
   output:=output+eval(IndefInt, va=-epsilon+1)-eval(IndefInt, va=epsilon);
   # If the power is >1 then the iteration of partial fraction decomposition and 
   # partial integration continues.
   elif degreeF>1  or formF=1 then
     PrefacComputePrimitive:=int(Prefac,va):
     NotReady:=NotReady-PrefacComputePrimitive*PartialDiff(va, bar(op(inpLists[2][i]))):   
     output:=output+MPLLimit(PrefacComputePrimitive*bar(op(inpLists[2][i])), va, 1)-MPLLimit(PrefacComputePrimitive*bar(op(inpLists[2][i])), va, 0);
   # If no fiber-form can be found in a prefactor which depends on the variable, the term is not appropriate.
   else  
   print("Inappropriate integrand"):
   end if:
  else print("Inappropriate integrand"):
  end if: 
end if: 
end do:
output:=output + PrepareIntegrand(va, NotReady):
return eval(output, {ONE=1, bar( d(epsilon)/epsilon ) = ln(epsilon)}):
end proc:  



# The following few auxiliary procedures compute some of the steps
# in the computation of definite integrals over cubical coordinates:

MPLintOneBar:=proc(va, inp, OmegaFtilde)
local j, ParFracList, pref, word, outp, NewRecognizedList, NewIntForm, NewComputePrimitive:
outp:=0:
pref:=eval(inp, bar=1):
if has(inp, bar) then
 word:=[op(op(selectfun(inp, bar)))]: 
else word:=[1]:
end if:
ParFracList:=ParFrac(va, pref):
for j from 1 to nops(ParFracList[1]) do
   NewRecognizedList:=recognize(op(j,ParFracList[1]), OmegaFtilde, va):
   NewIntForm:=NewRecognizedList[2]:
   NewComputePrimitive:=SymbolsToTotal(ComputePrimitive(op(Lift([NewIntForm])), bar(op(word)),  nops(word)+1)):
  outp:=outp + subs(va=-epsilon+1, MPLExpand(NewRecognizedList[1]*NewComputePrimitive, va, 1))-subs(va=epsilon, MPLExpand(NewRecognizedList[1]*NewComputePrimitive, va, 0)):
  end do:
return outp:
end proc:



MPLintOneBarCubical:=proc(va, inp, OmegaFtilde)
local j, ParFracList, pref, word, outp, NewRecognizedList, NewIntForm, NewComputePrimitive:
outp:=0:
pref:=eval(inp, bar=1):
if has(inp, bar) then
 word:=[op(op(selectfun(inp, bar)))]: 
else word:=[1]:
end if:
ParFracList:=ParFrac(va, pref):
for j from 1 to nops(ParFracList[1]) do
   NewRecognizedList:=recognize(op(j,ParFracList[1]), OmegaFtilde, va):
   NewIntForm:=NewRecognizedList[2]:
   NewComputePrimitive:=SymbolsToTotal(ComputePrimitive(op(Lift([NewIntForm])), bar(op(word)),  nops(word)+1)):
  outp:=outp + subs(va=-epsilon+1, MPLExpand(NewRecognizedList[1]*NewComputePrimitive, va, 1))-subs(va=epsilon, MPLExpand(NewRecognizedList[1]*NewComputePrimitive, va, 0)):
  end do:
return outp:
end proc:



MPLint:=proc(va, inp)
local inpt, outp:
inpt:=table():
BarToTable(inp, inpt):
outp:=table():
MPLintTable(va, inpt, outp):
return TableToBar(outp):
end proc:



MPLintCubical:=proc(va, inp)
local i, j, PreparedIntegrand, Integrand, BarLists, NewRecognizedList, NewIntForm, NewComputePrimitive, OmegaFtilde, ParFracList, output, finaloutput:
OmegaFtilde:=MPLFormsFiber(false):
# We firstly apply PrepareIntegrand to the input.
PreparedIntegrand:=PrepareIntegrand(va, inp):
# We split off the terms, where nothing has to be done anymore.
Integrand:=0;
if type(PreparedIntegrand,`+`) then 
 for i from 1 to nops(PreparedIntegrand) do
  if has(op(i,PreparedIntegrand), va) then
   Integrand:=Integrand + op(i,PreparedIntegrand):
  end if: 
 end do:
else
 if has(PreparedIntegrand, va) then 
  Integrand:=PreparedIntegrand:
 end if:
end if:
output:=PreparedIntegrand-Integrand;
# All terms in 'Integrand' are of the form f*bar(...) where f is in the fiber.
# Here we take the primitive and the limits at zero and one.
Integrand:=collect(Integrand, bar,`distributed`):
if type(Integrand, `+`) then 
 finaloutput:=output + map(proc(x) MPLintOneBarCubical(va, x, OmegaFtilde) end proc, Integrand):
else
 finaloutput:=output + MPLintOneBarCubical(va, Integrand, OmegaFtilde):
end if:
return EvalBar(finaloutput):
end proc:



MPLintTable:=proc(va, inp, outp)
local i, j, h, PreparedIntegrand, Integrand, BarLists, NewRecognizedList, NewIntForm, NewComputePrimitive, OmegaFtilde, ParFracList, output, finaloutput, newinpTerm, symbolinp:
OmegaFtilde:=MPLFormsFiber(false):
# First the symbol-map is applied to the integrand:
symbolinp:=IntWordsRecursiveTable(inp):
for h in indices(symbolinp,'nolist') do
 # We firstly apply PrepareIntegrand to the input.
 newinpTerm:=symbolinp[h]*bar(op(h)):
 PreparedIntegrand:=PrepareIntegrand(va, newinpTerm):
 # We split off the terms, where nothing has to be done anymore.
 Integrand:=0;
 if type(PreparedIntegrand,`+`) then 
  for i from 1 to nops(PreparedIntegrand) do
   if has(op(i,PreparedIntegrand), va) then
    Integrand:=Integrand + op(i,PreparedIntegrand):
   end if: 
  end do:
 else
  if has(PreparedIntegrand, va) then 
   Integrand:=PreparedIntegrand:
  end if:
 end if:
 output:=PreparedIntegrand-Integrand;
 # All terms in 'Integrand' are of the form f*bar(...) where f is in the fiber.
 # Here we take the primitive and the limits at zero and one.
 Integrand:=collect(Integrand, bar,`distributed`):
 if type(Integrand, `+`) then 
  for j from 1 to nops(Integrand) do
   output:=output + MPLintOneBar(va, op(j, Integrand), OmegaFtilde):
  end do:
 else
  output:=output + MPLintOneBar(va, Integrand, OmegaFtilde):
 end if:
 finaloutput:=EvalBar(output):
 BarToTable(finaloutput, outp):
end do:
return outp:
end proc:



# The following procedure computes integrations from 0 to 1 over integrands which are already in 
# cubical coordinates. If for example cubicalvar=u[4], the procedure does a number of integrations
# (the argument "integrations") in the ordering u[4], u[3], ...

MPLCubicalIntegrate:=proc(inp, cubicalvar, integrations)
local i, va, highest, newint, prepint, cubicalset, newset, intvar:
va:=op(0,cubicalvar):
highest:=op(1,cubicalvar):
cubicalset:=[]:
for i from 1 to highest do
 cubicalset:=[op(cubicalset), va[highest+1-i]]:
end do:
newint:=inp:
for i from 1 to integrations do
 if i=highest then 
  MPLInitialize(va, 1):
  intvar:=va[2]:
  newset:=[va[2]]:
  newint:=subs(va[1]=va[2], newint):
 else
  MPLInitialize(va, highest-i):
  intvar:=va[highest-i+1]:
  newset:=cubicalset[i..nops(cubicalset)]:
 end if:
 newint:=normal(MPLintCubical(intvar,normal(newint))):
end do:
return newint:
end proc:








####################################################################
####################################################################
#
#   FEYNMAN PARAMETER REPLACEMENTS
#
####################################################################
####################################################################




TrailingZeroes:=proc(inp, va)
local i, j, h, k, outp, BarLists, n, newword, wordw, letterb, worda, wordalog, firstbar:
BarLists:=BarToListsCollected(inp):
outp:=0:
for h from 1 to nops(BarLists[1]) do
 n:=0:
 newword:=BarLists[2][h]:
 j:=nops(newword):
 while (newword[j]=d(va)/va or newword[j]=-d(va)/va) and j>0 do
  n:=n+1:
  j:=j-1:
  if j=0 then break:
  end if:
 end do:
 if n=0 then 
  outp:=outp + BarLists[1][h]*bar(op(newword)):
 elif n=nops(newword) then
  outp:=outp + BarLists[1][h]*barlog(op(newword)):
 else
  wordw:=[]:
  for j from 1 to nops(newword)-n-1 do
   wordw:=[op(wordw),newword[j]]:
  end do:
  letterb:=newword[nops(newword)-n]:
  for i from 0 to n do
   worda:=[]:
   for k from 1 to i do 
    worda:=[op(worda), d(va)/va]:
   end do:
   wordalog:=[]:
   for k from 1 to n-i do 
    wordalog:=[op(wordalog), d(va)/va]:
   end do:
   if worda=[] then worda:=[ONE]:
   end if:
   if wordalog=[] then wordalog:=[ONE]:
   end if:
   if wordw=[] then wordw:=[ONE]:
   end if:
   firstbar:=eval(MPLShuffleProduct(bar(op(wordw)),bar(op(worda))),ONE=1):
   if not(has(firstbar,bar)) then 
    outp:=outp + (-1)^i*BarLists[1][h]*firstbar*bar(letterb)*barlog(op(wordalog)):
   else
    outp:=outp + (-1)^i*BarLists[1][h]*conc(firstbar,bar(letterb))*barlog(op(wordalog)):
   end if:
  end do:
 end if:
end do:
return eval(outp,barlog(ONE)=1):
end proc:






ReplaceBarLog:=proc(inp,reps, FeynPar, va)
global MPLSymbForms:
local i, j, h, outp, BarLog, BarLogList, RHS, barform, baseform, baseformexpl, barword, baseword, NewSymbRepsBack, nSymbRepsBack, alreadyinMPLSymbForms:
outp:=normal(inp):
NewSymbRepsBack:=MPLSymbForms:
if has(inp, barlog) then
 nSymbRepsBack:=nops(MPLSymbForms):
 BarLogList:=[op(selectfun(inp, barlog))]:
 for h from 1 to nops(BarLogList) do
  BarLog:=BarLogList[h]:
  barform:=ReplaceArgument(va, [1=1], reps, d(va), 1, FeynPar):
  baseformexpl:=ReplaceArgument(va, [1=1], reps, d(va), 2, FeynPar):
  alreadyinMPLSymbForms:=false:
  for i from 1 to nops(NewSymbRepsBack) do
   if op(2,NewSymbRepsBack[i])=baseformexpl then
    alreadyinMPLSymbForms:=true:
    baseform:=SymbForm[i]:
   end if:
  end do:
  if not(alreadyinMPLSymbForms) then 
   NewSymbRepsBack:=[op(NewSymbRepsBack), SymbForm[nSymbRepsBack+1]=baseformexpl]:
   baseform:=SymbForm[nSymbRepsBack+1]:
  end if:
  RHS:=0:
  for i from 0 to nops(BarLog) do
   barword:=[]:
   baseword:=[]:
   for j from 1 to nops(BarLog)-i do
    barword:=[op(barword),barform]:
   end do:
   for j from 1 to i do
    baseword:=[op(baseword),baseform]:
   end do:
   if barword=[] then
    barword:=ONE:
   end if:
   if baseword=[] then
    baseword:=ONE:
   end if:
   RHS:=RHS+barlog(op(barword))*base(op(baseword)):
  end do:
  MPLSymbForms:=NewSymbRepsBack:
  outp:=subs(ONE=1,subs(BarLog=RHS,outp)):
 end do:
end if:
return outp:
end proc:







PrepFeynInt:=proc(inp, FeynPar)
local i, j, h, SortedInput, outp, k, fn1, fn1List, fTens1, Co, CoTerm, va, NewList, leftSide, rightSide, rightList, rightbarList, RepList, RepBackList, nopsR:
outp:=0:
RepList:=[]:
RepBackList:=[]:
if nops(FeynPar)<2 then  
 return inp:
else
 va:=FeynPar[1]:
 NewList:=[]:
 for i from 2 to nops(FeynPar) do
  NewList:=[op(NewList), FeynPar[i]]:
 end do:
 # Sort the input by the length of the words.
 
 SortedInput:=SortByLength(inp):
 for k from 1 to ArrayNumElems(SortedInput[1]) do
  if SortedInput(1)(k)=0 then
   outp:=outp+SortedInput(2)(k):
  else
 # Take the co-product:
  Co:=TensToLists(MPLCoproduct(SortedInput(2)(k))):
  for j from 1 to nops(Co[1]) do
   leftSide := restrictFFeyn(Co[2][j],FeynPar,va,0):
   rightSide:=subs(bar=base,restrictRFeyn(Co[3][j],va,0,[])):
   rightbarList:=selectfun(rightSide, base):
   rightList:=[]:
   for h from 1 to nops(rightbarList) do
    rightList:=[op(rightList),op(rightbarList[h])]:
   end do:
   
   for h from 1 to nops(rightList) do
    if not(rightList[h]=ONE) and not(rightList[h]=0) and not(has(RepList, rightList[h])) then 
     nopsR:=nops(RepList):
     RepList:=[op(RepList), rightList[h]=SymbForm[nopsR+1]]:
     RepBackList:=[op(RepBackList), SymbForm[nopsR+1]=rightList[h]]:
    end if:
   end do:
   rightSide:=subs(RepList, rightSide):
   outp:=outp+ Co[1][j]*leftSide*rightSide:
  end do:
  end if:
 end do:
end if:
return [TrailingZeroes(eval(outp,ONE=1),FeynPar[1]), RepBackList]:
end proc:








Reshuffle:=proc(inp)
local i, j, BarLists, outp, BaseL, newterm, BaseCoeff, BaseShuffle:
outp:=0:
BarLists:=BarToListsCollected(inp):
for i from 1 to nops(BarLists[1]) do
 if has(BarLists[1][i],base) then 
  newterm:=expand(BarLists[1][i]):
  if type(newterm,`+`) then
   for j from 1 to nops(newterm) do
    BaseL:=selectfun(op(j,newterm),base):
    if nops(BaseL)=1 then
     # Check if the basefactor appears quadratic:
     if has(op(j,newterm), BaseL[1]^2) then 
      BaseCoeff:=coeff(op(j,newterm), BaseL[1]^2):
      BaseShuffle:=MPLShuffleProduct(subs(base=bar, BaseL[1]), subs(base=bar, BaseL[1])):
      outp:=outp + BaseCoeff * MPLShuffleProduct(BaseShuffle, bar(op(BarLists[2][i]))):
     else  
      outp:=outp + MPLShuffleProduct(subs(base=bar, op(j,newterm)), bar(op(BarLists[2][i]))):
     end if:
    elif nops(BaseL)=2 then 
     BaseCoeff:=coeff(coeff(op(j,newterm), BaseL[1]),BaseL[2]):
     BaseShuffle:=MPLShuffleProduct(subs(base=bar, BaseL[1]), subs(base=bar, BaseL[2])):
     outp:=outp + BaseCoeff * MPLShuffleProduct(BaseShuffle, bar(op(BarLists[2][i]))):
    elif nops(BaseL)=0 then 
     outp:=outp +  op(j,newterm)*bar(op(BarLists[2][i])):
    end if:
   end do:
  else
   BaseL:=selectfun(newterm,base):
   if nops(BaseL)=1 then
    # Check if the basefactor appears quadratic:
    if has(newterm, BaseL[1]^2) then   
     BaseCoeff:=coeff(newterm, BaseL[1]^2):
     BaseShuffle:=MPLShuffleProduct(subs(base=bar, BaseL[1]), subs(base=bar, BaseL[1])):
     outp:=outp + BaseCoeff * MPLShuffleProduct(BaseShuffle, bar(op(BarLists[2][i]))):
    else  
     outp:=outp + MPLShuffleProduct(subs(base=bar, newterm), bar(op(BarLists[2][i]))):
    end if:
   elif nops(BaseL)=2 then 
    BaseCoeff:=coeff(coeff(newterm, BaseL[1]),BaseL[2]):
    BaseShuffle:=MPLShuffleProduct(subs(base=bar, BaseL[1]), subs(base=bar, BaseL[2])):
    outp:=outp + BaseCoeff * MPLShuffleProduct(BaseShuffle, bar(op(BarLists[2][i]))):
   elif nops(BaseL)=0 then 
    outp:=outp +  newterm*bar(op(BarLists[2][i])):
   end if:
  end if:  
 else
  outp:=outp +  BarLists[1][i]*bar(op(BarLists[2][i])):
 end if:
end do:
return outp:
end proc:





ReshuffleLog:=proc(inp)
local i, BarLists, outp:
outp:=0:
BarLists:=BarToListsCollected(inp):
for i from 1 to nops(BarLists[1]) do
 if has(BarLists[1][i],barlog) then 
  outp:=outp + MPLShuffleProduct(subs(barlog=bar, BarLists[1][i]), bar(op(BarLists[2][i]))):
 else
  outp:=outp +  BarLists[1][i]*bar(op(BarLists[2][i])):
 end if:
end do:
return outp:
end proc:






# The following procedure takes a list of polynomials and derives the corresponding polynomials
# relevant after changing the integration domain from 0 to infinity to 0 to 1.

ChangeIntDomainPoly:=proc(polynomials, va)
local i, output:
output:=[]:
for i from 1 to nops(polynomials) do
 if has(polynomials[i], va) then 
  output:=[op(output), factor((va-1)*eval(polynomials[i], va=va/(1-va)))]:
 end if:
end do:
return output:
end proc:




# The following procedure derives rules for replacing polynomials in the e-parameters
# by terms involving new cubical coordinates.
# The main input specifies a list of polynomials and corresponding variables to solve for. E.g. this input may be
# [[[p1, p2, ...], [p3, ...]], [e[1], e[2]]], where p1, p2, p3 are polynomials in the e-parameters.
# In this case, in the following derivation of cobical coordinates, the equations p1=0, p2=0, ... are solved for e[1]
# and p3=0 is solved for e[2]. 

CubicalReplacements:=proc(polylists, letter, back::boolean)
local i, j, k, counter,  cubic, sing, quot, abstrcubic, abstrquot, reps, repsprelim, newnumer, repsback, singlevar, opts, byhand:
# As a fourth argument of the procedure, the user can add replacements by hand.
opts:=[args[4..nargs]];
if opts=[] then byhand:=[]
else byhand:=opts[1]:
end if:
cubic:=[]:
abstrcubic:=[]:
quot:=[]:
abstrquot:=[]:
reps:=[]:
repsprelim:=[]:
repsback:=[]:
singlevar:=[]:
counter:=0:
# Going through the list of given polynomials P, the program solves equations P=0 with respect to
# the corresponding (specified) variable and builds up cubical coordinates and corresponding replacement-rules
# from these solutions.
# If the list is empty then return a trivial repalcement
if nops(polylists[1][1])=0 then 
 if back then return [letter[2]=polylists[2][1]]:
 else return [polylists[2][1]=letter[2]]:
 end if:
end if: 
# Else:
for i from 1 to nops(polylists[1]) do
 counter:=counter+nops(polylists[1][i])+1:
 sing:=[1]:
 cubic:=[polylists[2][i], op(cubic)]:
 abstrcubic:=[letter[counter], op(abstrcubic)]:
 singlevar:=[op(singlevar), polylists[2][i]=letter[counter]]:
 quot:=[1/polylists[2][i], 1/(1-polylists[2][i])]:
 abstrquot:=[1/letter[nops(polylists[1][i])+1], 1/(1-letter[nops(polylists[1][i])+1])]:
 for j from 1 to nops(polylists[1][i]) do
  sing:=[op(sing),solve(polylists[1][i][j], polylists[2][i])]:
  cubic:=[sing[j]/sing[j+1], op(cubic)]:
  abstrcubic:=[letter[counter-j], op(abstrcubic)]:
  quot:=[op(quot), factor(subs(polylists[2][i]=polylists[2][i]*sing[j]/sing[j+1], quot[j+1]))]:
  abstrquot:=[op(abstrquot), factor(subs(letter[nops(polylists[1][i])+1]=letter[nops(polylists[1][i])+1]*letter[nops(polylists[1][i])+1-j], abstrquot[j+1]))]:
 end do:
 for k from 3 to nops(polylists[1][i])+2 do
  repsprelim:=[op(repsprelim), denom(quot[k])=denom(abstrquot[k])*numer(quot[k])/numer(abstrquot[k]), -denom(quot[k])=-denom(abstrquot[k])*numer(quot[k])/numer(abstrquot[k])]:
 end do:
end do:
# The replacements added by hand are taken into account:
repsprelim:=[op(repsprelim), op(byhand)]:
for k from 1 to nops(repsprelim) do
 reps:=[op(reps), op(1, repsprelim[k]) = subs(repsprelim, op(2, repsprelim[k]))]:
end do:
for k from 1 to nops(singlevar) do
 reps:=[op(reps), singlevar[k]]:
end do:
for k from 1 to nops(cubic) do 
 repsback:=[op(repsback), abstrcubic[k]=cubic[k]]:
end do:
if back then return repsback:
else return reps:
end if:
end proc:



# For a given function f=(a*b*...)/(u*v*...) in e-coordinates, the following procedure computes
# d(a)/a + d(b)/b +... - d(u)/u - d(w)/w -... in the new cubical coordinates.

ReplaceArgument:=proc(f, repback, reps, inpnumerator, dezero, FeynPar)
local i, output, numerators, denominators, fFeynNumer, fFeynDenom, SignPrefac, dfinpnum, inpnum:
dfinpnum:=normal(d(f)):
inpnum:=eval(inpnumerator):
if inpnumerator=-dfinpnum then
 SignPrefac:=-1:
elif (inpnumerator=dfinpnum or inpnumerator/f=1) then
 SignPrefac:=1:
elif not(has(inpnumerator,SymbForm)) then
 print("Warning: A differential one-form is not of the type df/f appeared:"):
 print(inpnumerator/f):
 SignPrefac:=1:
end if: 
numerators:=[]:
denominators:=[]:
output:=0:
if f=1 then
 return 1:
end if:
fFeynNumer:=numer(factor(subs(reps, f))):
fFeynDenom:=denom(factor(subs(reps, f))):
if type(fFeynNumer, `^`) then  
 for i from 1 to op(2,fFeynNumer) do 
  numerators:=[op(numerators), op(1,fFeynNumer)]:
 end do:
elif type(fFeynNumer, `*`) then  
 for i from 1 to nops(fFeynNumer) do 
  numerators:=[op(numerators), op(i,fFeynNumer)]:
 end do:
####if op(1, numerators)=(-1) then SignPrefac:=-1:
####end if:
else numerators:=[fFeynNumer]:
end if:
if type(fFeynDenom, `^`) then  
 for i from 1 to op(2,fFeynDenom) do 
  denominators:=[op(denominators), op(1,fFeynDenom)]:
 end do:
elif type(fFeynDenom, `*`) then  
 for i from 1 to nops(fFeynDenom) do 
  denominators:=[op(denominators), op(i,fFeynDenom)]:
 end do:
else denominators:=[fFeynDenom]:
end if:
# From here on we assume, that numerators and denominators only contain the new cubical coordinates.
for i from 1 to nops(numerators) do
 output:=output + d(numerators[i])/numerators[i]:
end do:
for i from 1 to nops(denominators) do
 output:=output - d(denominators[i])/denominators[i]:
end do:
if dezero=1 then
 for i from 1 to nops(FeynPar) do
  output:=subs(d(FeynPar[i])=0,output):
 end do:
elif dezero=2 then
 for i from 1 to nops(MPL_COORDINATES) do
  output:=subs(d(MPL_COORDINATES[i])=0,output):
 end do:
end if:
return SignPrefac*output:
end proc:








# A procedure to check that a polynomial is not trivial:

IsNotTrivial:=proc(inp, intvariable)
local s:
if (has(inp, intvariable) 
   and not(inp=intvariable-1) and not(inp=1-intvariable) 
   and not(inp=intvariable) and not(inp=-intvariable)
   and not(type(inp,numeric))
   and not(match(inp=afactor*intvariable-afactor, intvariable, 's') and type(op(2,op(s)), numeric))
   and not(match(inp=-afactor*intvariable+afactor, intvariable, 's') and type(op(2,op(s)), numeric))
   and not(match(inp=intvariable^auxvariable, auxvariable,'returnvalue'))) then 
 return true:
else
 return false:
end if:
end proc:






FindPoly:=proc(inp, repsbackold, domaintransf, intvariable)
global SymbPoly:
local i, j, output, restrictedoutput, BarLists, NumerNewArg, DenomNewArg, newPref, newPrefDenom, NewArgFunction, NewPoly, GenPref, DomainReps, auxvariable, s, afactor, counter, SymbolicReps, SymbolicInt, NewBarArgument:
# Changing the domain of integration for all variables in domaintransf:
BarLists:=BarToListsCollected(inp):
GenPref:=1:
DomainReps:=[]:
for i from 1 to nops(domaintransf) do
 GenPref:=GenPref * 1/(domaintransf[i]-1)^2:
 DomainReps:=[op(DomainReps), domaintransf[i] = domaintransf[i]/(1-domaintransf[i])]:
end do:
counter:=0:
output:=[]:
SymbolicInt:=0:
SymbolicReps:=[]:
# We collect all functions in the demoninators of the bar-arguments.
for i from 1 to nops(BarLists[2]) do
 for j from 1 to nops(BarLists[2][i]) do
  NewArgFunction:=normalM(denom(BarLists[2][i][j])):
  NumerNewArg:=numer(NewArgFunction):
  DenomNewArg:=denom(NewArgFunction):
  if type(NumerNewArg, `*`) then
   for j from 1 to nops(NumerNewArg) do
    if (not(has(output, op(j,NumerNewArg))) and not(has(output, -op(j,NumerNewArg))) and IsNotTrivial(op(j,NumerNewArg), intvariable)) then 
     output:=[op(output), op(j,NumerNewArg)]:
     counter:=counter+1:
     SymbolicReps:=[op(SymbolicReps), op(j,NumerNewArg)=SymbPoly[counter], -op(j,NumerNewArg)=-SymbPoly[counter]]:
    end if:
   end do:
  else 
   if (not(has(output, NumerNewArg)) and not(has(output, -NumerNewArg)) and IsNotTrivial(NumerNewArg, intvariable)) then  
    output:=[op(output), NumerNewArg]:
    counter:=counter+1:
    SymbolicReps:=[op(SymbolicReps), NumerNewArg=SymbPoly[counter], -NumerNewArg=-SymbPoly[counter]]:
   end if:
  end if:
  if type(DenomNewArg, `*`) then
   for j from 1 to nops(DenomNewArg) do
    if (not(has(output, op(j,DenomNewArg))) and not(has(output, -op(j,DenomNewArg))) and IsNotTrivial(op(j,DenomNewArg), intvariable)) then
     output:=[op(output), op(j,DenomNewArg)]:
     counter:=counter+1:
     SymbolicReps:=[op(SymbolicReps), op(j,DenomNewArg)=SymbPoly[counter], -op(j,DenomNewArg)=-SymbPoly[counter]]:
    end if:
   end do:
  else 
   if (not(has(output, DenomNewArg)) and not(has(output, -DenomNewArg)) and IsNotTrivial(DenomNewArg, intvariable)) then 
    output:=[op(output), DenomNewArg]:
    counter:=counter+1:
    SymbolicReps:=[op(SymbolicReps), op(j,DenomNewArg)=SymbPoly[counter], -op(j,DenomNewArg)=-SymbPoly[counter]]:
   end if:
  end if:
 end do:
 newPref:=normalM(GenPref*BarLists[1][i]):
 newPrefDenom:=denom(newPref):
 if type(newPrefDenom, `^`) then newPrefDenom:=op(1, newPrefDenom):
 end if:
 if type(newPrefDenom, `*`) then
  for j from 1 to nops(newPrefDenom) do
   if type(op(j,newPrefDenom), `^`) then NewPoly:=op(1, op(j,newPrefDenom)):
   else NewPoly:=op(j,newPrefDenom):
   end if:
   if (not(has(output, NewPoly)) and not(has(output, -NewPoly)) and IsNotTrivial(NewPoly, intvariable)) then  
    output:=[op(output), NewPoly]:
    counter:=counter+1:
    SymbolicReps:=[op(SymbolicReps), NewPoly=SymbPoly[counter], -NewPoly=-SymbPoly[counter]]:
   end if:
  end do:
 else 
  if (not(has(output, newPrefDenom)) and not(has(output, -newPrefDenom)) and IsNotTrivial(newPrefDenom, intvariable)) then 
   output:=[op(output), newPrefDenom]:
   counter:=counter+1:
   SymbolicReps:=[op(SymbolicReps), newPrefDenom=SymbPoly[counter], -newPrefDenom=-SymbPoly[counter]]:
  end if:
 end if:
end do:
for i from 1 to nops(BarLists[2]) do
 newPref:=subs(SymbolicReps, factorM(BarLists[1][i])):
 NewBarArgument:=[]:
 for j from 1 to nops(BarLists[2][i]) do
  NewArgFunction:=factorM(denom(BarLists[2][i][j])):
  NewArgFunction:=subs(SymbolicReps,NewArgFunction): 
  NewBarArgument:=[op(NewBarArgument), d(NewArgFunction)/NewArgFunction]:
 end do:
 if BarLists[2][i]=[1] then
  SymbolicInt:=SymbolicInt+newPref:
 else
  SymbolicInt:=SymbolicInt+newPref*bar(op(NewBarArgument)):
 end if:
end do:
return [output, SymbolicReps, SymbolicInt]:
end proc:




FindPolyTable:=proc(inp, repsbackold, intvariable)
global SymbPoly:
local i, j, h, output, restrictedoutput, BarLists, NumerNewArg, DenomNewArg, newPref, newPrefDenom, NewArgFunction, NewPoly, DomainReps, auxvariable, s, afactor, counter, SymbolicReps, SymbolicInt, NewBarArgument:
counter:=0:
output:=[]:
SymbolicInt:=0:
SymbolicReps:=[]:
# We collect all functions in the demoninators of the bar-arguments.
for i in indices(inp,'nolist') do
 for j from 1 to nops(i) do
  NewArgFunction:=normalM(denom(i[j])):
  NumerNewArg:=numer(NewArgFunction):
  DenomNewArg:=denom(NewArgFunction):
  if type(NumerNewArg, `*`) then
   for h from 1 to nops(NumerNewArg) do
    if (not(has(output, op(h,NumerNewArg))) and not(has(output, -op(h,NumerNewArg))) and IsNotTrivial(op(h,NumerNewArg), intvariable)) then 
     output:=[op(output), op(h,NumerNewArg)]:
     counter:=counter+1:
     SymbolicReps:=[op(SymbolicReps), op(h,NumerNewArg)=SymbPoly[counter], -op(h,NumerNewArg)=-SymbPoly[counter]]:
    end if:
   end do:
  else 
   if (not(has(output, NumerNewArg)) and not(has(output, -NumerNewArg)) and IsNotTrivial(NumerNewArg, intvariable)) then  
    output:=[op(output), NumerNewArg]:
    counter:=counter+1:
    SymbolicReps:=[op(SymbolicReps), NumerNewArg=SymbPoly[counter], -NumerNewArg=-SymbPoly[counter]]:
   end if:
  end if:
  if type(DenomNewArg, `*`) then
   for h from 1 to nops(DenomNewArg) do
    if (not(has(output, op(h,DenomNewArg))) and not(has(output, -op(h,DenomNewArg))) and IsNotTrivial(op(h,DenomNewArg), intvariable)) then
     output:=[op(output), op(h,DenomNewArg)]:
     counter:=counter+1:
     SymbolicReps:=[op(SymbolicReps), op(h,DenomNewArg)=SymbPoly[counter], -op(h,DenomNewArg)=-SymbPoly[counter]]:
    end if:
   end do:
  else 
   if (not(has(output, DenomNewArg)) and not(has(output, -DenomNewArg)) and IsNotTrivial(DenomNewArg, intvariable)) then 
    output:=[op(output), DenomNewArg]:
    counter:=counter+1:
    SymbolicReps:=[op(SymbolicReps), op(j,DenomNewArg)=SymbPoly[counter], -op(j,DenomNewArg)=-SymbPoly[counter]]:
   end if:
  end if:
 end do:
 newPref:=normalM(GenPref*inp[i]):
 newPrefDenom:=denom(newPref):
 if type(newPrefDenom, `^`) then newPrefDenom:=op(1, newPrefDenom):
 end if:
 if type(newPrefDenom, `*`) then
  for j from 1 to nops(newPrefDenom) do
   if type(op(j,newPrefDenom), `^`) then NewPoly:=op(1, op(j,newPrefDenom)):
   else NewPoly:=op(j,newPrefDenom):
   end if:
   if (not(has(output, NewPoly)) and not(has(output, -NewPoly)) and IsNotTrivial(NewPoly, intvariable)) then  
    output:=[op(output), NewPoly]:
    counter:=counter+1:
    SymbolicReps:=[op(SymbolicReps), NewPoly=SymbPoly[counter], -NewPoly=-SymbPoly[counter]]:
   end if:
  end do:
 else 
  if (not(has(output, newPrefDenom)) and not(has(output, -newPrefDenom)) and IsNotTrivial(newPrefDenom, intvariable)) then 
   output:=[op(output), newPrefDenom]:
   counter:=counter+1:
   SymbolicReps:=[op(SymbolicReps), newPrefDenom=SymbPoly[counter], -newPrefDenom=-SymbPoly[counter]]:
  end if:
 end if:
end do:
SymbolicInt:=table():
for i in indices(inp, 'nolist') do
 newPref:=subs(SymbolicReps, factorM(inp[i])):
 NewBarArgument:=[]:
 for j from 1 to nops(i) do
  NewArgFunction:=factorM(denom(i[j])):
  NewArgFunction:=subs(SymbolicReps,NewArgFunction): 
  NewBarArgument:=[op(NewBarArgument), d(NewArgFunction)/NewArgFunction]:
 end do:
 if i=[1] then 
  BarToTable(newPref, SymbolicInt):
 else
  BarToTable(newPref*bar(op(NewBarArgument)), SymbolicInt):
 end if:
end do:
return [output, SymbolicReps, SymbolicInt]:
end proc:






FindPoly2:=proc(inp, repsbackold, polyold, letter, domaintransf)
local i, j, output, BarLists, NumerNewArg, DenomNewArg, newPrefDenom, NewArgFunction, NewPoly, GenPref, DomainReps, newinp:
newinp:=SimplifyBarExpression(Transform(inp, repsbackold, polyold, v, domaintransf, true)):
BarLists:=BarToLists(newinp):
output:=[]:
# We collect all functions in the demoninators of the bar-arguments.
for i from 1 to nops(BarLists[2]) do
 for j from 1 to nops(BarLists[2][i]) do
  NewArgFunction:=factor(denom(BarLists[2][i][j])):
  NumerNewArg:=numer(NewArgFunction):
  DenomNewArg:=denom(NewArgFunction):
  if type(NumerNewArg, `*`) then
   for j from 1 to nops(NumerNewArg) do
    if not(has(output, op(j,NumerNewArg))) then 
     output:=[op(output), op(j,NumerNewArg)]:
    end if:
   end do:
  else 
   if not(has(output, NumerNewArg)) then 
    output:=[op(output), NumerNewArg]:
   end if:
  end if:
  if type(DenomNewArg, `*`) then
   for j from 1 to nops(DenomNewArg) do
    if not(has(output, op(j,DenomNewArg))) then 
     output:=[op(output), op(j,DenomNewArg)]:
    end if:
   end do:
  else 
   if not(has(output, DenomNewArg)) then 
    output:=[op(output), DenomNewArg]:
   end if:
  end if:
 end do:
end do:
for i from 1 to nops(BarLists[1]) do
 newPrefDenom:=denom(factor( BarLists[1][i])):
 if type(NewArgFunction, `^`) then newPrefDenom:=op(1, newPrefDenom):
 end if:
 if type(newPrefDenom, `*`) then
  for j from 1 to nops(newPrefDenom) do
   if type(op(j,newPrefDenom), `^`) then NewPoly:=op(1, op(j,newPrefDenom)):
   else NewPoly:=op(j,newPrefDenom):
   end if:
   if not(has(output, NewPoly)) then 
    output:=[op(output), NewPoly]:
   end if:
  end do:
 else 
  if not(has(output, newPrefDenom)) then 
   output:=[op(output), newPrefDenom]:
  end if:
 end if:
end do:
return output:
end proc:





TransformSymbolic:=proc(inp, polys, va, newvar, SymbolicReps, FeynPar, back)
global MPLSymbForms:
local i, j, newinp, outp, reps, repsback, ArgFunctions, BarLists, ArgReps, ArgRepsLog, ArgRepsBase, NewArgFunction, NewArg, newTerm,  newCoeff, DomainReps, word, pref, Jacobian:
ArgReps:=[]:
# Deriving the main replacements from the given polynomials:
if back=true then 
 repsback:=NewCubicalReplacements(polys, va, FeynPar, newvar, false);
 reps:=subs(SymbolicReps, NewCubicalReplacements(polys, va, FeynPar, newvar, true));
else
 reps:=subs(SymbolicReps, NewCubicalReplacements(polys, va, FeynPar, newvar, false));
 repsback:=NewCubicalReplacements(polys, va, FeynPar, newvar, true);
end if:
# Deriving the Jacobian:
if back then
 Jacobian:=1:
else
 Jacobian:=NewCubicalReplacements(polys, va, FeynPar, newvar, true, true):
end if:
# We collect all functions in the demoninators of the bar-arguments.
map(proc(x)
 if not(x=[1]) then 
  for j from 1 to nops(x) do
   NewArgFunction:=denom(x[j]):
   NewArg:=ReplaceArgument(NewArgFunction, [1=1], reps, numer(x[j]), 1, FeynPar):
   if not(has(ArgReps, x[j])) then 
    ArgReps:=[op(ArgReps), x[j]=NewArg]:
   end if:
  end do:
 end if:
end proc, [indices(inp,'nolist')]):
ArgRepsLog:=[d(va)/va = ReplaceArgument(va, [1=1], reps, d(va), 1, FeynPar), -d(va)/va = -ReplaceArgument(va, [1=1], reps, d(va), 1, FeynPar)]:
ArgRepsBase:=[d(va)/va = ReplaceArgument(va, [1=1], reps, d(va), 2, FeynPar), -d(va)/va = -ReplaceArgument(va, [1=1], reps, d(va), 2, FeynPar)]:
# Application of the replacements:
outp:=table():
for i in indices(inp,'nolist') do
 newCoeff:=ReplaceBarLog(inp[i],reps, FeynPar, va):
 newTerm:=normalM(Jacobian*ReshuffleLog(subs(reps,eval(newCoeff))*bar(op(subs(ArgReps, i))))):
 BarToTable(newTerm, outp):
end do:
return outp:
end proc:














Transform:=proc(inp, repsbackold, polylist, newvar, domaintransf)
local i, j, newinp, output, reps, repsback, ArgFunctions, BarLists, ArgReps, NewArgFunction, NewArg, newPref, newBar, GenPref, DomainReps, word, pref:
ArgReps:=[]:
output:=0:
GenPref:=1:
DomainReps:=[]:
# Changing the domain of integration for all variables in domaintransf:
if nargs<6 then 
 for i from 1 to nops(domaintransf) do
  GenPref:=GenPref * 1/(domaintransf[i]-1)^2:
  DomainReps:=[op(DomainReps), domaintransf[i] = domaintransf[i]/(1-domaintransf[i])]:
 end do:
end if:
# Deriving the main replacements from the given polynomials:
if nargs>5 then 
 if args[6]=true then 
  repsback:=CubicalReplacements(polylist, newvar, false);
  reps:=CubicalReplacements(polylist, newvar, true);
 else
  reps:=CubicalReplacements(polylist, newvar, false);
  repsback:=CubicalReplacements(polylist, newvar, true);
 end if:
else
 reps:=CubicalReplacements(polylist, newvar, false);
 repsback:=CubicalReplacements(polylist, newvar, true);
end if:
newinp:=collect(inp, bar,`distributed`):
# We collect all functions in the demoninators of the bar-arguments.
if type(newinp, `+`) then 
 map(proc(x)
  if has(x, bar) then
   word:=[op(op(selectfun(x, bar)))]: 
  else word:=[1]:
  end if:
  if not(word=[1]) then 
  for j from 1 to nops(word) do
    NewArgFunction:=denom(word[j]):
    NewArg:=ReplaceArgument(factorM(subs(DomainReps, subs(repsbackold, NewArgFunction))), repsback, reps,  numer(word[j]), 0, []):
    if not(has(ArgReps, word[j])) then 
     ArgReps:=[op(ArgReps), word[j]=NewArg]:
    end if:
   end do:
  end if:
  return x:
 end proc, newinp):
else
 if has(newinp, bar) then
  word:=[op(op(selectfun(newinp, bar)))]: 
 else word:=[1]:
 end if:
 if not(word=[1]) then 
  for j from 1 to nops(word) do
   if not(has(ArgFunctions, word[j])) then
    NewArgFunction:=denom(word[j]):
    NewArg:=ReplaceArgument(factorM(subs(DomainReps, subs(repsbackold, NewArgFunction))), repsback, reps, numer(word[j]), []):
    if not(has(ArgReps, word[j])) then 
     ArgReps:=[op(ArgReps), word[j]=NewArg]:
    end if:
   end if: 
  end do:
 end if:
end if:
if type(newinp, `+`) then 
 output:=map(proc(x)
  pref:=normal(eval(x, bar=1)):
  if has(x, bar) then
   word:=[op(op(selectfun(x, bar)))]: 
  else word:=[1]:
  end if:  
  if nargs>5 then 
   if args[6]=true then 
    newPref:=GenPref*subs(reps, subs(repsbackold, pref)):
   else
    newPref:=GenPref*subs(reps, normalM(subs(DomainReps,subs(repsbackold, pref)))):
   end if:
   else
   newPref:=GenPref*subs(reps, normalM(subs(DomainReps,subs(repsbackold, pref)))): 
  end if:
  newBar:=bar(op(subs(ArgReps, word))):
  output:=newPref*newBar:
 end proc, newinp):
else
 pref:=normal(eval(newinp, bar=1)):
 if has(newinp, bar) then
  word:=[op(op(selectfun(newinp, bar)))]: 
 else word:=[1]:
 end if: 
if nargs>5 then 
 if args[6]=true then 
 newPref:=GenPref*subs(reps, subs(repsbackold, pref)):
 else
  newPref:=GenPref*subs(reps, normalM(subs(DomainReps,subs(repsbackold, pref)))):
 end if:
 else
 newPref:=GenPref*subs(reps, normalM(subs(DomainReps,subs(repsbackold, pref)))):
end if:
 newBar:=bar(op(subs(ArgReps, word))):
 output:=newPref*newBar:
end if:
return eval(output, reps):
end proc:






normalM:=proc(inp)
return normal(inp):
end proc:
factorM:=proc(inp)
return factor(inp)
end proc:



TransformDomainOnly:=proc(inp, domaintransf)
local i, j, reps, repsback, ArgFunctions, ArgReps, NewArgFunction, NewArg, newTerm, GenPref, DomainReps, outp:
ArgReps:=[]:
GenPref:=1:
DomainReps:=[]:
# Changing the domain of integration for all variables in domaintransf:
for i from 1 to nops(domaintransf) do
 GenPref:=GenPref * 1/(domaintransf[i]-1)^2:
 DomainReps:=[op(DomainReps), domaintransf[i] = domaintransf[i]/(1-domaintransf[i])]:
end do:
# We collect all functions in the demoninators of the bar-arguments.
map(proc(x)
 if not(x=[1]) then 
  for j from 1 to nops(x) do
   NewArgFunction:=denom(x[j]):
   NewArg:=ReplaceArgument(NewArgFunction, [1=1], DomainReps, numer(x[j]),0,[]):
   if not(has(ArgReps, x[j])) then 
    ArgReps:=[op(ArgReps), x[j]=NewArg]:
   end if:
  end do:
 end if:
end proc, [indices(inp,'nolist')]):
# Application of the replacements:
outp:=table():
for i in indices(inp,'nolist') do
 newTerm:=normalM(GenPref*subs(DomainReps,inp[i]))*normal(bar(op(subs(ArgReps, i)))):
 BarToTable(newTerm, outp):
end do:
return outp:
end proc:




TransformTable:=proc(inp, repsbackold, polys, va, newvar, FeynPar, back)
local i, j, newinp, output, reps, repsback, ArgFunctions, BarLists, ArgReps, NewArgFunction, NewArg, newPref, newBar, GenPref, DomainReps, word, pref, newTerm, outp, Jacobian:
ArgReps:=[]:
output:=0:
GenPref:=1:
DomainReps:=[]:
# Deriving the main replacements from the given polynomials:
if back=true then 
 repsback:=NewCubicalReplacements(polys, va, FeynPar, newvar, false);
 reps:=NewCubicalReplacements(polys, va, FeynPar, newvar, true);
else
 reps:=NewCubicalReplacements(polys, va, FeynPar, newvar, false);
 repsback:=NewCubicalReplacements(polys, va, FeynPar, newvar, true);
end if:
# Deriving the Jacobian:
if back then 
 Jacobian:=1:
else
 Jacobian:=NewCubicalReplacements(polys, va, FeynPar, newvar, true, true):
end if:
# We collect all functions in the demoninators of the bar-arguments.
map(proc(x)
 if not(x=[1]) then 
  for j from 1 to nops(x) do
   NewArgFunction:=denom(x[j]):
   NewArg:=ReplaceArgument(NewArgFunction, [1=1], reps, numer(x[j]), 0, FeynPar):
   if not(has(ArgReps, x[j])) then 
    ArgReps:=[op(ArgReps), x[j]=NewArg]:
   end if:
  end do:
 end if:
end proc, [indices(inp,'nolist')]):
# Application of the replacements:
outp:=table():
for i in indices(inp,'nolist') do
 newTerm:=normal(Jacobian*subs(reps,inp[i])*bar(op(subs(ArgReps, i)))):
 BarToTable(newTerm, outp):
end do:
return outp:
end proc:








# The following procedure computes one integration over a Feynman parameter intvariable.
# The other Arguments: integr is the integrand in Feynman parameters or Feynman and cubical parameters.
# repsback is a set of rules to replace cubical variables of the previous step back to Feynman parameters.
# cubicalva is a symbol for the new cubical variables.
# howmuchoutput determines the output mode:
# howmuchoutput=1: only the result of the integration,
# howmuchoutput=2: the result and the new replacement rules back to Feynman parameters,
# howmuchoutput=3: the result, the rules and the result after replacing back to Feynman parameters

FeynmanIntegrationStep:=proc(integr, repsback, intvariable, NewRemainingFeynPar, cubicalva, howmuchoutput, changedomain)
global MPLStoredLimits, CC4, CC4repsback, CC4polylist, CorrTerm, UncorrzetaCoeff, IntegralResultCubical, MPLSymbForms, ResX:
global MPL_CoefflnZeroList, IntC3, Ergebnis3, IntC8, Ergebnis8, IntC2, Ergebnis2:
local i, FoundPoly, IntegrandCubical, Newrepsback, ResultFeynmanPar, SingularTerm, Newn, domainset, CorrectedRes, newintegr, domchangedrepsback, FindPolyOutp, poly, newintegrbar, ResultFeynmanParTable:
MPL_CoefflnZeroList:=[]:
MPLSymbForms:=[]:
# Check that input is a table or transform it to a table:
if type(integr, table) then 
 newintegrbar:=PrepFeynInt(TableToBar(integr), [intvariable,op(NewRemainingFeynPar)]):
else
 newintegrbar:=PrepFeynInt(integr, [intvariable,op(NewRemainingFeynPar)]):
end if:
newintegr:=table():
MPLSymbForms:=newintegrbar[2]:
BarToTable(newintegrbar[1], newintegr):
FindPolyOutp:=FindPolyTable(newintegr, [1=1], intvariable, true):
FoundPoly:=FindPolyOutp[1]:
if nops(FoundPoly)<2 then 
 Newn:=2:
 MPLInitialize(cubicalva, 1, 2):
else
 Newn:=nops(FoundPoly):
 MPLInitialize(cubicalva, Newn-1, 2):
end if:
IntegrandCubical:=TransformSymbolic(FindPolyOutp[3], FoundPoly, intvariable, cubicalva, FindPolyOutp[2], NewRemainingFeynPar, false):
IntegralResultCubical:=table():
MPLintTable(cubicalva[Newn], IntegrandCubical, IntegralResultCubical):
IntegralResultCubical:=SimplifyTable(IntegralResultCubical):
# Different output modes:
if howmuchoutput=1 then 
 return IntegralResultCubical:
elif howmuchoutput=2 then 
 Newrepsback:=NewCubicalReplacements(FoundPoly, intvariable, NewRemainingFeynPar, cubicalva, true):
 return [IntegralResultCubical, Newrepsback]:
elif howmuchoutput=3 then 
 Newrepsback:=NewCubicalReplacements(FoundPoly, intvariable, NewRemainingFeynPar, cubicalva, true):
 CorrectedRes:=NewComputeCorrection(IntegralResultCubical, NewRemainingFeynPar, Newrepsback):
 ResultFeynmanParTable:=SimplifyTable(TransformTable(CorrectedRes, repsback, FoundPoly, intvariable, cubicalva,  NewRemainingFeynPar, true)):
 ResultFeynmanPar:=eval(subs(base=bar,subs(MPLSymbForms,Reshuffle(eval(TableToBar(ResultFeynmanParTable)))))):
 ResultFeynmanParTable:=table():
 BarToTable(expand(ResultFeynmanPar),ResultFeynmanParTable):
 CorrTerm[intvariable]:=normal(-TableToBar(TransformTable(IntegralResultCubical, repsback, FoundPoly, intvariable, cubicalva, NewRemainingFeynPar, true))+ ResultFeynmanPar):
 UncorrzetaCoeff[intvariable]:=coeff(TableToBar(TransformTable(IntegralResultCubical, repsback, FoundPoly, intvariable, cubicalva, NewRemainingFeynPar, true)),zeta(2)):
 return [IntegralResultCubical, Newrepsback, SimplifyTable(ResultFeynmanParTable), CorrectedRes]:
end if:
end proc:









# The following procedure integrates out a given sequence of parameters (FeynParameters), doing the intermediate
# changes to cubical coordinates. integr is the integrand, CubicalParameters is a list of letters to be used for the 
# cubical coordinates, and with howmuchoutput>1 the procedure shows intermediate results.

MPLFeynmanIntegrate:=proc(integr, FeynParameters, AllFeynParameters)
global IntermediateResults:
local i, j, NewIntegrand, OutpIntStep, CubicalVar, Newrepsback, RemainingFeynPar, NewRemainingFeynPar, numberofintegrations, CubicalParameters, howmuchoutput, changedomain:
# Allowing for additional arguments changing some default conditions:
if nargs>3 then
 CubicalParameters:=args[4]:
 if nargs>4 then
  howmuchoutput:=args[5]:
  if nargs>5 then
   changedomain:=args[6]:
  else
   changedomain:=false:
  end if: 
 else
  howmuchoutput:=1:
  changedomain:=false:
 end if:
else
 CubicalParameters:=[]:
 howmuchoutput:=1:
 changedomain:=false:
end if:

# Create sufficiently many symbols for cubical variables:
CubicalVar:=CubicalParameters:
if nops(CubicalParameters)<nops(FeynParameters) then
 for i from nops(CubicalParameters)+1 to nops(FeynParameters) do
  if type(i,odd) then
   CubicalVar:=[op(CubicalVar), cubicA]:
  else
   CubicalVar:=[op(CubicalVar), cubicB]:
  end if:
 end do:
end if: 
for i from 1 to nops(CubicalVar) do
 defform(CubicalVar[i]=0):
end do:
# Integration procedure:
NewIntegrand:=integr:
Newrepsback:=[1=1]:
RemainingFeynPar:=AllFeynParameters:
if nargs>6 then 
 if args[7]=true then 
  numberofintegrations:=nops(FeynParameters)-1:
 else
  numberofintegrations:=nops(FeynParameters):
 end if:
 else
 numberofintegrations:=nops(FeynParameters):
end if:
for i from 1 to numberofintegrations do
 # Determine, which Feynman parameters are still not integrated out:
 if (nops(RemainingFeynPar)=1 or nops(RemainingFeynPar)=0) then 
  NewRemainingFeynPar:=[]:
 else 
  NewRemainingFeynPar:=[]:
  for j from 2 to nops(RemainingFeynPar) do
   NewRemainingFeynPar:=[op(NewRemainingFeynPar), RemainingFeynPar[j]]:
  end do:
 end if:
 RemainingFeynPar:=NewRemainingFeynPar:
 if howmuchoutput>-1 then
  printf("%s\n",cat("Integration over ",convert(FeynParameters[i],string),".")):
 end if:
 OutpIntStep:=FeynmanIntegrationStep(NewIntegrand, Newrepsback, FeynParameters[i], NewRemainingFeynPar, CubicalVar[i], 3, changedomain):
 NewIntegrand:= OutpIntStep[3]:
 Newrepsback:=OutpIntStep[2]:
 
 IntermediateResults[op(FeynParameters[1..i])]:=TableToBar(NewIntegrand):
 
 if howmuchoutput>1 then
 # printf("%s\n","In cubical coordinates: "):
 # print(TableToBar(OutpIntStep[1])):
 end if:
 if howmuchoutput>2 then
  printf("%s\n","Changes of Variables: "):
  print(normal(OutpIntStep[2])):
  printf("%s\n","Only in Feynman parameters: "):
 ##### print(TableToBar(NewIntegrand)):
 end if:
end do:
if howmuchoutput>1 then
  printf("%s\n","Last result:"):
end if:
if nargs>6 then 
 if args[7]=true then
 return FeynParLimit(TableToBar(NewIntegrand), FeynParameters[nops(FeynParameters)], 1);
 else
  return RewriteFeyn(TableToBar(OutpIntStep[3]), NewRemainingFeynPar, []):
 end if:
 else
 return RewriteFeyn(TableToBar(OutpIntStep[3]), NewRemainingFeynPar, []):
end if:
end proc:





# The following procedure transforms an integrand in Feynman parameters to cubical coordinates and takes a limit with respect to one coordinate.
# va is the Feynman parameter and u is the value (0, 1 or infinity) where it shall be evaluated.

FeynParLimit:=proc(inp, va, u)
local outp, FoundPoly, PolyList, IntegrandCubical, domainset, auxva, Newn:
FoundPoly:=FindPoly(inp, [1=1], [], va, true)[1]:
PolyList:=[[FoundPoly], [va]]:
if nops(FoundPoly)=0 then 
 Newn:=1:
else
 Newn:=nops(FoundPoly):
end if:
IntegrandCubical:=SimplifyBarExpression(Transform(inp, [1=1], PolyList, auxva, [])):
MPLInitialize(auxva, Newn, false):
outp:=MPLLimit(IntegrandCubical, auxva[Newn+1], u):
return SimplifyBarExpression(Transform(outp, [1=1], PolyList, auxva, [], true)):
end proc:














# The following procedure derives the replacement rules for variables such that
# limits at infinity can be computed from taking limits at one.

CreateInfReps:=proc(oldva, newva, varN)
local i, j, Reps, NewProd, NewTerm:
Reps:=[]:
for i from 1 to varN do
 if i=varN then 
  Reps:=[op(Reps), oldva[varN]=newva[varN]/(newva[varN]-1)]:
 else
  NewProd:=1:
  for j from i to varN do
   NewProd:=NewProd*newva[j]:
  end do:
  Reps:=[op(Reps), oldva[i]=(newva[i]-NewProd)/(1-NewProd)]:
 end if:
end do:
return Reps:
end proc:





# In order to allow the procedure MPLLimit to take limits at infinity,
# the following procedure changes variables carefully, such that limits at infinity
# can be computed from limits at one.

VarChangeInfinity:=proc(inp, va, varN)
local i, j, NewArg, ArgReps, BarLists, auxva, DiffFormReps:
DiffFormReps:=CreateInfReps(va, auxva, varN):
BarLists:=normal(BarToListsCollected(inp)):
ArgReps:=[]:
NewArg:=0:
# Create a list of replacements, to replace the differential forms:
for i from 1 to nops(BarLists[1]) do 
 for j from 1 to nops(BarLists[2][i]) do
  NewArg:=ReplaceArgument(denom(BarLists[2][i][j]), [1=1], DiffFormReps, numer(BarLists[2][i][j]), 0, []):
  ArgReps:=[op(ArgReps), BarLists[2][i][j]=NewArg]:
 end do:
end do:
return normal(subs(auxva=va,subs(va=auxva,subs(DiffFormReps,eval(subs(ArgReps,inp)))))):
end proc:




# The following procedure uses the replacement-rules between Feynman parameters and cubical coordinates,
# to derive, which limits in cubical coordinates correspond to the limit, of all Feynman parameters going to zero.
# The order in which the Feynman parameters go to zero is given. The order in which the limits w.r.t. cubical coordinates has
# to be computed is derived by GetLimitOrder.

GetListOfLimits:=proc(FeynPar, repsback)
local i, j, LimitAtZero, ListOfLimits:
ListOfLimits:=[]:
for i from 1 to nops(repsback) do
 LimitAtZero:=op(2,repsback[i]):
 for j from 1 to nops(FeynPar) do
  LimitAtZero:=eval(limit(LimitAtZero,FeynPar[j]=0)):
 end do:
 if LimitAtZero=undefined then 
  ListOfLimits:=[op(ListOfLimits),op(1,repsback[i])=infinity]:
  print("A limit at infinity appears."):
  print(op(1,repsback[i])=infinity):
 elif (not(i=nops(repsback)) and (not(LimitAtZero=0 or LimitAtZero=1 or LimitAtZero=undefined))) then
  print("Warning: In one of the changes of variables, a limit at a value different from 0, 1 or infinity appears. Limit disregarded."):
  print(LimitAtZero):
  return repsback:
 else
  ListOfLimits:=[op(ListOfLimits),op(1,repsback[i])=LimitAtZero]:
 end if:
end do:
return GetLimitOrder(FeynPar, repsback, ListOfLimits):
end proc:




#The following procedure derives the order, in which limits have to be taken w.r.t. cubical coordinates. 


GetLimitOrder:=proc(FeynPar, repsbackin, ListOfLimitsin)
local i, j, outp, bigger, smaller, positions, preloutp, repsback, ListOfLimits, z1, z2:
# Ignore the last element of repsback and ListOfLimits, because it 
# corresponds to the integration variable:
repsback:=repsbackin[1..nops(repsbackin)-1]:
ListOfLimits:=ListOfLimitsin[1..nops(ListOfLimitsin)-1]:
for i from 1 to nops(repsback) do
 bigger[i]:={}:
 smaller[i]:={}:
end do:
for i from 1 to nops(repsback) do
 for j from i+1 to nops(repsback) do
  z1:=normal(op(2,repsback[i])-op(2,ListOfLimits[i])):
  z2:=normal(op(2,repsback[j])-op(2,ListOfLimits[j])):
 if FirstBiggerSecondSeries(z1,z2,FeynPar, FeynPar) then 
   smaller[i]:={op(smaller[i]),j}:
   bigger[j]:={op(bigger[j]), i}:
  else
   smaller[j]:={op(smaller[j]),i}:
   bigger[i]:={op(bigger[i]), j}:
  end if:
 end do:
end do:
positions:=[]:
for i from 1 to nops(repsback) do
 positions:=[op(positions), nops(smaller[i])]:
end do: 
return SortDoubleList(ListOfLimits, positions):
end proc:












MPLMultipleLimit:=proc(inp, ListLimits)
local j, va, vasymbol, newlimit, newterm, listnumbers:
listnumbers:=[]:
for j from 1 to nops(ListLimits) do
 listnumbers:=[op(listnumbers),op(1,op(1,ListLimits[j]))]:
end do:
newterm:=inp:
vasymbol:=op(0,op(1,ListLimits[1])):
MPLInitialize(vasymbol, max(op(listnumbers))-1, false):
for j from 1 to nops(ListLimits) do 
 va:=op(1, ListLimits[j]):
 newlimit:=op(2, ListLimits[j]):
 newterm:=eval(MPLLimit(newterm, va, newlimit)):
end do:
return newterm:
end proc:





LimitsOfBar:=proc(inp, ListLimits)
local i, j, k, BarArray, ArrayOfBarTerms, NewArrayOfBarTerms, outp, LimitTerm, va, vasymbol, newlimit, TensList, MultLimit:
outp:=0:
if ListLimits=[] then 
 return inp:
end if:
BarArray:=BarToArrayCollected(inp):
# Write the BarArray as an actual Array of bar-terms:
ArrayOfBarTerms:=Array([]):
for i from 1 to ArrayNumElems(BarArray(1)) do
 ArrayOfBarTerms(ArrayNumElems(ArrayOfBarTerms)+1):=bar(op(BarArray(2)(i))):
end do:
# Determine cubical variable:
va:=op(1, ListLimits[1]):
vasymbol:=op(0,va):
NewArrayOfBarTerms:=Array([]):
for i from 1 to ArrayNumElems(BarArray(1)) do
 if (ArrayOfBarTerms(i)=1 or ArrayOfBarTerms(i)=bar(1)) then 
  LimitTerm:=1:
 elif not(has(ArrayOfBarTerms(i), vasymbol)) then 
  LimitTerm:=ArrayOfBarTerms(i):
 else
  LimitTerm:=0:
  TensList:=TensToLists(Coproduct(ArrayOfBarTerms(i))):
  for k from 1 to nops(TensList[1]) do
   if not(has(TensList[3][k], vasymbol)) then 
    if TensList[3][k]=ONE then 
     MultLimit:=1:
    else
     MultLimit:=0:
    end if:
   else
    MultLimit:=MPLMultipleLimit(TensList[3][k], ListLimits, vasymbol):
   end if:
   if has(MultLimit, bar) then 
    LimitTerm:=LimitTerm +  TensList[1][k]*subs(ONE=1, MPLShuffleProduct(TensList[2][k], MultLimit)):
   else
    LimitTerm:=LimitTerm + TensList[1][k]*subs(ONE=1, TensList[2][k]*MultLimit):
   end if:
  end do:
 end if:
 NewArrayOfBarTerms(ArrayNumElems(NewArrayOfBarTerms)+1):=LimitTerm:
end do:
for i from 1 to ArrayNumElems(BarArray(1)) do
 outp:=outp+BarArray(1)(i)*NewArrayOfBarTerms(i):
end do:
return outp:
end proc:




LimitsOfBarTable:=proc(inp, ListLimits)
local i, j, k, BarArray, ArrayOfBarTerms, NewArrayOfBarTerms, outp, LimitTerm, va, vasymbol, newlimit, TensList, MultLimit:
outp:=table():
if ListLimits=[] then 
 return inp:
end if:
# Determine cubical variable:
va:=op(1, ListLimits[1]):
vasymbol:=op(0,va):
for i in indices(inp,'nolist') do
 if (i=1 or i=[1]) then 
  LimitTerm:=1:
 elif not(has(i, vasymbol)) then 
  LimitTerm:=bar(op(i)):
 else
 LimitTerm:=0:
  TensList:=TensToLists(Coproduct(bar(op(i)))):
  for k from 1 to nops(TensList[1]) do
   if not(has(TensList[3][k], vasymbol)) then 
    if TensList[3][k]=ONE then 
     MultLimit:=1:
    else
     MultLimit:=0:
    end if:
   else
    MultLimit:=MPLMultipleLimit(TensList[3][k], ListLimits, vasymbol):
   end if:
   if has(MultLimit, bar) then 
    LimitTerm:=LimitTerm +  TensList[1][k]*subs(ONE=1, MPLShuffleProduct(TensList[2][k], MultLimit)):
   else
    LimitTerm:=LimitTerm + TensList[1][k]*subs(ONE=1, TensList[2][k]*MultLimit):
   end if:
  end do:
 end if:
 BarToTable(inp[i]*LimitTerm, outp):
end do:
return outp:
end proc:





SortDoubleList:=proc(ListSymbols, ListValues)
local i, j, ListValuesSorted, outp:
outp:=[]:
ListValuesSorted:=sort(ListValues):
for i from 1 to nops(ListValuesSorted) do
 for j from 1 to nops(ListSymbols) do
  if (not(member(ListSymbols[j],outp)) and ListValues[j]=ListValuesSorted[i]) then
   outp:=[op(outp), ListSymbols[j]]:
  end if:
 end do:
end do:
return outp:
end proc:









# When changing back from cubical coordinates to Feynman parameters, certain cases of coordinate changes
# require the addition of certain limits due to the normalization of our functions.
# The following procedure computes these additional terms.

ComputeCorrection:=proc(inp, FeynPar, repsback)
global auxva:
local i, j, InfReps, cubicalsymb, ListOfLimits, ChangedRepsback:
if FeynPar=[] then
 return inp:
end if:
cubicalsymb:=op(0, op(1, repsback[1])):
InfReps:=CreateInfReps(auxva, cubicalsymb, nops(repsback)-1):
ChangedRepsback:=normal(subs(repsback, InfReps)):
ListOfLimits:=subs(auxva=cubicalsymb, GetListOfLimits(FeynPar, ChangedRepsback)):
return LimitsOfBarTable(inp, ListOfLimits):
end proc:



NewComputeCorrection:=proc(inp, FeynPar, repsback)
global auxva:
local i, j, InfReps, cubicalsymb, ListOfLimits, ChangedRepsback:
if FeynPar=[] then
 return inp:
end if:
cubicalsymb:=op(0, op(1, repsback[1])):
ListOfLimits:=subs(auxva=cubicalsymb, GetListOfLimits(FeynPar, repsback)):
return LimitsOfBarTable(inp, ListOfLimits):
end proc:










ChangeDomain:=proc(inp, listva)
local i, oldinp, newinp:
oldinp:=inp:
newinp:=inp:
for i from 1 to nops(listva) do
 if has(oldinp, listva[i]) then 
  newinp:=subs(listva[i]=listva[i]/(1-listva[i]), oldinp)/(listva[i]-1)^2:
  oldinp:=newinp:
 end if:
end do:
return normal(newinp):
end proc:



# For a given set of linear polynomials and a variable, the following procedure derives a list of triples:
# [polynomial, coefficient of va, zero w.r.t. va]

GetPolytripples:=proc(polys, va)
local i, outp:
outp:=[]:
for i from 1 to nops(polys) do
 outp:=[op(outp), [polys[i], normal(coeff(polys[i],va)), normal(solve(polys[i]=0,va))]]:
end do:
return outp:
end proc:




# The following procedure determines whether one rational function is bigger than another
# close to a tangential basepoint, which is given by Feynman parameters going to zero in a given ordering.


FirstBiggerSecond:=proc(zero1, zero2, FeynPar, AllFeynPar)
local i, j, quotient, newlimit, outp, series1, series2, auxe, auxFeynPar, counter, ldeg, series1list, series2list, coeff1, coeff2,zero1aux, zero2aux, n:
# I introduce a set of auxiliary Feynman parameters on which I can introduce assumptions without later consequences.
if zero1=zero2 then return "undecided":
end if:
zero1aux:=zero1:
zero2aux:=zero2:
n:=nops(AllFeynPar):
for i from 1 to nops(FeynPar) do
 zero1aux:=subs(FeynPar[i]=0,normal(zero1aux)):
 zero2aux:=subs(FeynPar[i]=0,normal(zero2aux)):
 if zero1aux=0 then return false:
 elif zero2aux=0 then return true:
 end if:
end do:
return true:
end proc:




FirstBiggerSecondNumeric:=proc(zero1, zero2, FeynPar, AllFeynPar)
local i, j, quotient, newlimit, outp, series1, series2, auxe, auxFeynPar, counter, ldeg, series1list, series2list, coeff1, coeff2,zero1aux, zero2aux, n:
# I introduce a set of auxiliary Feynman parameters on which I can introduce assumptions without later consequences.
if zero1=zero2 then return "undecided":
end if:
zero1aux:=zero1:
zero2aux:=zero2:
n:=nops(AllFeynPar):
for i from 1 to nops(FeynPar) do
 zero1aux:=subs(FeynPar[i]=0.1^((n+1-i)),zero1aux):
 zero2aux:=subs(FeynPar[i]=0.1^((n+1-i)),zero2aux):
end do:
return is(abs(zero1aux)>abs(zero2aux)):
end proc:







FirstBiggerSecondOld2:=proc(zero1, zero2, FeynPar, AllFeynPar)
local i, j, quotient, newlimit, outp, series1, series2, auxe, auxFeynPar, counter, ldeg, series1list, series2list, coeff1, coeff2,zero1aux, zero2aux:
# I introduce a set of auxiliary Feynman parameters on which I can introduce assumptions without later consequences.
if zero1=zero2 then return "undecided":
end if:
auxFeynPar:=[]:
for i from 1 to nops(AllFeynPar) do
 additionally(auxe[op(1,AllFeynPar[i])]>0,auxe[op(1,AllFeynPar[i])]<1):
 if i<nops(AllFeynPar) then 
  additionally(auxe[op(1,AllFeynPar[i])]<auxe[op(1,AllFeynPar[i+1])]):
 end if:
 auxFeynPar:=[op(auxFeynPar),auxe[op(1,AllFeynPar[i])]]:
 zero1aux:=normal(subs(e=auxe, zero1)):
 zero2aux:=normal(subs(e=auxe, zero2)):
end do:
outp:=is(abs(zero1aux)>abs(zero2aux)):
for i from 1 to nops(AllFeynPar) do
 auxe[op(1,AllFeynPar[i])] := 'auxe[op(1,AllFeynPar[i])]': 
end do:
return outp:
end proc:





FirstBiggerSecondOld1:=proc(zero1, zero2, FeynPar, AllFeynPar)
local i, j, quotient, newlimit, outp, series1, series2, auxe, auxFeynPar, counter, ldeg, series1list, series2list, coeff1, coeff2:
# I introduce a set of auxiliary Feynman parameters on which I can introduce assumptions without later consequences.
if zero1=zero2 then return "undecided":
end if:
quotient:=normal(zero1/zero2):
auxFeynPar:=[]:
for i from 1 to nops(AllFeynPar) do
 assume(auxe[op(1,AllFeynPar[i])]>0,auxe[op(1,AllFeynPar[i])]<1):
 auxFeynPar:=[op(auxFeynPar),auxe[op(1,AllFeynPar[i])]]:
 quotient:=normal(subs(AllFeynPar[i]=auxe[op(1,AllFeynPar[i])], quotient));
end do:
for i from 1 to nops(FeynPar) do
 newlimit:=eval(limit(quotient, auxFeynPar[i]=0,right)):
 quotient:=newlimit:
 if newlimit=infinity or newlimit=undefined or newlimit=-infinity then
  return true:
 elif newlimit=0 then 
  return false:
# If the limit of the quotient is constant other than 0 or +/-infinity, we series-expand
# and compare the lowdegrees. If they are equal, we compare each coefficient.
# If the first six coefficients don't give an answer, we print a warning and assume that 
# zero1>zero2.
 elif not(has(newlimit, {op(auxFeynPar)})) then 
  series1:=convert(series(zero1,FeynPar[i],6),polynom):
  series2:=convert(series(zero2,FeynPar[i],6),polynom):
 if ldegree(series1)<ldegree(series2) then
   return false:
  elif ldegree(series1)>ldegree(series2) then
   return true:
  elif ldegree(series1)=ldegree(series2) then
   ldeg:=ldegree(series1, va):
   for j from 1 to 6 do 
    coeff1:=normal(coeff(series1,FeynPar[i],ldeg-1+j)):
    coeff2:=normal(coeff(series2,FeynPar[i],ldeg-1+j)):
  if coeff1=0 and not(coeff2=0) then 
     return false:
    elif not(coeff1=0) and coeff2=0 then 
     return true:
    elif not(coeff1=0) and not(coeff2=0) then 
   outp:=FirstBiggerSecond(coeff1, coeff2, FeynPar[2..nops(FeynPar)], AllFeynPar):
     if outp=true or outp=false then
      return outp:
     end if:  
    end if:
   end do:
  end if:
 end if:
end do:
return "undecided":
end proc:




SignAtTangentialBasepoint:=proc(inp, FeynPar)
local i, lowestcoeff, newterm:
newterm:=inp:
for i from 1 to nops(FeynPar) do
 lowestcoeff:=tcoeff(numer(newterm)/denom(newterm), FeynPar[i]):
 if lowestcoeff=0 then
  error "It was not possible to find a unique order at a tangential basepoint. Possibly, two of the polynomials in a given set are equal.": 
 elif (not(has(lowestcoeff,FeynPar)) and type(lowestcoeff, `numeric`)) then
  return sign(lowestcoeff):
 elif (not(has(lowestcoeff,FeynPar)) and not(type(lowestcoeff, `numeric`))) then
  error "Not all parameters are sent to their limit.":
 else
  newterm:=lowestcoeff:
 end if:
end do:
end proc:




FirstBiggerSecondSeries:=proc(zero1, zero2, FeynPar)
local i, j, quotient, newlimit, zerosquotient:
zerosquotient:=normal(zero1/zero2-1):
if SignAtTangentialBasepoint(zerosquotient, FeynPar)>0 then 
 return true:
else
 return false
end if:
end proc:




# With respect to the above greater/smaller at a tangential basepoint the following orders rational functions.
# The preliminary list is ordered such that the smallest (closest to the basepoint) is on the left, then comes the next bigger and so on.
# This first element ist then put to the very right. So we get
# [f[1], f[2], ..., f[n]]
# where f[n]<f[1]<f[2]<...<f[n-2]<f[n-1] w.r.t. being close to the tangential basepoint.



OrderByZeroes:=proc(polytripples, FeynPar)
global z1, z2, FP:
local i, j, outp, bigger, smaller, positions, preloutp:
for i from 1 to nops(polytripples) do
 bigger[i]:={}:
 smaller[i]:={}:
end do:
for i from 1 to nops(polytripples) do
 for j from i+1 to nops(polytripples) do
  z1:=polytripples[i][3]:
  z2:=polytripples[j][3]:
  FP:=FeynPar:
  if FirstBiggerSecondSeries(polytripples[i][3],polytripples[j][3],FeynPar) then 
   smaller[i]:={op(smaller[i]),j}:
   bigger[j]:={op(bigger[j]), i}:
  else
   smaller[j]:={op(smaller[j]),i}:
   bigger[i]:={op(bigger[i]), j}:
  end if:
 end do:
end do:
positions:=[]:
for i from 1 to nops(polytripples) do
 positions:=[op(positions), nops(smaller[i])]:
end do: 
preloutp:=SortDoubleList(polytripples, positions):
outp:=[op(preloutp[2..nops(preloutp)]),preloutp[1]]:
return outp:
end proc:



OrderByZeroesOLD:=proc(polytripples, FeynPar)
global z1, z2, FP:
local i, j, outp, bigger, smaller, positions, preloutp:
for i from 1 to nops(polytripples) do
 bigger[i]:={}:
 smaller[i]:={}:
end do:
for i from 1 to nops(polytripples) do
 for j from i+1 to nops(polytripples) do
  z1:=polytripples[i][3]:
  z2:=polytripples[j][3]:
  FP:=FeynPar:
  if FirstBiggerSecond(polytripples[i][3],polytripples[j][3],FeynPar, FeynPar) then 
   smaller[i]:={op(smaller[i]),j}:
   bigger[j]:={op(bigger[j]), i}:
  else
   smaller[j]:={op(smaller[j]),i}:
   bigger[i]:={op(bigger[i]), j}:
  end if:
 end do:
end do:
positions:=[]:
for i from 1 to nops(polytripples) do
 positions:=[op(positions), nops(smaller[i])]:
end do: 
preloutp:=SortDoubleList(polytripples, positions):
outp:=[op(preloutp[2..nops(preloutp)]),preloutp[1]]:
return outp:
end proc:







NewCubicalReplacements:=proc(polys, va, FeynPar, cubical, back::boolean, jacobian)
local i, j, orderedtripples, outp, auxprod, reps, repsback, n, lastrep:
# If the list of polynomials is empty then return a trivial repalcement
if nops(polys)=0 then 
 if nargs>5 then 
  if args[6]=true then
   return 1:
  end if:
 end if:
 if back then return [cubical[2]=va]:
 else return [va=cubical[2]]:
 end if:
elif nops(polys)=1 then
 orderedtripples:=GetPolytripples(polys, va):
 if nargs>5 then 
  if args[6]=true then
   return -orderedtripples[1][3]/(cubical[2]-1)^2:
  end if:
 end if:
 if back then return [cubical[2]=va/(va-orderedtripples[1][3])]:
 else 
return [orderedtripples[1][1]=orderedtripples[1][2]*orderedtripples[1][3]/(cubical[2]-1),
              -orderedtripples[1][1]=-orderedtripples[1][2]*orderedtripples[1][3]/(cubical[2]-1),
        va=orderedtripples[1][3]*cubical[2]/(cubical[2]-1)]:
 end if:
else
 # From the given list of non-ordered polynomials I compute the ordered list of tripples:
 # [polynomial, coefficient of va, zero w.r.t.va].
 # In this ordering from the left to right the first is the one with the smallest zero (w.r.t. tangential basepoint).
 orderedtripples:=OrderByZeroes(GetPolytripples(polys, va),FeynPar):
 n:=nops(orderedtripples):
 if nargs>5 then 
  if args[6]=true then
   return -orderedtripples[n][3]/(cubical[n]-1)^2:
  end if:
 end if:
 reps:=[]:
 repsback:=[]:
 for i from 1 to n-1 do
  auxprod:=1:
  for j from i to n do
   auxprod:=auxprod*cubical[j]:
  end do:
  reps:=[op(reps), orderedtripples[i][1] = orderedtripples[i][2]*(-1)*orderedtripples[i][3]*(auxprod-1)/(cubical[n]-1),
                   -orderedtripples[i][1] = -orderedtripples[i][2]*(-1)*orderedtripples[i][3]*(auxprod-1)/(cubical[n]-1)]:
  if i=n-1 then 
   repsback:=[op(repsback), normal(cubical[n-1] = 1-orderedtripples[n][3]/orderedtripples[n-1][3])]:
  else
   repsback:=[op(repsback), normal(cubical[i] = (1-orderedtripples[n][3]/orderedtripples[i][3])/(1-orderedtripples[n][3] /orderedtripples[i+1][3]))]:
  end if:
 end do:
 reps:=[op(reps), orderedtripples[n][1] = orderedtripples[n][2]*orderedtripples[n][3]/(cubical[n]-1),
                  -orderedtripples[n][1] = -orderedtripples[n][2]*orderedtripples[n][3]/(cubical[n]-1),
                  va=orderedtripples[n][3]*cubical[n]/(cubical[n]-1)]:
 repsback:=[op(repsback), normal(cubical[n]=va/(va-orderedtripples[n][3]))]:
 if back then return repsback:
 else return reps:
 end if:
end if:
end proc:





CheckBarSigns:=proc(barlist, elimvar)
global probbar:
local i, j, newbarlist1, newbarlist2, bararg, Signfact, argfact:
newbarlist1:=[]:
newbarlist2:=[]:
for i from 1 to nops(barlist[1]) do
 Signfact:=1:
 bararg:=[]:
 for j from 1 to nops(barlist[2][i]) do
  #argfact:=factors(barlist[2][i][j]):
  if numer(barlist[2][i][j]) = -eval(subs(elimvar,d(denom(barlist[2][i][j])))) then
   #probbar:=[op(probbar), ListsToBar(barlist)]:
   Signfact:=Signfact*(-1):
   bararg:=[op(bararg), normal(-barlist[2][i][j])]:
  else
   bararg:=[op(bararg), barlist[2][i][j]]:
  end if: 
 end do:
 newbarlist1:=[op(newbarlist1), Signfact*barlist[1][i]]:
 newbarlist2:=[op(newbarlist2), bararg]:
end do:
return [newbarlist1, newbarlist2]:
end proc:






   





####################################################################
####################################################################
#
#   POLYNOMIAL REDUCTION AND CHECK OF ORDER
#
####################################################################
####################################################################





# From a given list of polynomials, the following procedure cancels all monomials.

ExtractPolynomials:=proc(polys)
local i, j, pfact, outp:
outp:=[]:
for i from 1 to nops(polys) do
 pfact:=op(2,factors(polys[i])):
 for j from 1 to nops(pfact) do
  if not(type(op(1,pfact[j]),`monomial`)) and not(has(outp, op(1,pfact[j]))) then 
   outp:=[op(outp), op(1,pfact[j])]:
  end if:
 end do:
end do:
return outp:
end proc:


# If all polynomials in a given list are linear in a given variable, 
# the following procedures returns true and otherwise false.

CheckLinearity:=proc(polys, var)
local i, islinear:
islinear:=true:
for i in [indices(polys,'nolist')] do
 if degree(polys[i],var)>1 then 
  islinear:=false:
 end if:
end do:
return islinear:
end proc:



# For a given list of compatibilities, the following procedure returns true, if a given pair is
# compatible, and false otherwise.

CheckCompatibility:=proc(prevc, pair)
local A1, A2, B1, B2, prevcomps:
prevcomps:=[op(prevc),{0,infty}]:
A1:=op(1,op(1,pair)):
 A2:=op(2,op(1,pair)):
 B1:=op(1,op(2,pair)):
 B2:=op(2,op(2,pair)):
 if (A1=B1 and (member({A2,B2}, prevcomps) or member({B2,A2}, prevcomps))) 
 or (A1=B2 and (member({A2,B1}, prevcomps) or member({B1,A2}, prevcomps)))
 or (A2=B1 and (member({A1,B2}, prevcomps) or member({B2,A1}, prevcomps)))
 or (A2=B2 and (member({A1,B1}, prevcomps) or member({B1,A1}, prevcomps))) 
 or ((A1=B1 and A2=B2) or (A1=B2 and A2=B1))
 then
  return true:
 else
  return false
 end if:
end proc:




# For a given compatibility graph and a given variable, the following 
# computes the compatibility graph of the next stage, after reduction 
# with respect to this variable.
#
# If the global vatriable COMPATIBILITY_GRAPH is set true, the previous
# compatibility graph plays a role in this computation. Otherwise, the 
# old graph is assumed to be the complete graph, which corresponds 
# to simple Fubini reduction.

CompGraph:=proc(prevCompGraph, var)
global COMPATIBILITY_GRAPH:
local i, j, p, pu, pl, newpolys, newcomps, polys, comps, indexpairs, relindexpairs, poly1, poly2 :
if prevCompGraph=[] then 
 return []:
elif prevCompGraph=NULL then
 return NULL:
end if:
polys:=op(1,prevCompGraph):
comps:=op(2,prevCompGraph):
# An empty graph is returned, if not all given polynomials are linear:
if not(CheckLinearity(polys, var)) then 
 return NULL:
end if: 
p:=table():
for i in [indices(polys,'nolist')] do
 pu[i]:=expand(coeff(polys[i],var)):
 pl[i]:=expand(subs(var=0,polys[i])):
 if pu[i]=0 then 
  if not(type(pl[i],'monomial')) then
   p[{i,infty}]:=pl[i]:
  end if:
 else 
  if not(type(pu[i],'monomial')) then
   p[{i,infty}]:=pu[i]:
  end if:
 end if:
  if not(type(pl[i],'monomial')) then
   p[{i,0}]:=pl[i]:
  end if:
 for j in [indices(polys,'nolist')] do
  if j>i then
   if (member({i,j},comps) or not(COMPATIBILITY_GRAPH)) then
    pu[j]:=coeff(polys[j],var):
    pl[j]:=subs(var=0,polys[j]):
    if not(type(expand(pu[i]*pl[j]-pl[i]*pu[j]),'monomial')) then
     p[{i,j}]:=pu[i]*pl[j]-pl[i]*pu[j]:
    end if:
   end if:
  end if:
 end do:
end do:
# At this stage, the set of all new polynomials p[{n,m}] was created.
# Now the compatibilities are computed from the previous ones.
indexpairs:=choose({indices(p,'nolist')},2):
relindexpairs:=[]:
newcomps:=[]:
if COMPATIBILITY_GRAPH then
 for i from 1 to nops(indexpairs) do
  if CheckCompatibility(comps, indexpairs[i]) then
   newcomps:=[op(newcomps), indexpairs[i]]:
  end if:
 end do:
else
 newcomps:=[]:
end if:
if nops([entries(p,'nolist')])=0 then 
 return []:
end if:
return CondenseGraph([p,newcomps]):
end proc:





# For a given compatibility graph, possibly with the same polynomial
# contained repeatedly, the following procedure returns a compatibility graph where 
# each polynomial appears only once. The corresponding edges of the graph are 
# connected accordingly. 

CondenseGraph:=proc(CG)
global COMPATIBILITY_GRAPH:
local i, j, k,p, polys, indp, counter, newpolys, nummerp, indexl, newp, newindices, polyfact, polyfactlist, repindices, repindicesold, 
repindicesnew, oldcomps, newcomps, relatedfactors, new, old, oldindices:
p:=op(1,CG):
if nops([entries(p,'nolist')])=0 then 
 return CG:
end if:
oldcomps:=op(2,CG):
oldindices:=[indices(p,'nolist')]:
repindicesold:=[]:
for i from 1 to nops(oldindices) do
 repindicesold:=[op(repindicesold),oldindices[i]=old[i]]: 
end do:
oldcomps:=subs(repindicesold,oldcomps):
newindices:=table():
newpolys:=table():
indexl:=table():
counter:=0:
newcomps:=[]:
for i in indices(p,'nolist') do
 # Extract list of irreducible, non-monomial factors:
 polyfact:=op(2,factors(p[i])):
 polyfactlist:=[]:
 for j from 1 to nops(polyfact) do
  if not(type(op(1,polyfact[j]),'monomial')) then
   polyfactlist:=[op(polyfactlist), op(1,polyfact[j])]:
  end if:
 end do:
 relatedfactors:=[]:
 for j from 1 to nops(polyfactlist) do
  newp:=polyfactlist[j]:
  if member(newp,[entries(newpolys,'nolist')],'nummerp') then
   indexl[nummerp]:={op(indexl[nummerp]),subs(repindicesold,i)}:
   relatedfactors:=[op(relatedfactors),nummerp]:
  else
    counter:=counter+1:
    newpolys[counter]:=newp:
    indexl[counter]:={subs(repindicesold,i)}:
    relatedfactors:=[op(relatedfactors),counter]:
    newcomps:=[op(newcomps), {new[counter],0}, {new[counter],infty}]:
  end if:
 end do:
 if nops(relatedfactors)>1 then 
  # Connect factors of the same polynomial between each other:
  for j from 1 to nops(relatedfactors) do
   for k from j+1 to nops(relatedfactors) do
    newcomps:=[op(newcomps),{new[relatedfactors[j]],new[relatedfactors[k]]}]:
   end do:
  end do:
  # Connect with all connections of the parent polynomial:
  for k from 1 to nops([entries(p,'nolist')]) do
   if member({old[k],subs(repindicesold,i)},oldcomps) then
    for j from 1 to nops(relatedfactors) do
     newcomps:=[op(newcomps),{old[k],new[relatedfactors[j]]}]:
    end do:
   end if:
  end do:
 end if:
end do:
repindicesnew:=[]:
for i from 1 to counter do
  repindicesnew:=[op(repindicesnew), new[i]=i]:
end do:
if COMPATIBILITY_GRAPH then
 repindices:=[]:
 for i in [indices(indexl,'nolist')] do
  for j from 1 to nops(indexl[i]) do
   repindices:=[op(repindices),op(j,indexl[i])=new[i]]:
  end do
 end do:
 newcomps:=MakeUnique(subs(repindicesnew,(subs(repindices,([op(newcomps), op(oldcomps)]))))):
 for i in newcomps do
  if nops(i)=1 then 
   newcomps:=subs(i=NULL,newcomps):
  end if:
 end do:
else
 newcomps:=[]:
end if:
return [newpolys, newcomps]:
end proc:





# Out of two given compatibility graphs, the following procedure creates a new one as their
# intersection. This graph consists only of polynomials and compatibilities, which are 
# contained in both of the input graphs.

IntersectCompGraphs:=proc(CG1,CG2)
local i, j, polys1, polys2, positionin2, counter, a, b, auxlist, comps1, comps1c, comps2,comps2c, newpolys, newcomps, repa:
if CG1=[] then 
 return CG2:
elif CG2=[] then
 return CG1:
end if:
polys1:=[entries(op(1,CG1),'nolist')]:
polys2:=[entries(op(1,CG2),'nolist')]:
comps1:=[]:
comps2:=[]:
for i from 1 to nops(op(2,CG1)) do
 comps1:=[op(comps1),{b[op(1,op(i,op(2,CG1)))], b[op(2,op(i,op(2,CG1)))]}]:
end do:
for i from 1 to nops(op(2,CG2)) do
 comps2:=[op(comps2),{b[op(1,op(i,op(2,CG2)))], b[op(2,op(i,op(2,CG2)))]}]:
end do:
counter:=0:
newpolys:=table():
newcomps:=[]:
repa:=[]:
for i from 1 to nops(polys1) do
 if member(polys1[i],polys2,'positionin2') then
  counter:=counter+1:
  newpolys[counter]:=polys1[i]:
  comps1:=subs(b[i]=a[counter],comps1):
  comps2:=subs(b[positionin2]=a[counter],comps2):
  repa:=[op(repa),a[counter]=counter]:
 end if:
end do:
comps1c:=[]:
comps2c:=[]:
for i from 1 to nops(comps1) do 
 if ((has(op(1,comps1[i]),a) or has(op(1,comps1[i]),0) or has(op(1,comps1[i]),infty)) 
 and (has(op(2,comps1[i]),a) or has(op(2,comps1[i]),0) or has(op(2,comps1[i]),infty))) then
  comps1c:=[op(comps1c), comps1[i]]:
 end if:
end do:
for i from 1 to nops(comps2) do 
 if ((has(op(1,comps2[i]),a) or has(op(1,comps2[i]),0) or has(op(1,comps2[i]),infty)) 
 and (has(op(2,comps2[i]),a) or has(op(2,comps2[i]),0) or has(op(2,comps2[i]),infty))) then
  comps2c:=[op(comps2c), comps2[i]]:
 end if:
end do:
newcomps:=subs([b[infty]=infty,b[0]=0],subs(repa,{op(comps1c)} intersect {op(comps2c)})):
return [newpolys, [op(newcomps)]]:
end proc:





# For a given list of polynomials and a list of variables, the following 
# procedure computes the linear reduction. In the case of 
# COMPATIBILITY_GRAPH=true, it uses compatibility graphs in this procedure.
# Else, it computes the Fubini reduction.

MPLPolynomialReduction:=proc(polys, vars)
global COMPATIBILITY_GRAPH:
local i, j, k, p, CG, oldlayer, newlayer, fillednewlayer, subsets, intersectCG,
newvar, polytable, newCG, comps:
CG:=table():
polytable:=table:
comps:=[]:
# The first compatibility graph is the complete graph:
for i from 1 to nops(polys) do
 polytable[i]:=polys[i]:
 if COMPATIBILITY_GRAPH then 
  comps:=[op(comps), {i,0},{i,infty}]:
  for j from i+1 to nops(polys) do
   comps:=[op(comps),{i,j}]:
  end do:
 end if:
end do:
# Stage 0:
CG[{}]:=[polytable,comps]:
# Stage 1:
oldlayer:=[]:
for i from 1 to nops(vars) do
 newCG:=CompGraph(CG[{}],vars[i]):
 if not(newCG=NULL) then
  CG[{vars[i]}]:=newCG:
  oldlayer:=[op(oldlayer),{vars[i]}]:
 end if:
end do:
for i from 2 to nops(vars) do
 newlayer:=[op(choose({op(vars)},i))]:
 fillednewlayer:=[]:
 for j from 1 to nops(newlayer) do
  intersectCG:=NULL:
  for k from 1 to nops(oldlayer) do 
   if oldlayer[k] subset newlayer[j] then
    newvar:=op(newlayer[j] minus oldlayer[k]):
    newCG:=CompGraph(CG[oldlayer[k]], newvar):
    if not(newCG=NULL) then
     if intersectCG=[] or intersectCG=NULL then
      intersectCG:=newCG:
     else
      intersectCG:=IntersectCompGraphs(intersectCG, newCG):
     end if:
    end if:
   end if:
  end do:
  if not(intersectCG=NULL) then
   CG[newlayer[j]]:=intersectCG:
   fillednewlayer:=[op(fillednewlayer),newlayer[j]]:
  end if:
 end do:
 oldlayer:=fillednewlayer:
end do:
return ReductionToLists(CG, nops(vars)):
end proc:




# Before the output of a reduction, the following procedure is used to remove the placeholders 
# for denoting that each polynomial is compatible with itself.

HideTrivialCompatibilities:=proc(complist)
local i, outp:
outp:=[]:
for i from 1 to nops(complist) do
 if not(has(complist[i],0) or has(complist[i],infty)) then
  outp:=[op(outp),complist[i]]:
 end if:
end do:
return outp:
end proc:


# The following returns a given compatibility graph as a list.

ReductionToLists:=proc(CG,nvars)
local i, j, outp:
outp:=[]:
if CG=[] then 
 return outp:
end if:
for j from 0 to nvars do
 for i in [indices(CG,'nolist')] do
  if CG[i]=[] and nops(i)=j then 
   outp:=[op(outp),[i, [],[]]]:
  elif COMPATIBILITY_GRAPH and nops(i)=j then 
   outp:=[op(outp),[i, [entries(op(1,CG[i]),'nolist')], HideTrivialCompatibilities(op(2,CG[i]))]]:
  elif nops(i)=j then
   outp:=[op(outp),[i, [entries(op(1,CG[i]),'nolist')]]]:
  end if:
 end do:
end do:
return outp:
end proc:




# The following procedure was used to simplify checks of the above reduction procedures 
# by comparing with results generated with a private program of Francis Brown 
# for Fubini reduction. 

CompareReductionsWithFrancis:=proc(MyRed, FrancisRed, nvars)
local i, j, differencefound, MyRedUnified, FrancisRedUnified, repvars, diffset:
repvars:=[]:
for i from 1 to nvars do
 repvars:=[op(repvars), i=e[i]]:
end do:
MyRedUnified:={}:
for i from 1 to nops(MyRed) do
 MyRedUnified:={op(MyRedUnified), [op(1,MyRed[i]), {op(op(2,MyRed[i]))}]}:
end do:
FrancisRedUnified:={}:
for i from 1 to nops(FrancisRed) do
 if op(2,FrancisRed[i])={} then
  FrancisRedUnified:={op(FrancisRedUnified), [subs(repvars,{op(op(1,FrancisRed[i]))}), {}]}:
 else
  FrancisRedUnified:={op(FrancisRedUnified), [subs(repvars,{op(op(1,FrancisRed[i]))}), {op(ExtractPolynomials([op(op(2,FrancisRed[i]))]))}]}:
 end if:
end do:
diffset:=FrancisRedUnified minus MyRedUnified:
if not(diffset={}) then 
 print("MyRedUnified"):
 print(MyRedUnified):
 print("FrancisRedUnified"):
 print(FrancisRedUnified):
 print("Difference:"):
 print(diffset):
else
 print("Test ok."):
end if:
end proc:




# The following procedure was used to simplify checks of the above reduction procedures 
# by comparing with results generated with Erik Panzer's program. 

CompareReductionsWithErik:=proc(MyRed, EriksRed)
local i,j,k,index, polys, comps, translcomps, isinEriksRed, testok:
testok:=true:
if not(nops(EriksRed)=nops(MyRed)) then
 print("Different number of reduction stages."):
else
 for i from 1 to nops(MyRed) do
  index:=op(1,MyRed[i]):
  polys:=op(2,MyRed[i]):
  comps:=op(3, MyRed[i]):
  translcomps:=[]:
  if comps=[] then
   traslcomps=comps:
  elif nops(comps)>0 then
   for k from 1 to nops(comps) do
    translcomps:=[op(translcomps),{polys[op(1,comps[k])], polys[op(2,comps[k])]}]:
   end do:
  end if: 
  isinEriksRed:=false:
  for j from 1 to nops(EriksRed) do
   if op(1,EriksRed[j])=index then
    isinEriksRed:=true:
    if not(op(1,op(2,EriksRed[j]))={op(polys)} and op(2,op(2,EriksRed[j]))={op(translcomps)}) then
     print("One entry does not agree with Erik's reduction:"):
     print(MyRed[i]):
     testok:=false:
    end if:
   end if:
  end do:
  if not(isinEriksRed) then 
   print("One entry is not in Erik's reduction:"):
   print(MyRed[i]):
   testok:=false:
  end if:
 end do:
end if:
if testok then
 print("Test ok."):
end if:
end proc:



# Deletes all polynomials from polys which do not depend on va.

CleanList:=proc(polys,va)
local i, outp:
outp:=[]:
for i from 1 to nops(polys) do
 if has(polys[i],va) then
  outp:=[op(outp),polys[i]]:
 end if:
end do:
return outp:
end proc:


# For a given polynomial reduction and order of integration variables, 
# the following procedure returns a list of the lists of polynomials at each stage.
# It returns an error message if linear reducibility is failed.

SelectPolynomialsFromReduction:=proc(reduction, orderedpar)
local i, j, newset, newpolys, outp:
outp:=[]:
newset:={}:
for i from 1 to nops(orderedpar) do
 newpolys:=0:
 for j from 1 to nops(reduction) do
  if op(1,reduction[j])=newset then
   newpolys:=CleanList(op(2,reduction[j]),orderedpar[i]):
   outp:=[op(outp),newpolys]:
  end if:
 end do:
 if newpolys=0 then
  error "Linear reducibility is not satisfied with respect to the chosen order of integrations.":
  return 0:
 end if:
 newset:={op(newset),orderedpar[i]}:
end do:
return outp:
end proc:


# The following procedure checks, whether the terms rho_i associated
# to a list of polynomials are smaller than zero near the tangentianl basepoint,
# as required by the criterion to be properly ordered.

CheckZeroesSmallerZero:=proc(polys,va,AllParameters)
local i, nextzero:
for i from 1 to nops(polys) do
 nextzero:=-eval(polys[i],va=0)/diff(polys[i],va):
 if not(SignAtTangentialBasepoint(nextzero,AllParameters)<0) then
  print("Polynomial causing a problem:"):
  print(polys[i]):
  print("Corresponding rho_i:"):
  print(nextzero);
  error("Not all terms rho_i are smaller than zero at the tangential basepoint.")
 end if:
end do:
print("All rho_i are smaller than zero at the tangential basepoint: Check OK."):
end proc:



# For a given polynomial reduction and a chosen order of variables,
# the following procedure checks, whether the limits, which have to be computed in the 
# integration procedure, will be in {0,1} and whether it is properly ordered
# with respect to the polynomials.

MPLCheckOrder:=proc(reduction, IntParameters, AllParameters)
local i, j, outp, selectedpolys, repsback, uaux, limitlist:
# The following seclects the sets of polynomials from the reduction, which
# belong to the chosen order of integration parameters.
# It also checks linear reducibility.
selectedpolys:=SelectPolynomialsFromReduction(reduction, IntParameters):
for i from 1 to nops(selectedpolys) do
 printf("%s\n",cat("Checks for integration over ",convert(IntParameters[i],string),":"));
 # Check the criterion "properly ordered": 
 # Check that the terms rho_i are smaller than 0 at the tangential basepoint:
 CheckZeroesSmallerZero(selectedpolys[i],IntParameters[i],AllParameters):
 # Check that the limits of cubical coordinates at the tangential basepoint
 # are in {0, 1}:
 repsback:=NewCubicalReplacements(selectedpolys[i], IntParameters[i], AllParameters, uaux, true);
 limitlist:=GetListOfLimits(AllParameters, repsback):
 if nops(limitlist)>0 then
  for j from 1 to nops(limitlist) do
   if not(op(2,limitlist[j])=0) and not(op(2,limitlist[j])=1) then
    print("Limit causing a problem:"):
    print(limitlist[j]):
    error("A limit unequal to 0 and 1 has appeared."):
   end if:
  end do:
  print("Limits in {0, 1}: Check OK."):
 else
  print("No limits to be computed: Check OK."):
 end if:

end do:
end proc:










####################################################################
####################################################################
#
#   PROCEDURES FOR CHECKS WITH ERIK PANZER'S PROGRAM
#
####################################################################
####################################################################


# The following procedures act on the left- and right-hand side of the coproduct in 
# the procedure RewriteFeyn below.

restrictFFeyn:=proc(inp, FeynPar, va, u)
local i, j, DelCoordinates, output, ReplaceCoords, ZetaTerm:
output:=inp:
ReplaceCoords:=FeynPar: 
if has(va, ReplaceCoords) then 
 DelCoordinates:=subs(va=NULL,ReplaceCoords):
 for i from 1 to nops(DelCoordinates) do
  output:=subs(d(DelCoordinates[i])=0, output):
  ####output:=subs(DelCoordinates[i]=0, output):
 end do:
end if:
ZetaTerm:=0:
if u=1 then
 for j from 1 to nops(ReplaceCoords) do
  if not(ReplaceCoords[j]=va) and not(inp=ONE) then
   ZetaTerm:=ZetaTerm+RegularizedZeta(inp, ReplaceCoords[j]);
  end if:
 end do:
end if:
return eval(output + ZetaTerm):
end proc:



restrictRFeyn:=proc(inp, va, u, elimvar)
global Restrinp:
local i, j, k, output, BarLists, reprhs, reps, denombar, numerbar, Signfact, argfact:
output:= subs(d(va)=0,normal(inp)):
output:=eval(subs(va=u,output)):
BarLists:=CheckBarSigns(BarToListsCollected(output), elimvar):
reps:=[]:
for i from 1 to nops(BarLists[1]) do
 for k from 1 to nops(BarLists[2][i]) do
  argfact:=factors(BarLists[2][i][k]):
  if nops(argfact[2])>2 then 
   reprhs:=0:
   for j from 1 to nops(argfact[2]) do
    if argfact[2][j][2]=-1 then 
     reprhs:=reprhs+subs(elimvar,d(argfact[2][j][1]))/argfact[2][j][1]:
    end if:
   end do:
   reps:=[op(reps), BarLists[2][i][k]=reprhs]:
  end if:
 end do:
end do:
return eval(subs(reps,output)):
end proc:










# This procedure writes my Feynman-parametric bar-expressions as hyperlogarithms,
# according to a given order on the parameters.

RewriteFeyn:=proc(inp, FeynPar, elimvar)
local i, j, SortedInput, outp, k, fn1, fn1List, fTens1, Co, CoTerm, va, NewList:
outp:=0:
if nops(FeynPar)<2 then  
 return inp:
else
 va:=FeynPar[1]:
 NewList:=[]:
 for i from 2 to nops(FeynPar) do
  NewList:=[op(NewList), FeynPar[i]]:
 end do:
 # Sort the input by the length of the words.
 SortedInput:=SortByLength(inp):
 for k from 1 to ArrayNumElems(SortedInput(1)) do
  if SortedInput(1)(k)=0 then
   outp:=outp+SortedInput(2)(k):
  else
 # Take the co-product:
  Co:=TensToLists(MPLCoproduct(SortedInput(2)(k))):
  for j from 1 to nops(Co[1]) do
   outp:=outp+ Co[1][j]*restrictFFeyn(Co[2][j],FeynPar,va,0)*RewriteFeyn(restrictRFeyn(Co[3][j],va,0,elimvar), NewList, [op(elimvar),d(va)=0]):
  end do:
  end if:
 end do:
end if:
return eval(outp,ONE=1):
end proc:






# The following procedure translates from the iInt-expressions of Erik Panzer's program to
# hyperlogarithms in the bar-notation of my program.

iIntToBar:=proc(inp)
local i, j, k, reps, iIntList, NewList, NewBar, outp, va, factArg, barArg:
reps:=[]:
iIntList:=[op(selectfun(inp, iInt))]:
for i from 1 to nops(iIntList) do
 va:=op(1,iIntList[i]): 
 NewList:=op(2,iIntList[i]):
 NewBar:=[]:
 for j from 1 to nops(NewList) do
  factArg:=factors(va-NewList[j]):
  barArg:=0:
  if nops(factArg[2])=0 then 
   barArg:=d(va)/va:
  else
   for k from 1 to nops(factArg[2]) do
    barArg:=barArg + coeff(factArg[2][k][1],va)*factArg[2][k][2]*d(va)/(factArg[1]*factArg[2][k][1]):
   end do:
  end if:
  NewBar:=[op(NewBar), barArg]:
 end do:
 reps:=[op(reps), iIntList[i] = eval(bar(op(NewBar)))]:
end do: 
return subs(reps, inp):
end proc:





MPLHlogToBar:=proc(inp)
local i, j, k, reps, iIntList, NewList, NewBar, outp, va, factArg, barArg:
reps:=[]:
iIntList:=[op(selectfun(inp, Hlog))]:
for i from 1 to nops(iIntList) do
 va:=op(1,iIntList[i]): 
 NewList:=op(2,iIntList[i]):
 NewBar:=[]:
 for j from 1 to nops(NewList) do
  factArg:=factors(va-NewList[j]):
  barArg:=0:
  if nops(factArg[2])=0 then 
   barArg:=d(va)/va:
  else
   for k from 1 to nops(factArg[2]) do
    barArg:=barArg + coeff(factArg[2][k][1],va)*factArg[2][k][2]*d(va)/(factArg[2][k][1]):
   end do:
  end if:
  NewBar:=[op(NewBar), barArg]:
 end do:
 reps:=[op(reps), iIntList[i] = eval(bar(op(NewBar)))]:
end do: 
return subs(reps, inp):
end proc:













####################################################################
####################################################################
#
#   TESTS
#
####################################################################
####################################################################



# This procedure checks ExpandAtOne for some examples. For comparisons we used
# RegValue1[3] from Francis' program.







# This procedure checks MPLLimit for some examples. For comparisons we used
# RegValue1[3] from Francis' program.
TestLimitAtOne:=proc(outputinfo)
local i, newterm, mistakes, ListInput, ListCorrectResults, newdifference:
MPLInitialize(v, 2, false, true):
NULL;
# The list of terms to be expanded is:
ListInput:=[1, bar(d(v[3])/v[3]), bar(d(v[3])/(1-v[3])), bar((v[3]*d(v[2])+v[2]*d(v[3]))/(-v[2]*v[3]+1)), bar((v[2]*v[3]*d(v[1])+v[1]*v[3]*d(v[2])+v[1]*v[2]*d(v[3]))/(1-v[1]*v[2]*v[3])), 
bar(d(v[3])/v[3], d(v[3])/v[3]),
bar(d(v[3])/(1-v[3]), d(v[3])/v[3]),
SymbolsToTotal(IntWordsRecursive(bar(v[2]*d(v[3])/(1-v[2]*v[3]), d(v[3])/v[3]))), 
SymbolsToTotal(IntWordsRecursive(bar(v[1]*v[2]*d(v[3])/(1-v[1]*v[2]*v[3]), d(v[3])/v[3]))), 
SymbolsToTotal(IntWordsRecursive(bar(d(v[3])/(v[3]), d(v[3])/(1-v[3])))), 
SymbolsToTotal(IntWordsRecursive(bar(d(v[3])/(1-v[3]), d(v[3])/(1-v[3])))), 
SymbolsToTotal(IntWordsRecursive(bar(v[2]*d(v[3])/(1-v[2]*v[3]),d(v[3])/(1-v[3])))),
SymbolsToTotal(IntWordsRecursive(bar(v[1]*v[2]*d(v[3])/(1-v[1]*v[2]*v[3]), d(v[3])/(1-v[3])))),
SymbolsToTotal(IntWordsRecursive(bar(d(v[3])/(v[3]), v[2]*d(v[3])/(1-v[2]*v[3])))),
SymbolsToTotal(IntWordsRecursive(bar(d(v[3])/(1-v[3]), v[2]*d(v[3])/(1-v[2]*v[3])))),
SymbolsToTotal(IntWordsRecursive(bar(v[2]*d(v[3])/(1-v[2]*v[3]), v[2]*d(v[3])/(1-v[2]*v[3])))),
SymbolsToTotal(IntWordsRecursive(bar(v[1]*v[2]*d(v[3])/(1-v[1]*v[2]*v[3]), v[2]*d(v[3])/(1-v[2]*v[3])))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[3])/(v[3]), v[1]*v[2]*d(v[3])/(1-v[1]*v[2]*v[3]) ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[3])/(1-v[3]), v[1]*v[2]*d(v[3])/(1-v[1]*v[2]*v[3]) ))),
SymbolsToTotal(IntWordsRecursive(bar( v[2]*d(v[3])/(1-v[2]*v[3]), v[1]*v[2]*d(v[3])/(1-v[1]*v[2]*v[3]) )))
]:
# The corresponding correct expansions at v[3]=1 are:
ListCorrectResults:=[1,
0,
infinity,
-bar(d(v[2])/(v[2]-1)),
-bar((v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2])),
0,
-Zeta(2),
bar(d(v[2])/v[2], d(v[2])/(v[2]-1)),
bar(d(v[1])/v[1], (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))+bar(d(v[2])/v[2], (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2])),
Zeta(2),
0,
-bar(d(v[2])/v[2], d(v[2])/(v[2]-1))+bar(d(v[2])/(v[2]-1), d(v[2])/(v[2]-1)),
bar((v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]), (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))-bar(d(v[1])/v[1], (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))-bar(d(v[2])/v[2], (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2])),
-bar(d(v[2])/v[2], d(v[2])/(v[2]-1)),
infinity,
bar(d(v[2])/(v[2]-1), d(v[2])/(v[2]-1)),
bar((v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]), d(v[2])/(v[2]-1))-bar(d(v[1])/v[1], (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))+bar(d(v[1])/(v[1]-1), (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))-bar(d(v[1])/(v[1]-1), d(v[2])/(v[2]-1)),
-bar(d(v[1])/v[1], (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))-bar(d(v[2])/v[2], (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2])),
infinity,
bar(d(v[1])/v[1], (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))-bar(d(v[1])/(v[1]-1), (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))+bar(d(v[1])/(v[1]-1), d(v[2])/(v[2]-1))+bar(d(v[2])/(v[2]-1), (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))
]:
print(nops(ListCorrectResults));
mistakes:=[]:
for i from 1 to nops(ListCorrectResults) do
 # Don't test the cases where the limit is infinite.
 if (not(i=3) and not(i=15) and not(i=19)) then 
  newterm:=factor(MPLLimit(ListInput[i], v[3], 1)):
  newdifference:=eval(eval(factor(newterm-ListCorrectResults[i]), zeta=Zeta)):
  if not(newdifference=0) then mistakes:=[op(mistakes), ListInput[i]]:
  end if:
 end if:
end do:
# If outputinfo=true the inputs which gave wrong results are shown.
if outputinfo=true then
 if mistakes=[] then print("All checks for the procedure MPLLimit at one are ok."):
 else
  print("Error: The procedude MPLLimit gives wrong results for the following test arguments, evaluated at v[3]=1:"):
  print(mistakes):
 end if:
end if:
# The return value is true if everything was correct and false otherwise.
if mistakes=[] then return true:
else return false:
end if:
end proc:





# This procedure checks MPLLimit for some examples. For comparisons we used
# RegValue0[3] from Francis' program.
TestLimitAtZero:=proc(outputinfo)
local i, newterm, mistakes, ListInput, ListCorrectResults, newdifference:
MPLInitialize(v, 2,false, true):
NULL;
# The list of terms to be expanded is:
ListInput:=[1, bar(d(v[3])/v[3]), bar(d(v[3])/(1-v[3])), bar((v[3]*d(v[2])+v[2]*d(v[3]))/(-v[2]*v[3]+1)), bar((v[2]*v[3]*d(v[1])+v[1]*v[3]*d(v[2])+v[1]*v[2]*d(v[3]))/(1-v[1]*v[2]*v[3])), 
bar(d(v[3])/v[3], d(v[3])/v[3]),
bar(d(v[3])/(1-v[3]), d(v[3])/v[3]),
SymbolsToTotal(IntWordsRecursive(bar(v[2]*d(v[3])/(1-v[2]*v[3]), d(v[3])/v[3]))), 
SymbolsToTotal(IntWordsRecursive(bar(v[1]*v[2]*d(v[3])/(1-v[1]*v[2]*v[3]), d(v[3])/v[3]))), 
SymbolsToTotal(IntWordsRecursive(bar(d(v[3])/(v[3]), d(v[3])/(1-v[3])))), 
SymbolsToTotal(IntWordsRecursive(bar(d(v[3])/(1-v[3]), d(v[3])/(1-v[3])))), 
SymbolsToTotal(IntWordsRecursive(bar(v[2]*d(v[3])/(1-v[2]*v[3]),d(v[3])/(1-v[3])))),
SymbolsToTotal(IntWordsRecursive(bar(v[1]*v[2]*d(v[3])/(1-v[1]*v[2]*v[3]), d(v[3])/(1-v[3])))),
SymbolsToTotal(IntWordsRecursive(bar(d(v[3])/(v[3]), v[2]*d(v[3])/(1-v[2]*v[3]))))
]:
# The corresponding correct limits at v[3]=0 are:
ListCorrectResults:=[1,
infinity,
0,
0,
0,
infinity,
0,
0,
0,
0,
0,
0]:
print(nops(ListCorrectResults));
mistakes:=[]:
for i from 1 to nops(ListCorrectResults) do
 # Don't test the cases where the limit is infinite.
 if (not(i=2) and not(i=6)) then 
  newterm:=factor(MPLLimit(ListInput[i], v[3], 0)):
  newdifference:=eval(eval(factor(newterm-ListCorrectResults[i]), zeta=Zeta)):
  if not(newdifference=0) then mistakes:=[op(mistakes), ListInput[i]]:
  end if:
 end if:
end do:
# If outputinfo=true the inputs which gave wrong results are shown.
if outputinfo=true then
 if mistakes=[] then print("All checks for the procedure MPLLimit at zero are ok."):
 else
  print("Error: The procedude MPLLimit gives wrong results for the following test arguments, evaluated at v[3]=0:"):
  print(mistakes):
 end if:
end if:
# The return value is true if everything was correct and false otherwise.
if mistakes=[] then return true:
else return false:
end if:
end proc:


TestRegularizedZeta:=proc(outputinfo)
local i, mistakes, List1, CorrectResults, newdifference:
# The lists of all test-arguments and the corresponding correct results.
mistakes:=[]:
List1:=[ bar(), bar(d(x)/x), bar(d(x)/x, d(x)/x), bar(d(x)/(x-1), d(x)/x), bar(d(x)/x, d(x)/(x-1)), bar(d(x)/(x-1), d(x)/(x-1)),
bar(d(x)/x, d(x)/x, d(x)/x), bar(d(x)/(x-1), d(x)/x, d(x)/x), bar(d(x)/(x), d(x)/(x-1), d(x)/x), bar(d(x)/(x-1), d(x)/(x-1), d(x)/(x)), bar(d(x)/(x), d(x)/(x), d(x)/(x-1)), bar(d(x)/(x-1), d(x)/(x), d(x)/(x-1)),bar(d(x)/(x), d(x)/(x-1), d(x)/(x-1)), bar(d(x)/(x-1), d(x)/(x-1), d(x)/(x-1))]:
CorrectResults:=[ 0, 0, 0, zeta(2), -zeta(2), 0, 0, -zeta(3), 2*zeta(3), zeta(3), -zeta(3), -2*zeta(3), zeta(3), 0]:
# Compare with correct results:

print(nops(CorrectResults)):
for i from 1 to nops(CorrectResults) do
 newdifference:=factor(CorrectResults[i]-RegularizedZeta(List1[i], x)):
 if not(newdifference=0) then mistakes:=[op(mistakes), List1[i]]:
 end if:
end do:
# If outputinfo=true the inputs which gave wrong results are shown.
if outputinfo=true then
 if mistakes=[] then print("Checks for RegularizedZeta are ok."):
 else
  print("Error: The procedure RegularizedZeta gives wrong results for the following arguments:"):
  print(mistakes):
 end if:
end if:
# The return value is true if everything was correct and false otherwise.
if mistakes=[] then return true:
else return false:
end if:
end proc:


# The following test computes a four-fold integral closely related to a cell-zeta value.
# After each integration we compare with intermediate results of Francis' program.
TestCellZeta1:=proc(outputinfo)
local i, mistakes, Int1, Int2, Int3, Int4, FinalResult, CorrectIntermediateResults, IntermediateResults, newdifference:
MPLInitialize(u, 3, false, true):
# The list of all correct intermediate results:
CorrectIntermediateResults:=[(u[2]*u[3]*(1-u[4])*u[4]*u[1])/((1-u[1]*u[2])*(1-u[1]*u[2]*u[3])*(1-u[4]*u[2]*u[3])*(1-u[4]*u[1]*u[2]*u[3])), 
-(-u[1]*u[2]*u[3]-u[1]^2*bar((u[3]*d(u[2])+u[2]*d(u[3]))/(u[2]*u[3]-1))*u[2]*u[3]+u[1]^2*u[2]*u[3]+bar((u[2]*u[3]*d(u[1])+u[1]*u[3]*d(u[2])+u[1]*u[2]*d(u[3]))/(-1+u[1]*u[2]*u[3]))*u[1]*u[2]*u[3]-bar((u[2]*u[3]*d(u[1])+u[1]*u[3]*d(u[2])+u[1]*u[2]*d(u[3]))/(-1+u[1]*u[2]*u[3]))+u[1]^2*bar((u[3]*d(u[2])+u[2]*d(u[3]))/(u[2]*u[3]-1)))/((u[1]-1)*u[1]*u[3]^2*u[2]^2*(-1+u[1]*u[2]*u[3])*(-1+u[1]*u[2])),
-(-bar(d(u[1])/(u[1]-1), (u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]))*u[1]^2*u[2]+bar(d(u[1])/(u[1]-1), d(u[2])/(u[2]-1))*u[1]^2*u[2]-u[1]*u[2]-u[1]^3*bar(d(u[2])/u[2], d(u[2])/(u[2]-1))*u[2]+u[1]^2*u[2]+u[1]^3*u[2]*bar(d(u[1])/(u[1]-1), (u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]))+bar(d(u[1])/u[1], (u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]))*u[1]^2*u[2]-u[1]^2*bar(d(u[2])/(u[2]-1))*u[2]+u[1]^3*u[2]*bar((u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]), d(u[2])/(u[2]-1))-u[1]^3*u[2]*bar(d(u[1])/u[1], (u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]))+u[1]^2*bar(d(u[2])/u[2], d(u[2])/(u[2]-1))*u[2]+bar((u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]))*u[1]^2*u[2]-bar((u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]), d(u[2])/(u[2]-1))*u[1]^2*u[2]-u[1]^3*u[2]*bar(d(u[1])/(u[1]-1), d(u[2])/(u[2]-1))-bar((u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]))+u[1]^2*bar(d(u[2])/(u[2]-1)))/((u[1]-1)*u[1]*u[2]^2*(-1+u[1]*u[2])),
-(-bar(d(u[1])/u[1], d(u[1])/(u[1]-1))*u[1]^2+bar(d(u[1])/u[1], d(u[1])/u[1], d(u[1])/(u[1]-1))*u[1]^2-bar(d(u[1])/(u[1]-1), d(u[1])/u[1], d(u[1])/(u[1]-1))*u[1]^2-bar(d(u[1])/u[1], d(u[1])/(u[1]-1), d(u[1])/(u[1]-1))*u[1]^2+bar(d(u[1])/(u[1]-1), d(u[1])/(u[1]-1))*u[1]^2+u[1]^2*zeta(2)+bar(d(u[1])/(u[1]-1), d(u[1])/(u[1]-1), d(u[1])/(u[1]-1))*u[1]^2-u[1]^2*zeta(3)+bar(d(u[1])/(u[1]-1))*u[1]+u[1]-bar(d(u[1])/u[1], d(u[1])/(u[1]-1))*u[1]+bar(d(u[1])/(u[1]-1), d(u[1])/(u[1]-1))*u[1]+bar(d(u[1])/(u[1]-1)))/u[1],
(3/2)*zeta(3)-(1/2)*zeta(2)-1/2]:
# Computation:
mistakes:=[]:
Int1:=CorrectIntermediateResults[1]:
Int2:=MPLCubicalIntegrate(Int1, u[4], 1):
Int3:=MPLCubicalIntegrate(Int2, u[3], 1):
Int4:=MPLCubicalIntegrate(Int3, u[2], 1):
FinalResult:=MPLCubicalIntegrate(Int4, u[1], 1):
IntermediateResults:=[Int1, Int2, Int3, Int4, FinalResult]: 
# Compare with correct results:
for i from 1 to nops(CorrectIntermediateResults) do
 newdifference:=factor(CorrectIntermediateResults[i]-IntermediateResults[i]):
 if not(newdifference=0) then mistakes:=[op(mistakes), IntermediateResults[i-1]]:
 end if:
end do:
# If outputinfo=true the inputs which gave wrong results are shown.
if outputinfo=true then
 if mistakes=[] then print("Checks for Cellzeta1 are ok."):
 else
  print("Error: The procedure MPLint gives wrong results for the following integrand during the evaluation of Cellzeta1:"):
  print(mistakes):
 end if:
end if:
# The return value is true if everything was correct and false otherwise.
if mistakes=[] then return true:
else return false:
end if:
end proc:



TestCellZeta2:=proc(outputinfo)
local i, mistakes, Int1, Int2, Int3, Int4, FinalResult, CorrectIntermediateResults, IntermediateResults, newdifference:
# The list of all correct intermediate results:
CorrectIntermediateResults:=[
u[1]^3*(1-u[1])*u[2]^4*(1-u[2])*u[3]^3*(1-u[3])*u[4]^2*(1-u[4])^2/((1-u[1]*u[2]*u[3])^2*(1-u[4]*u[2]*u[3])^2*(1-u[4]*u[1]*u[2]*u[3])^2*(1-u[1]*u[2])),
(2*u[1]^4*u[3]^2*u[2]-2*u[1]^4*u[3]+2*u[1]^4-2*u[1]^4*u[2]-2*u[1]^4*u[2]^2*u[3]^2+2*u[1]^4*u[2]^2*u[3]+2*u[1]^3*u[2]*u[3]-6*u[1]^3*u[2]^2*u[3]+4*u[1]^3*u[2]^2*u[3]^2-6*u[1]^3*u[3]^2*u[2]+4*u[1]^3*u[2]+2*u[1]^3*u[2]^3*u[3]^2+4*u[1]^3*u[3]-4*u[1]^3-2*u[1]^3*u[2]^3*u[3]^3+2*u[1]^3*u[2]^2*u[3]^3)*bar((u[3]*d(u[2])+u[2]*d(u[3]))/(u[2]*u[3]-1))/(u[2]*(u[1]-1)^2*u[3]^2*(-1+u[1]*u[2])*(-1+u[1]*u[2]*u[3])^2)+(2*u[3]+6*u[1]*u[2]*u[3]-6*u[1]^2*u[2]^2*u[3]^2+2*u[1]^3*u[2]^3*u[3]^3+2*u[1]^3*u[2]^2*u[3]^2-2*u[1]^3*u[2]^2*u[3]^3+6*u[3]*u[1]^2*u[2]^2-2*u[1]^3*u[2]^3*u[3]^2+2*u[2]^2*u[3]^2*u[1]-6*u[1]^2*u[2]*u[3]-2*u[1]*u[2]^2*u[3]+6*u[1]^2*u[2]*u[3]^2-2*u[3]^2*u[1]*u[2]-2+2*u[2]+4*u[1]-4*u[3]*u[1]-4*u[1]*u[2]-2*u[2]*u[3])*bar((u[2]*u[3]*d(u[1])+u[1]*u[3]*d(u[2])+u[1]*u[2]*d(u[3]))/(-1+u[1]*u[2]*u[3]))/(u[2]*(u[1]-1)^2*u[3]^2*(-1+u[1]*u[2])*(-1+u[1]*u[2]*u[3])^2)+(-2*u[2]^2*u[3]^2*u[1]+4*u[1]^3*u[3]^2*u[2]+u[1]^4*u[2]^2*u[3]^2-4*u[1]^3*u[2]^2*u[3]^2+5*u[1]^2*u[2]^2*u[3]^2-4*u[1]^3*u[2]*u[3]+2*u[1]*u[2]^2*u[3]-2*u[1]*u[2]*u[3]+4*u[1]^2*u[2]*u[3]-u[1]^2*u[2]^3*u[3]^2+u[1]^2*u[2]^3*u[3]^3-u[1]^2*u[2]^2*u[3]^3-4*u[1]^2*u[2]*u[3]^2+2*u[3]^2*u[1]*u[2]-2*u[1]^4*u[3]^2*u[2]+2*u[1]^4*u[2]*u[3]-4*u[3]*u[1]^2*u[2]^2-u[1]^4*u[2]^3*u[3]^3+u[1]^4*u[2]^3*u[3]^2+u[1]^4*u[3]^3*u[2]^2-2*u[1]^4*u[2]^2*u[3]+4*u[1]^3*u[2]^2*u[3])/(u[2]*(u[1]-1)^2*u[3]^2*(-1+u[1]*u[2])*(-1+u[1]*u[2]*u[3])^2),
-(2*u[1]+3*u[1]^2-2*u[1]^3-4*u[1]^4*u[2]^2+4*u[1]^4*u[2]-6*u[1]^3*u[2]-u[1]^2*u[2]+8*u[1]^3*u[2]^2-2*u[1]*u[2]-2*u[1]^2*u[2]^2+u[2]-1)*bar((u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]))/(u[2]*(u[1]-1)^2*(-1+u[1]*u[2]))-(4*u[1]^4-8*u[1]^3*u[2]^2-8*u[1]^4*u[2]+16*u[1]^3*u[2]+4*u[1]^4*u[2]^2+2*u[1]^2-4*u[1]^2*u[2]+2*u[1]^2*u[2]^2-8*u[1]^3)*bar(d(u[2])/(u[2]-1))/(u[2]*(u[1]-1)^2*(-1+u[1]*u[2]))-(-2*u[2]-2*u[1]+2*u[2]^2*u[1]+2*u[1]^2*u[2]-2*u[1]^2*u[2]^2+2)*bar((u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]), (u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]))/(u[2]*(u[1]-1)^2*(-1+u[1]*u[2]))-(4*u[1]^5*u[2]-4*u[1]^5*u[2]^2-8*u[1]^4*u[2]-2*u[1]+4*u[1]^3-2*u[1]^4+10*u[1]^4*u[2]^2-6*u[1]^3*u[2]^2+2*u[1]^3*u[2]+2*u[1]*u[2])*bar((u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]), d(u[2])/(u[2]-1))/(u[2]*(u[1]-1)^2*(-1+u[1]*u[2]))-(2*u[2]-4*u[1]^5*u[2]+4*u[1]^5*u[2]^2+8*u[1]^4*u[2]+6*u[1]-4*u[1]^3+2*u[1]^4-10*u[1]^4*u[2]^2-2*u[1]^3*u[2]+6*u[1]^3*u[2]^2-2*u[1]^2*u[2]-4*u[1]*u[2]+2*u[1]^2*u[2]^2-2*u[2]^2*u[1]-2)*bar(d(u[1])/u[1], (u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]))/(u[2]*(u[1]-1)^2*(-1+u[1]*u[2]))-(4*u[1]^5*u[2]-4*u[1]^5*u[2]^2-8*u[1]^4*u[2]-2*u[1]+4*u[1]^3-2*u[1]^4+10*u[1]^4*u[2]^2-6*u[1]^3*u[2]^2+2*u[1]^3*u[2]+2*u[1]*u[2])*bar(d(u[1])/(u[1]-1), (u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]))/(u[2]*(u[1]-1)^2*(-1+u[1]*u[2]))-(-4*u[1]^5*u[2]-2*u[1]^3*u[2]+2*u[1]+8*u[1]^4*u[2]-4*u[1]^3+2*u[1]^4+6*u[1]^3*u[2]^2+4*u[1]^5*u[2]^2-10*u[1]^4*u[2]^2-2*u[1]*u[2])*bar(d(u[1])/(u[1]-1), d(u[2])/(u[2]-1))/(u[2]*(u[1]-1)^2*(-1+u[1]*u[2]))-(2*u[1]^2*u[2]^2-2*u[1]*u[2]+4*u[1]-2*u[1]^2*u[2]-2-2*u[2]^2*u[1]+2*u[2])*bar(d(u[2])/u[2], (u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]))/(u[2]*(u[1]-1)^2*(-1+u[1]*u[2]))-(-4*u[1]^5*u[2]-2*u[1]^3*u[2]+8*u[1]^4*u[2]-4*u[1]^3+2*u[1]^4+6*u[1]^3*u[2]^2-10*u[1]^4*u[2]^2+4*u[1]^5*u[2]^2)*bar(d(u[2])/u[2], d(u[2])/(u[2]-1))/(u[2]*(u[1]-1)^2*(-1+u[1]*u[2]))-(-8*u[1]^2*u[2]^2-4*u[1]^4*u[2]^2+4*u[1]^4*u[2]+8*u[1]^2*u[2]-9*u[1]^3*u[2]-3*u[1]*u[2]+3*u[2]^2*u[1]+9*u[1]^3*u[2]^2)/(u[2]*(u[1]-1)^2*(-1+u[1]*u[2])),
(12*u[1]^4*zeta(2)-4*u[1]^5*zeta(2)-12*u[1]^3*zeta(2)+4*u[1]^2*zeta(2)+u[1]^3-7*u[1]^2+9*u[1]-3)*bar(d(u[1])/(u[1]-1))/(u[1]*(u[1]-1)^2)+(9*u[1]^3-6*u[1]^2+3*u[1]-4*u[1]^4)*bar(d(u[1])/u[1], d(u[1])/(u[1]-1))/(u[1]*(u[1]-1)^2)+(1+u[1]^3-u[1]^2-u[1])*bar(d(u[1])/(u[1]-1), d(u[1])/(u[1]-1))/(u[1]*(u[1]-1)^2)+(12*u[1]^3+2*u[1]^2-2*u[1]+6*u[1]^5-16*u[1]^4)*bar(d(u[1])/u[1], d(u[1])/u[1], d(u[1])/(u[1]-1))/(u[1]*(u[1]-1)^2)+(-2*u[1]^5+4*u[1]^4-6*u[1]^2+4*u[1])*bar(d(u[1])/u[1], d(u[1])/(u[1]-1), d(u[1])/(u[1]-1))/(u[1]*(u[1]-1)^2)+(-4*u[1]^2+2*u[1]-2*u[1]^5+4*u[1]^4)*bar(d(u[1])/(u[1]-1), d(u[1])/u[1], d(u[1])/(u[1]-1))/(u[1]*(u[1]-1)^2)+(-2*u[1]^5+8*u[1]^4+8*u[1]^2-2*u[1]-12*u[1]^3)*bar(d(u[1])/(u[1]-1), d(u[1])/(u[1]-1), d(u[1])/(u[1]-1))/(u[1]*(u[1]-1)^2)+(8*u[1]^2-9*u[1]^3+4*u[1]^3*zeta(2)+4*u[1]^4*zeta(3)+4*u[1]^4-2*u[1]^5*zeta(3)-3*u[1]-2*u[1]^4*zeta(2))/(u[1]*(u[1]-1)^2),
(5/3)*zeta(3)+(26/9)*zeta(2)-(17/5)*zeta(2)^2+22/9
]:
# Computation:
mistakes:=[]:
MPLInitialize(u, 3):
Int1:=CorrectIntermediateResults[1]:
Int2:=MPLCubicalIntegrate(Int1, u[4], 1):
Int3:=MPLCubicalIntegrate(Int2, u[3], 1):
Int4:=MPLCubicalIntegrate(Int3, u[2], 1):
FinalResult:=MPLCubicalIntegrate(Int4, u[1], 1):
IntermediateResults:=[Int1, Int2, Int3, Int4, FinalResult]: 
# Compare with correct results:
for i from 1 to nops(CorrectIntermediateResults) do
 newdifference:=factor(CorrectIntermediateResults[i]-IntermediateResults[i]):
 if not(newdifference=0) then 
mistakes:=[op(mistakes), IntermediateResults[i-1]]:
 end if:
end do:
# If outputinfo=true the inputs which gave wrong results are shown.
if outputinfo=true then
 if mistakes=[] then print("Checks for Cellzeta2 are ok."):
 else
  print("Error: The procedure MPLint gives wrong results for the following integrand during the evaluation of Cellzeta2:"):
  print(mistakes):
 end if:
end if:
# The return value is true if everything was correct and false otherwise.
if mistakes=[] then return true:
else return false:
end if:
end proc:




TestCellZeta3:=proc(outputinfo)
local i, mistakes, Int1, Int2, Int3, Int4, FinalResult, CorrectIntermediateResults, IntermediateResults, newdifference:
# The list of all correct intermediate results:
CorrectIntermediateResults:=[
u[1]^5*(1-u[1])^2*u[2]^7*(1-u[2])^2*u[3]^5*(1-u[3])^2*u[4]^3*(1-u[4])^3/((1-u[1]*u[2]*u[3])^3*(1-u[4]*u[2]*u[3])^3*(1-u[4]*u[1]*u[2]*u[3])^3*(1-u[1]*u[2])),
-(1/2)*u[1]*(-60*u[1]^4*u[3]-174*u[1]^4*u[2]^2*u[3]^2+30*u[1]^4*u[2]^2-60*u[1]^4*u[2]+12*u[1]^4*u[2]^4*u[3]^4+78*u[1]^4*u[2]^3*u[3]^3+48*u[1]^5*u[2]-24*u[1]^5*u[2]^2-6*u[1]^5*u[2]^5*u[3]^3+36*u[1]^4*u[2]^4*u[3]^2-60*u[1]^4*u[2]^3*u[3]+6*u[1]^6-24*u[1]^5+30*u[1]^4-6*u[1]^5*u[2]^5*u[3]^5+30*u[1]^4*u[3]^2+6*u[1]^6*u[2]^2-6*u[1]^4*u[2]^5*u[3]^5+12*u[3]^5*u[1]^4*u[2]^4-60*u[3]^4*u[1]^4*u[2]^3+12*u[1]^4*u[2]^5*u[3]^4-60*u[1]^4*u[2]^4*u[3]^3-12*u[1]^6*u[2]-66*u[1]^5*u[2]*u[3]-12*u[1]^5*u[2]*u[3]^2-18*u[1]^6*u[2]^2*u[3]^2+12*u[1]^6*u[2]^2*u[3]^3-12*u[1]^5*u[3]*u[2]^2+12*u[1]^6*u[2]^3*u[3]^2+60*u[1]^4*u[2]^2*u[3]-6*u[1]^6*u[2]^3*u[3]^3-24*u[1]^5*u[2]^4*u[3]^4+12*u[1]^5*u[3]^5*u[2]^4+12*u[1]^5*u[3]^4*u[2]^3+12*u[1]^5*u[2]^5*u[3]^4+12*u[1]^5*u[2]^4*u[3]^3+60*u[1]^4*u[3]^2*u[2]+24*u[1]^5*u[2]^3*u[3]^3-60*u[1]^5*u[3]^3*u[2]^2+60*u[1]^4*u[2]*u[3]-60*u[1]^5*u[2]^3*u[3]^2+96*u[1]^5*u[2]^2*u[3]^2+48*u[1]^4*u[3]^3*u[2]^2+48*u[1]^4*u[2]^3*u[3]^2+48*u[1]^5*u[3]+18*u[1]^6*u[2]*u[3]-6*u[1]^6*u[2]^3*u[3]+30*u[1]^5*u[2]*u[3]^3-60*u[1]^4*u[2]*u[3]^3-6*u[3]^5*u[1]^4*u[2]^3+36*u[3]^4*u[1]^4*u[2]^2-6*u[1]^5*u[3]^5*u[2]^3+30*u[1]^5*u[2]^3*u[3]-6*u[1]^4*u[2]^5*u[3]^3+6*u[1]^6*u[3]^2-12*u[1]^6*u[3]-6*u[3]^3*u[1]^6*u[2]-24*u[3]^2*u[1]^5)*bar((u[3]*d(u[2])+u[2]*d(u[3]))/(u[2]*u[3]-1))/((u[1]-1)^3*u[3]^2*(-1+u[1]*u[2]*u[3])^3*(-1+u[1]*u[2]))-(1/2)*u[1]*(-6+48*u[2]^2*u[3]^2*u[1]+60*u[1]^3*u[2]*u[3]-36*u[1]^4*u[2]^2*u[3]^2-6*u[2]^2*u[3]^2-6*u[3]^2-6*u[2]^2-150*u[1]^2*u[2]^2*u[3]^2+60*u[1]^3*u[2]^3*u[3]^3-30*u[1]^2*u[3]^2+102*u[1]*u[2]*u[3]-150*u[1]^2*u[2]*u[3]+60*u[1]^2*u[2]^3*u[3]^2-60*u[1]*u[2]^2*u[3]+60*u[1]^2*u[2]^2*u[3]^3+120*u[1]^2*u[2]*u[3]^2-60*u[3]^2*u[1]*u[2]+240*u[1]^3*u[2]^2*u[3]^2-12*u[1]^4*u[2]^4*u[3]^4-138*u[1]^4*u[2]^3*u[3]^3-30*u[1]^2*u[2]^3*u[3]^3-120*u[1]^3*u[2]^2*u[3]^3-48*u[3]*u[1]-48*u[1]*u[2]-24*u[2]*u[3]+12*u[2]+12*u[3]+24*u[1]-30*u[1]^2+24*u[2]^2*u[1]+60*u[1]^2*u[2]-30*u[1]^2*u[2]^2+12*u[2]*u[3]^2+12*u[3]*u[2]^2+6*u[3]^3*u[1]*u[2]+6*u[1]^5*u[2]^5*u[3]^3-36*u[1]^4*u[2]^4*u[3]^2-30*u[1]^2*u[2]^3*u[3]+6*u[2]^3*u[1]*u[3]+120*u[3]*u[1]^2*u[2]^2-120*u[1]^3*u[2]^3*u[3]^2-30*u[1]^2*u[2]*u[3]^3+6*u[1]^5*u[2]^5*u[3]^5+60*u[1]^3*u[2]^3*u[3]+24*u[3]^2*u[1]+60*u[3]*u[1]^2+6*u[1]^4*u[2]^5*u[3]^5-12*u[3]^5*u[1]^4*u[2]^4+60*u[3]^4*u[1]^4*u[2]^3-12*u[1]^4*u[2]^5*u[3]^4+60*u[1]^4*u[2]^4*u[3]^3-12*u[3]^3*u[1]*u[2]^2-12*u[1]*u[2]^3*u[3]^2+6*u[2]^3*u[3]^3*u[1]+24*u[1]^5*u[2]^4*u[3]^4-12*u[1]^5*u[3]^5*u[2]^4-12*u[1]^5*u[3]^4*u[2]^3-12*u[1]^5*u[2]^5*u[3]^4-12*u[1]^5*u[2]^4*u[3]^3+6*u[1]^5*u[2]^3*u[3]^3+72*u[1]^4*u[3]^3*u[2]^2-120*u[1]^3*u[2]^2*u[3]+72*u[1]^4*u[2]^3*u[3]^2-120*u[1]^3*u[3]^2*u[2]+60*u[1]^3*u[2]*u[3]^3+6*u[3]^5*u[1]^4*u[2]^3-36*u[3]^4*u[1]^4*u[2]^2+6*u[1]^5*u[3]^5*u[2]^3+6*u[1]^4*u[2]^5*u[3]^3)*bar((u[2]*u[3]*d(u[1])+u[1]*u[3]*d(u[2])+u[1]*u[2]*d(u[3]))/(-1+u[1]*u[2]*u[3]))/((u[1]-1)^3*u[3]^2*(-1+u[1]*u[2]*u[3])^3*(-1+u[1]*u[2]))-(1/2)*u[1]*(-24*u[2]^2*u[3]^2*u[1]+3*u[1]^2*u[2]^4*u[3]^2-30*u[1]^3*u[2]*u[3]+120*u[1]^4*u[2]^2*u[3]^2+99*u[1]^2*u[2]^2*u[3]^2-101*u[1]^3*u[2]^3*u[3]^3-6*u[1]*u[2]*u[3]+24*u[1]^2*u[2]*u[3]-54*u[1]^2*u[2]^3*u[3]^2+12*u[1]*u[2]^2*u[3]-54*u[1]^2*u[2]^2*u[3]^3-48*u[1]^2*u[2]*u[3]^2+12*u[3]^2*u[1]*u[2]-138*u[1]^3*u[2]^2*u[3]^2+36*u[1]^4*u[2]^4*u[3]^4+39*u[1]^4*u[2]^3*u[3]^3+36*u[1]^2*u[2]^3*u[3]^3+96*u[1]^3*u[2]^2*u[3]^3-6*u[3]^3*u[1]*u[2]-9*u[1]^5*u[2]^5*u[3]^3+3*u[3]^4*u[1]^2*u[2]^2+24*u[1]^2*u[2]^3*u[3]+u[1]^3*u[2]^3*u[3]^5-6*u[2]^3*u[1]*u[3]+30*u[1]^4*u[2]^3*u[3]-48*u[3]*u[1]^2*u[2]^2+96*u[1]^3*u[2]^3*u[3]^2+u[1]^3*u[2]^5*u[3]^3+24*u[1]^2*u[2]*u[3]^3-18*u[1]^3*u[2]^4*u[3]^2-9*u[1]^5*u[2]^5*u[3]^5-30*u[1]^3*u[2]^3*u[3]+3*u[2]^4*u[3]^4*u[1]^2+9*u[1]^4*u[2]^5*u[3]^5-18*u[3]^5*u[1]^4*u[2]^4-18*u[3]^4*u[1]^4*u[2]^3-18*u[1]^4*u[2]^5*u[3]^4-18*u[1]^4*u[2]^4*u[3]^3+u[1]^3*u[2]^5*u[3]^5-2*u[3]^5*u[1]^3*u[2]^4+12*u[3]^3*u[1]*u[2]^2-6*u[3]^4*u[1]^2*u[2]^3-2*u[1]^3*u[2]^5*u[3]^4+12*u[1]*u[2]^3*u[3]^2-6*u[1]^2*u[2]^4*u[3]^3-14*u[2]^4*u[3]^4*u[1]^3-6*u[2]^3*u[3]^3*u[1]+34*u[1]^3*u[2]^4*u[3]^3+34*u[3]^4*u[1]^3*u[2]^3-24*u[1]^5*u[2]*u[3]+48*u[1]^5*u[2]*u[3]^2+21*u[1]^6*u[2]^2*u[3]^2-6*u[1]^6*u[2]^2*u[3]^3+48*u[1]^5*u[3]*u[2]^2-6*u[
1]^6*u[2]^3*u[3]^2-u[1]^6*u[2]^5*u[3]^5+2*u[1]^6*u[2]^4*u[3]^5+2*u[1]^6*u[2]^5*u[3]^4-7*u[1]^6*u[2]^4*u[3]^4+8*u[1]^6*u[2]^3*u[3]^4-60*u[1]^4*u[2]^2*u[3]+8*u[1]^6*u[2]^4*u[3]^3-7*u[1]^6*u[2]^3*u[3]^3-18*u[1]^5*u[2]^4*u[3]^4+18*u[1]^5*u[3]^5*u[2]^4-18*u[1]^5*u[3]^4*u[2]^3+18*u[1]^5*u[2]^5*u[3]^4-18*u[1]^5*u[2]^4*u[3]^3-60*u[1]^4*u[3]^2*u[2]+39*u[1]^5*u[2]^3*u[3]^3+12*u[1]^5*u[3]^3*u[2]^2+30*u[1]^4*u[2]*u[3]+12*u[1]^5*u[2]^3*u[3]^2-78*u[1]^5*u[2]^2*u[3]^2-60*u[1]^4*u[3]^3*u[2]^2+60*u[1]^3*u[2]^2*u[3]-60*u[1]^4*u[2]^3*u[3]^2+60*u[1]^3*u[3]^2*u[2]-12*u[1]^6*u[2]*u[3]^2+6*u[1]^6*u[2]*u[3]+6*u[1]^6*u[2]^3*u[3]-12*u[1]^6*u[2]^2*u[3]-24*u[1]^5*u[2]*u[3]^3-u[3]^5*u[1]^6*u[2]^3-3*u[3]^4*u[1]^6*u[2]^2+18*u[3]^4*u[1]^5*u[2]^2+30*u[1]^4*u[2]*u[3]^3-30*u[1]^3*u[2]*u[3]^3+9*u[3]^5*u[1]^4*u[2]^3-18*u[3]^4*u[1]^3*u[2]^2-9*u[1]^5*u[3]^5*u[2]^3-24*u[1]^5*u[2]^3*u[3]-3*u[1]^6*u[2]^4*u[3]^2+18*u[1]^5*u[2]^4*u[3]^2-u[1]^6*u[2]^5*u[3]^3+9*u[1]^4*u[2]^5*u[3]^3+6*u[3]^3*u[1]^6*u[2])/((u[1]-1)^3*u[3]^2*(-1+u[1]*u[2]*u[3])^3*(-1+u[1]*u[2])),
-(1/2)*(12+18*u[1]^7*u[2]^2-36*u[1]^7*u[2]^3+18*u[1]^7*u[2]^4+59*u[1]^4*u[2]^2-40*u[1]^4*u[2]+12*u[2]^2-18*u[1]^3*u[2]+42*u[1]^5*u[2]+3*u[1]^5*u[2]^2+34*u[1]*u[2]-24*u[2]-24*u[1]+4*u[2]^2*u[1]+42*u[1]^2*u[2]-84*u[1]^2*u[2]^2-12*u[1]^3*u[2]^3-14*u[1]*u[2]^3-3*u[1]^3*u[2]^4+42*u[1]^2*u[2]^3-21*u[1]^4*u[2]^4+33*u[1]^3*u[2]^2+2*u[1]^4*u[2]^3-45*u[1]^6*u[2]^2+87*u[1]^5*u[2]^4-132*u[1]^5*u[2]^3+126*u[1]^6*u[2]^3-69*u[1]^6*u[2]^4-12*u[1]^6*u[2])*bar((u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]))/(u[2]*(-1+u[1]*u[2])*(u[1]-1)^3)+(3/2)*u[1]^2*(-6-3*u[1]^3+6*u[2]^3-66*u[1]^4*u[2]^2+20*u[1]^4*u[2]-18*u[2]^2-20*u[1]^3*u[2]-6*u[1]^5*u[2]+18*u[1]^5*u[2]^2-8*u[1]*u[2]+18*u[2]+3*u[1]+u[1]^2+6*u[2]^2*u[1]+4*u[1]^2*u[2]-18*u[1]^2*u[2]^2-84*u[1]^3*u[2]^3-u[1]*u[2]^4+29*u[1]^3*u[2]^4+20*u[1]^2*u[2]^3-7*u[1]^2*u[2]^4-23*u[1]^4*u[2]^4+78*u[1]^3*u[2]^2+u[1]^4+68*u[1]^4*u[2]^3+6*u[1]^5*u[2]^4-18*u[1]^5*u[2]^3)*bar(d(u[2])/(u[2]-1))/(u[2]*(-1+u[1]*u[2])*(u[1]-1)^3)+(3*(5*u[1]*u[2]^3-10*u[2]^2*u[1]+5*u[1]*u[2]-2*u[2]^3+u[2]^2-3+4*u[2]))*u[1]*bar((u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]), (u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]))/((u[1]-1)^2*u[2])-3*u[1]*(-6*u[1]^6*u[2]^3+3*u[1]^6*u[2]^4+3*u[1]^6*u[2]^2+18*u[1]^5*u[2]^3-6*u[1]^5*u[2]^2-10*u[1]^5*u[2]^4-2*u[1]^5*u[2]+6*u[1]^4*u[2]-2*u[1]^4*u[2]^2+10*u[1]^4*u[2]^4-14*u[1]^4*u[2]^3+8*u[1]^3*u[2]^2-4*u[1]^3*u[2]-4*u[1]^3*u[2]^3+8*u[1]^2*u[2]^2-4*u[1]^2*u[2]-4*u[1]^2*u[2]^3+4*u[2]^2*u[1]-2*u[1]*u[2]-2*u[1]*u[2]^3+3*u[2]^2-6*u[2]+3)*bar((u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]), d(u[2])/(u[2]-1))/(u[2]*(u[1]-1)^2*(-1+u[1]*u[2]))+3*u[1]*(-3+3*u[1]^7*u[2]^2-6*u[1]^7*u[2]^3+3*u[1]^7*u[2]^4+2*u[2]^3+10*u[1]^4*u[2]^2-10*u[1]^4*u[2]-7*u[2]^2+8*u[1]^5*u[2]+4*u[1]^5*u[2]^2-12*u[1]*u[2]+8*u[2]+3*u[1]+13*u[2]^2*u[1]+12*u[1]^2*u[2]-17*u[1]^2*u[2]^2+10*u[1]^3*u[2]^3-2*u[1]*u[2]^3-2*u[1]*u[2]^4-5*u[1]^3*u[2]^4-2*u[1]^2*u[2]^3+7*u[1]^2*u[2]^4-10*u[1]^4*u[2]^4-5*u[1]^3*u[2]^2+10*u[1]^4*u[2]^3-9*u[1]^6*u[2]^2+20*u[1]^5*u[2]^4-32*u[1]^5*u[2]^3+24*u[1]^6*u[2]^3-13*u[1]^6*u[2]^4-2*u[1]^6*u[2])*bar(d(u[1])/u[1], (u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]))/(u[2]*(-1+u[1]*u[2])*(u[1]-1)^3)-3*u[1]*(-6*u[1]^6*u[2]^3+3*u[1]^6*u[2]^4+3*u[1]^6*u[2]^2+18*u[1]^5*u[2]^3-6*u[1]^5*u[2]^2-10*u[1]^5*u[2]^4-2*u[1]^5*u[2]+6*u[1]^4*u[2]-2*u[1]^4*u[2]^2+10*u[1]^4*u[2]^4-14*u[1]^4*u[2]^3+8*u[1]^3*u[2]^2-4*u[1]^3*u[2]-4*u[1]^3*u[2]^3+8*u[1]^2*u[2]^2-4*u[1]^2*u[2]-4*u[1]^2*u[2]^3+4*u[2]^2*u[1]-2*u[1]*u[2]-2*u[1]*u[2]^3+3*u[2]^2-6*u[2]+3)*bar(d(u[1])/(u[1]-1), (u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]))/(u[2]*(u[1]-1)^2*(-1+u[1]*u[2]))+3*u[1]*(-6*u[1]^6*u[2]^3+3*u[1]^6*u[2]^4+3*u[1]^6*u[2]^2+18*u[1]^5*u[2]^3-6*u[1]^5*u[2]^2-10*u[1]^5*u[2]^4-2*u[1]^5*u[2]+6*u[1]^4*u[2]-2*u[1]^4*u[2]^2+10*u[1]^4*u[2]^4-14*u[1]^4*u[2]^3+8*u[1]^3*u[2]^2-4*u[1]^3*u[2]-4*u[1]^3*u[2]^3+8*u[1]^2*u[2]^2-4*u[1]^2*u[2]-4*u[1]^2*u[2]^3+4*u[2]^2*u[1]-2*u[1]*u[2]-2*u[1]*u[2]^3+3*u[2]^2-6*u[2]+3)*bar(d(u[1])/(u[1]-1), d(u[2])/(u[2]-1))/(u[2]*(u[1]-1)^2*(-1+u[1]*u[2]))-3*u[1]*(4*u[1]^2*u[2]^2-7*u[1]^2*u[2]^3+5*u[1]^3*u[2]-10*u[1]^3*u[2]^2+5*u[1]^3*u[2]^3+4*u[2]^2*u[1]-14*u[1]*u[2]+13*u[1]^2*u[2]+2*u[1]*u[2]^3-10*u[1]^2+4*u[2]-2+8*u[1]-2*u[2]^2)*bar(d(u[2])/u[2], (u[2]*d(u[1])+u[1]*d(u[2]))/(-1+u[1]*u[2]))/((-1+u[1]*u[2])*(u[1]-1)^3)+3*u[1]^5*(20*u[1]*u[2]^3-13*u[1]^2*u[2]^3+24*u[1]^2*u[2]^2+4*u[1]*u[2]+3*u[1]^3*u[2]^3-32*u[2]^2*u[1]-6*u[1]^3*u[2]^2-9*u[1]^2*u[2]+3*u[1]^3*u[2]-10*u[2]^3+8*u[1]-10-2*u[1]^2+10*u[2]+10*u[2]^2)*bar(d(u[2])/u[2], d(u[2])/(u[2]-1))/((-1+u[1]*u[2])*(u[1]-1)^3)-(1/4)*(-72*u[1]^5*u[2]^2+36*u[1]^5*u[2]^3+36*u[1]^5*u[2]-99*u[1]^4*u[2]-6*u[1]^4+216*u[1]^4*u[2]^2-111*u[1]^4*u[2]^3+12*u[1]^3-176*u[1]^3*u[2]^2+70*u[1]^3*u[2]+94*u[1]^3*u[2]^3-83*u[1]^2*u[2]^3+6*u[1]^2+172*u[1]^2*u[2]^2-95*u[1]^2*u[2]-92*u[2]^2*u[1]-12*u[1]+64*u[1]*u[2]+40*u[1]*u[2]^3-24+48*u[2]-24*u[2]^2)*u[1]/((u[1]-1)^2*(-1+u[1]*u[2])),
-(1/24)*(-60+1872*u[1]^3-1416*u[1]^2+468*u[1]+960*u[1]^6-1032*u[1]^5-444*u[1]^4+72*u[1]^8-420*u[1]^7-504*u[1]^3*zeta(2)+72*u[1]^8*zeta(2)-504*u[1]^7*zeta(2)+1512*u[1]^6*zeta(2)-2520*u[1]^5*zeta(2)+1944*u[1]^4*zeta(2))*bar(d(u[1])/(u[1]-1))/((u[1]-1)^3*u[1]^2)-(1/24)*(1248*u[1]^6+24*u[1]^4-408*u[1]^5-72*u[1]^9+456*u[1]^8-1128*u[1]^7+180*u[1]+744*u[1]^3-756*u[1]^2)*bar(d(u[1])/u[1], d(u[1])/(u[1]-1))/((u[1]-1)^3*u[1]^2)-(1/24)*(-1716*u[1]^6+1692*u[1]^5-1368*u[1]^4+648*u[1]^3+60*u[1]^2-156*u[1]+72*u[1]^9-456*u[1]^8+1200*u[1]^7+24)*bar(d(u[1])/(u[1]-1), d(u[1])/(u[1]-1))/((u[1]-1)^3*u[1]^2)-(1/24)*(288*u[1]^3-1512*u[1]^6-1728*u[1]^4+2520*u[1]^5+504*u[1]^7-72*u[1]^8)*bar(d(u[1])/u[1], d(u[1])/u[1], d(u[1])/(u[1]-1))/((u[1]-1)^3*u[1]^2)-(1/24)*(792*u[1]^3-504*u[1]^2+72*u[1]-360*u[1]^4)*bar(d(u[1])/u[1], d(u[1])/(u[1]-1), d(u[1])/(u[1]-1))/((u[1]-1)^3*u[1]^2)-(1/24)*(-576*u[1]^4+1008*u[1]^3-504*u[1]^2+72*u[1])*bar(d(u[1])/(u[1]-1), d(u[1])/u[1], d(u[1])/(u[1]-1))/((u[1]-1)^3*u[1]^2)-(1/24)*(-504*u[1]^7+1512*u[1]^6-2520*u[1]^5+2520*u[1]^4+72*u[1]^8-1512*u[1]^3+504*u[1]^2-72*u[1])*bar(d(u[1])/(u[1]-1), d(u[1])/(u[1]-1), d(u[1])/(u[1]-1))/((u[1]-1)^3*u[1]^2)-(1/24)*(-1901*u[1]^3-474*u[1]^7-504*u[1]^4*zeta(2)+72*u[1]^8-60*u[1]+606*u[1]^2+1200*u[1]^7*zeta(2)+1692*u[1]^5*zeta(2)-1716*u[1]^6*zeta(2)+72*u[1]^9*zeta(2)-456*u[1]^8*zeta(2)+2529*u[1]^4+1325*u[1]^6-2097*u[1]^5)/((u[1]-1)^3*u[1]^2),
(225/4)*zeta(3)-(266/5)*zeta(2)+(33/5)*zeta(2)^2+391/192]:
# Computation:
mistakes:=[]:
MPLInitialize(u, 3):
Int1:=CorrectIntermediateResults[1]:
Int2:=MPLCubicalIntegrate(Int1, u[4], 1);
Int3:=MPLCubicalIntegrate(Int2, u[3], 1);
Int4:=MPLCubicalIntegrate(Int3, u[2], 1);
FinalResult:=MPLCubicalIntegrate(Int4, u[1], 1):
IntermediateResults:=[Int1, Int2, Int3, Int4, FinalResult]: 
# Compare with correct results:
for i from 1 to nops(CorrectIntermediateResults) do
 newdifference:=factor(CorrectIntermediateResults[i]-IntermediateResults[i]):
 if not(newdifference=0) then 
mistakes:=[op(mistakes), IntermediateResults[i-1]]:
 end if:
end do:
# If outputinfo=true the inputs which gave wrong results are shown.
if outputinfo=true then
 if mistakes=[] then print("Checks for Cellzeta3 are ok."):
 else
  print("Error: The procedure MPLint gives wrong results for the following integrand during the evaluation of Cellzeta3:"):
  print(mistakes):
 end if:
end if:
# The return value is true if everything was correct and false otherwise.
if mistakes=[] then return true:
else return false:
end if:
end proc:







# This procedure checks MPLLimit for some examples. For comparisons we used
# RegValue1[2] from Francis' program.
TestRegLength2:=proc(outputinfo)
local i, newterm, mistakes, ListInput, ListCorrectResults, newdifference:
MPLInitialize(v, 2,false, true):
NULL;
# The list of terms to be expanded is:
ListInput:=[1, bar(d(v[3])/v[3]), bar(d(v[3])/(v[3]-1)), bar((v[3]*d(v[2])+v[2]*d(v[3]))/(v[2]*v[3]-1)), bar((v[2]*v[3]*d(v[1])+v[1]*v[3]*d(v[2])+v[1]*v[2]*d(v[3]))/(v[1]*v[2]*v[3]-1)), 
bar(d(v[3])/v[3], d(v[3])/v[3]),
bar(d(v[3])/(v[3]-1), d(v[3])/v[3]),
SymbolsToTotal(IntWordsRecursive(bar(v[2]*d(v[3])/(v[2]*v[3]-1), d(v[3])/v[3]))), 
SymbolsToTotal(IntWordsRecursive(bar(v[1]*v[2]*d(v[3])/(v[1]*v[2]*v[3]-1), d(v[3])/v[3]))), 
SymbolsToTotal(IntWordsRecursive(bar(d(v[3])/(v[3]), d(v[3])/(v[3]-1)))), 
SymbolsToTotal(IntWordsRecursive(bar(d(v[3])/(v[3]-1), d(v[3])/(v[3]-1)))), 
SymbolsToTotal(IntWordsRecursive(bar(v[2]*d(v[3])/(v[2]*v[3]-1),d(v[3])/(v[3]-1)))),
SymbolsToTotal(IntWordsRecursive(bar(v[1]*v[2]*d(v[3])/(v[1]*v[2]*v[3]-1), d(v[3])/(v[3]-1)))),
SymbolsToTotal(IntWordsRecursive(bar(d(v[3])/(v[3]), v[2]*d(v[3])/(v[2]*v[3]-1)))),

SymbolsToTotal(IntWordsRecursive(bar(d(v[3])/(v[3]-1), v[2]*d(v[3])/(v[2]*v[3]-1)))),
SymbolsToTotal(IntWordsRecursive(bar(v[2]*d(v[3])/(v[2]*v[3]-1), v[2]*d(v[3])/(v[2]*v[3]-1)))),
SymbolsToTotal(IntWordsRecursive(bar(v[1]*v[2]*d(v[3])/(v[1]*v[2]*v[3]-1), v[2]*d(v[3])/(v[2]*v[3]-1)))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[3])/(v[3]), v[1]*v[2]*d(v[3])/(v[1]*v[2]*v[3]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[3])/(v[3]-1), v[1]*v[2]*d(v[3])/(v[1]*v[2]*v[3]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( v[2]*d(v[3])/(v[2]*v[3]-1), v[1]*v[2]*d(v[3])/(v[1]*v[2]*v[3]-1) )))
]:
# The corresponding correct expansions at v[3]=1 are:
ListCorrectResults:=[1, 0, 0, bar(d(v[2])/(v[2]-1)), bar((v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2])), 0, Zeta(2), -bar(d(v[2])/v[2], d(v[2])/(v[2]-1)), -bar(d(v[1])/v[1], (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))-bar(d(v[2])/v[2], (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2])), -Zeta(2), 0, -bar(d(v[2])/v[2], d(v[2])/(v[2]-1))+bar(d(v[2])/(v[2]-1), d(v[2])/(v[2]-1)), bar((v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]), (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))-bar(d(v[1])/v[1], (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))-bar(d(v[2])/v[2], (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2])), bar(d(v[2])/v[2], d(v[2])/(v[2]-1)), bar(d(v[2])/v[2], d(v[2])/(v[2]-1))-bar(d(v[2])/(v[2]-1), d(v[2])/(v[2]-1)), bar(d(v[2])/(v[2]-1), d(v[2])/(v[2]-1)), bar((v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]), d(v[2])/(v[2]-1))-bar(d(v[1])/v[1], (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))+bar(d(v[1])/(v[1]-1), (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))-bar(d(v[1])/(v[1]-1), d(v[2])/(v[2]-1)), bar(d(v[1])/v[1], (v[2]*d(v[1])+v[1]*d(v[2]))/(-
1+v[1]*v[2]))+bar(d(v[2])/v[2], (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2])), -bar((v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]), (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))+bar(d(v[1])/v[1], (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))+bar(d(v[2])/v[2], (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2])), bar(d(v[1])/v[1], (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))-bar(d(v[1])/(v[1]-1), (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))+bar(d(v[1])/(v[1]-1), d(v[2])/(v[2]-1))+bar(d(v[2])/(v[2]-1), (v[2]*d(v[1])+v[1]*d(v[2]))/(-1+v[1]*v[2]))]:
print(nops(ListCorrectResults));
mistakes:=[]:
for i from 1 to nops(ListCorrectResults) do
 # Don't test the cases where the limit is infinite.
 if (not(i=3) and not(i=15) and not(i=19)) then 
  newterm:=factor(MPLLimit(ListInput[i], v[3], 1)):
  newdifference:=eval(eval(factor(newterm-ListCorrectResults[i]), zeta=Zeta)):
  if not(newdifference=0) then mistakes:=[op(mistakes), ListInput[i]]:
  end if:
 end if:
end do:
# If outputinfo=true the inputs which gave wrong results are shown.
if outputinfo=true then
 if mistakes=[] then print("All checks for the procedure Reg for length 2 are ok."):
 else
  print("Error: The procedude Reg gives wrong results for the following test arguments, evaluated at v[3]=1:"):
  print(mistakes):
 end if:
end if:
# The return value is true if everything was correct and false otherwise.
if mistakes=[] then return true:
else return false:
end if:
end proc:






# This procedure checks Reg for all words examples of up to length 3 with two variables. For comparisons we used
# RegValue1[3] from Francis' program.
TestRegLength3:=proc(outputinfo)
local i, newterm, mistakes, ListInput, ListCorrectResults, newdifference:
MPLInitialize(v, 1, false, true):
NULL;
# The list of terms to be expanded is:
ListInput:=eval(subs(MPLb[3]=0,[1,
bar(d(v[2])/v[2]),
bar(d(v[2])/(v[2]-1)),
bar((v[2]*d(v[1])+v[1]*d(v[2]))/(v[1]*v[2]-1)),
bar(d(v[2])/v[2], d(v[2])/v[2]),
bar( d(v[2])/(v[2]-1), d(v[2])/v[2]),
SymbolsToTotal(IntWordsRecursive(bar( (v[1]*d(v[2]))/(v[1]*v[2]-1)) , d(v[2])/v[2] )),
bar( d(v[2])/v[2] , d(v[2])/(v[2]-1) ),
bar( d(v[2])/(v[2]-1) , d(v[2])/(v[2]-1)),
SymbolsToTotal(IntWordsRecursive(bar( v[1]*d(v[2])/(v[1]*v[2]-1)  , d(v[2])/(v[2]-1)  ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/v[2] , v[1]*d(v[2])/(v[1]*v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/(v[2]-1) , v[1]*d(v[2])/(v[1]*v[2]-1) ))), 
SymbolsToTotal(IntWordsRecursive(bar( v[1]*d(v[2])/(v[1]*v[2]-1) , v[1]*d(v[2])/(v[1]*v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/v[2] , d(v[2])/v[2] , d(v[2])/v[2] ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/(v[2]-1) , d(v[2])/v[2] , d(v[2])/v[2]  ))),
SymbolsToTotal(IntWordsRecursive(bar( v[1]*d(v[2])/(v[1]*v[2]-1) , d(v[2])/v[2] , d(v[2])/v[2] ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/v[2] , d(v[2])/(v[2]-1) , d(v[2])/v[2] ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/(v[2]-1) , d(v[2])/(v[2]-1) , d(v[2])/v[2]))),
SymbolsToTotal(IntWordsRecursive(bar( v[1]*d(v[2])/(v[1]*v[2]-1) , d(v[2])/(v[2]-1) ,d(v[2])/v[2] ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/v[2] , v[1]*d(v[2])/(v[1]*v[2]-1) , d(v[2])/v[2] ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/(v[2]-1) , v[1]*d(v[2])/(v[1]*v[2]-1) , d(v[2])/v[2] ))),
SymbolsToTotal(IntWordsRecursive(bar( v[1]*d(v[2])/(v[1]*v[2]-1) , v[1]*d(v[2])/(v[1]*v[2]-1) , d(v[2])/v[2] ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/v[2] , d(v[2])/v[2] , d(v[2])/(v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/(v[2]-1) , d(v[2])/v[2] , d(v[2])/(v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( v[1]*d(v[2])/(v[1]*v[2]-1) , d(v[2])/v[2] , d(v[2])/(v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/v[2] , d(v[2])/(v[2]-1) , d(v[2])/(v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/(v[2]-1) , d(v[2])/(v[2]-1) , d(v[2])/(v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( v[1]*d(v[2])/(v[1]*v[2]-1) , d(v[2])/(v[2]-1) , d(v[2])/(v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/v[2] , v[1]*d(v[2])/(v[1]*v[2]-1) , d(v[2])/(v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/(v[2]-1) , v[1]*d(v[2])/(v[1]*v[2]-1) , d(v[2])/(v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( v[1]*d(v[2])/(v[1]*v[2]-1) , v[1]*d(v[2])/(v[1]*v[2]-1) , d(v[2])/(v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/v[2] , d(v[2])/v[2] ,  v[1]*d(v[2])/(v[1]*v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/(v[2]-1) , d(v[2])/v[2] , v[1]*d(v[2])/(v[1]*v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( v[1]*d(v[2])/(v[1]*v[2]-1) , d(v[2])/v[2] , v[1]*d(v[2])/(v[1]*v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/v[2] , d(v[2])/(v[2]-1) , v[1]*d(v[2])/(v[1]*v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/(v[2]-1) , d(v[2])/(v[2]-1) , v[1]*d(v[2])/(v[1]*v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( v[1]*d(v[2])/(v[1]*v[2]-1) , d(v[2])/(v[2]-1) , v[1]*d(v[2])/(v[1]*v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/v[2] , v[1]*d(v[2])/(v[1]*v[2]-1) , v[1]*d(v[2])/(v[1]*v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( d(v[2])/(v[2]-1) , v[1]*d(v[2])/(v[1]*v[2]-1) , v[1]*d(v[2])/(v[1]*v[2]-1) ))),
SymbolsToTotal(IntWordsRecursive(bar( v[1]*d(v[2])/(v[1]*v[2]-1) , v[1]*d(v[2])/(v[1]*v[2]-1) , v[1]*d(v[2])/(v[1]*v[2]-1) )))
])):
# The corresponding correct values at v[2]=1 are:
ListCorrectResults:=[1, 0, 0, bar(d(v[1])/(v[1]-1)), 0, Zeta(2), bar(d(v[1])/(v[1]-1)), -Zeta(2), 0, -bar(d(v[1])/v[1], d(v[1])/(v[1]-1))+bar(d(v[1])/(v[1]-1), d(v[1])/(v[1]-1)), bar(d(v[1])/v[1], d(v[1])/(v[1]-1)), bar(d(v[1])/v[1], d(v[1])/(v[1]-1))-bar(d(v[1])/(v[1]-1), d(v[1])/(v[1]-1)), bar(d(v[1])/(v[1]-1), d(v[1])/(v[1]-1)), 0, -Zeta(3), bar(d(v[1])/v[1], d(v[1])/v[1], d(v[1])/(v[1]-1)), 2*Zeta(3), Zeta(3), bar(d(v[1])/v[1], d(v[1])/v[1], d(v[1])/(v[1]-1))-bar(d(v[1])/(v[1]-1), d(v[1])/v[1], d(v[1])/(v[1]-1)), -2*bar(d(v[1])/v[1], d(v[1])/v[1], d(v[1])/(v[1]-1)), -2*bar(d(v[1])/v[1], d(v[1])/v[1], d(v[1])/(v[1]-1))+bar(d(v[1])/v[1], d(v[1])/(v[1]-1), d(v[1])/(v[1]-1))+bar(d(v[1])/(v[1]-1), d(v[1])/v[1], d(v[1])/(v[1]-1))+bar(d(v[1])/(v[1]-1))*Zeta(2), -bar(d(v[1])/(v[1]-1), d(v[1])/v[1], d(v[1])/(v[1]-1))-bar(d(v[1])/v[1], d(v[1])/(v[1]-1), d(v[1])/(v[1]-1)), -Zeta(3), -2*Zeta(3), -bar(d(v[1])/(v[1]-1))*Zeta(2)+bar(d(v[1])/v[1], d(v[1])/v[1], d(v[1])/(v[1]-1))-bar(d(v[1])/v[1], d(v[1])/(v[1]-1), d(v[1]
)/(v[1]-1)), Zeta(3), 0, bar(d(v[1])/v[1], d(v[1])/v[1], d(v[1])/(v[1]-1))-bar(d(v[1])/v[1], d(v[1])/(v[1]-1), d(v[1])/(v[1]-1))-bar(d(v[1])/(v[1]-1), d(v[1])/v[1], d(v[1])/(v[1]-1))+bar(d(v[1])/(v[1]-1), d(v[1])/(v[1]-1), d(v[1])/(v[1]-1)), -2*bar(d(v[1])/v[1], d(v[1])/v[1], d(v[1])/(v[1]-1))+bar(d(v[1])/v[1], d(v[1])/(v[1]-1), d(v[1])/(v[1]-1))+bar(d(v[1])/(v[1]-1), d(v[1])/v[1], d(v[1])/(v[1]-1))+bar(d(v[1])/(v[1]-1))*Zeta(2), -2*bar(d(v[1])/v[1], d(v[1])/v[1], d(v[1])/(v[1]-1))+2*bar(d(v[1])/v[1], d(v[1])/(v[1]-1), d(v[1])/(v[1]-1))+2*bar(d(v[1])/(v[1]-1), d(v[1])/v[1], d(v[1])/(v[1]-1))-2*bar(d(v[1])/(v[1]-1), d(v[1])/(v[1]-1), d(v[1])/(v[1]-1)), bar(d(v[1])/(v[1]-1), d(v[1])/(v[1]-1), d(v[1])/(v[1]-1))-bar(d(v[1])/v[1], d(v[1])/(v[1]-1), d(v[1])/(v[1]-1)), bar(d(v[1])/v[1], d(v[1])/v[1], d(v[1])/(v[1]-1)), bar(d(v[1])/v[1], d(v[1])/v[1], d(v[1])/(v[1]-1))-bar(d(v[1])/v[1], d(v[1])/(v[1]-1), d(v[1])/(v[1]-1)), bar(d(v[1])/(v[1]-1), d(v[1])/v[1], d(v[1])/(v[1]-1)), bar(d(v[1])/v[1], d(v[1])/v[1], d(v[1])/
(v[1]-1))-bar(d(v[1])/(v[1]-1), d(v[1])/v[1], d(v[1])/(v[1]-1))-bar(d(v[1])/(v[1]-1))*Zeta(2), bar(d(v[1])/v[1], d(v[1])/v[1], d(v[1])/(v[1]-1))-bar(d(v[1])/v[1], d(v[1])/(v[1]-1), d(v[1])/(v[1]-1))-bar(d(v[1])/(v[1]-1), d(v[1])/v[1], d(v[1])/(v[1]-1))+bar(d(v[1])/(v[1]-1), d(v[1])/(v[1]-1), d(v[1])/(v[1]-1)), -bar(d(v[1])/(v[1]-1), d(v[1])/v[1], d(v[1])/(v[1]-1))+bar(d(v[1])/(v[1]-1), d(v[1])/(v[1]-1), d(v[1])/(v[1]-1)), bar(d(v[1])/v[1], d(v[1])/(v[1]-1), d(v[1])/(v[1]-1)), bar(d(v[1])/v[1], d(v[1])/(v[1]-1), d(v[1])/(v[1]-1))-2*bar(d(v[1])/(v[1]-1), d(v[1])/(v[1]-1), d(v[1])/(v[1]-1))+bar(d(v[1])/(v[1]-1), d(v[1])/v[1], d(v[1])/(v[1]-1)), bar(d(v[1])/(v[1]-1), d(v[1])/(v[1]-1), d(v[1])/(v[1]-1))]:
print(nops(ListCorrectResults));
mistakes:=[]:
for i from 1 to nops(ListCorrectResults) do
 # Don't test the cases where the limit is infinite.
 if (not(i=3) ) then 
  newterm:=factor(Reg(ListInput[i], v[2])):
  newdifference:=eval(eval(factor(newterm-ListCorrectResults[i]), zeta=Zeta)):
  if not(newdifference=0) then mistakes:=[op(mistakes), ListInput[i]]:
  end if:
 end if:
end do:
# If outputinfo=true the inputs which gave wrong results are shown.
if outputinfo=true then
 if mistakes=[] then print("All checks for the procedure Reg with two variables and up to length 3 are ok."):
 else
  print("Error: The procedure Reg gives wrong results for the following test arguments, evaluated at v[2]=1:"):
  print(mistakes):
 end if:
end if:
# The return value is true if everything was correct and false otherwise.
if mistakes=[] then return true:
else return false:
end if:
end proc:


# The following tests the procedure MPLUnshuffle, also using MPLSymbolAndShuffle. 

TestMPLUnshuffle:=proc()
local i, unsh, TestInputList1, TestInputList2, ProblemList, ErrorOcurred, diff:
ProblemList:=[]:
ErrorOcurred:=0:
MPLInitialize(z, 1):
TestInputList1:=[4+bar(d(z[2])/z[2], (z[2]*d(z[1])+z[1]*d(z[2]))/(1-z[1]*z[2]))+5*bar((d(z[1]))/(z[1]),d(z[2])/(1-z[2]))+bar(d(z[2])/z[2])+3*bar(d(z[1])/z[1], d(z[1])/(1-z[1]))+bar(d(z[1])/z[1]),
bar((z[2]*d(z[1])+z[1]*d(z[2]))/(1-z[1]*z[2]))+8,
5,
20*bar((z[2]*d(z[1])+z[1]*d(z[2]))/(1-z[1]*z[2]), d(z[2])/(1-z[2]),d(z[1])/(1-z[1]),d(z[1])/(1-z[1]),d(z[2])/z[2])+bar(d(z[2])/z[2])]:
for i from 1 to nops(TestInputList1) do
 unsh:=MPLUnshuffle(TestInputList1[i], z[2]):
 diff:=eval(TestInputList1[i]-MPLSymbolAndShuffle(unsh)):
 if not(diff=0) then
  ProblemList:=[op(ProblemList), TestInputList1[i]]:
  ErrorOcurred:=1:
 end if:
end do:
MPLInitialize(z, 3):
TestInputList2:=[bar(d(z[4])/(1-z[4])),
bar((z[2]*d(z[1])+z[1]*d(z[2]))/(1-z[1]*z[2]), d(z[2])/(1-z[2]), d(z[3])/z[3], (z[2]*z[3]*d(z[1])+z[1]*z[3]*d(z[2])+z[1]*z[2]*d(z[3]))/(1-z[1]*z[2]*z[3]))+8,
bar((z[3]*z[4]*d(z[2])+z[2]*z[4]*d(z[3])+z[2]*z[3]*d(z[4]))/(1-z[2]*z[3]*z[4]), (z[2]*z[3]*d(z[1])+z[1]*z[3]*d(z[2])+z[1]*z[2]*d(z[3]))/(1-z[1]*z[2]*z[3]),d(z[4])/z[4],(z[2]*z[3]*z[4]*d(z[1])+z[1]*z[3]*z[4]*d(z[2])+z[1]*z[2]*z[4]*d(z[3])+z[1]*z[2]*z[3]*d(z[4]))/(1-z[1]*z[2]*z[3]*z[4]))+7*bar((z[2]*z[3]*d(z[1])+z[1]*z[3]*d(z[2])+z[1]*z[2]*d(z[3]))/(1-z[1]*z[2]*z[3]), (z[3]*d(z[2])+z[2]*d(z[3]))/(1-z[2]*z[3]), (z[4]*d(z[3])+z[3]*d(z[4]))/(1-z[3]*z[4])),
99+78*z[1]+17*bar((z[2]*z[3]*z[4]*d(z[1])+z[1]*z[3]*z[4]*d(z[2])+z[1]*z[2]*z[4]*d(z[3])+z[1]*z[2]*z[3]*d(z[4]))/(1-z[1]*z[2]*z[3]*z[4]))]:
for i from 1 to nops(TestInputList2) do
 unsh:=MPLUnshuffle(TestInputList2[i], z[4]):
 diff:=eval(TestInputList2[i]-MPLSymbolAndShuffle(unsh)):
 if not(diff=0) then
  ProblemList:=[op(ProblemList), TestInputList2[i]]:
  ErrorOcurred:=1:
 end if:
end do:
if not(ErrorOcurred=0) then
 print("Error: The procedure MPLUnshuffle (or MPLSymbolAndShuffle) gives wrong results for the following test arguments:"):
 print(ProblemList):
else 
 print("All checks for the procedure MPLUnshuffle are ok."):
end if:
end proc:




# The following procedure wraps up some of the automated tests above:

MPLAutomatedTests:=proc()
TestLimitAtOne(true);
TestLimitAtZero(true);
TestRegularizedZeta(true);
TestCellZeta1(true);
TestCellZeta2(true);
TestCellZeta3(true);
TestRegLength2(true);
TestRegLength3(true);
TestMPLUnshuffle();
end proc:





####################################################################
####################################################################
#
#   EXECUTE
#
####################################################################
####################################################################

# The Arnold Equations from MPLnumberofvar=0 to MPLnumberofvar=12:

MPLLowestArnoldEquations:=[[[[1, -1, -1], [0, 0, 0], [-MPLft[2], MPLft[1], -MPLft[2]]]], [[[1, -1, -1], [0, 0, MPLb[1]], [-MPLft[2], MPLft[1], -MPLft[2]]], [[1, -1, 1, -1], [MPLb[1], MPLb[1], MPLb[1], MPLb[1]], [-MPLft[3], MPLft[1], MPLft[1], -MPLft[3]]], [[1, -1, -1], [-MPLb[2], -MPLb[2], MPLb[1]], [-MPLft[2], -MPLft[3], -MPLft[2]]]], [[[1, -1, -1, -1], [0, 0, MPLb[1], MPLb[3]], [-MPLft[2], MPLft[1], -MPLft[2], -MPLft[2]]], [[1, -1, 1, -1, -1], [MPLb[1], MPLb[1], MPLb[1], MPLb[1], MPLb[3]], [-MPLft[3], MPLft[1], MPLft[1], -MPLft[3], -MPLft[3]]], [[1, -1, -1], [-MPLb[2], -MPLb[2], MPLb[1]], [-MPLft[2], -MPLft[3], -MPLft[2]]], [[1, 1, -1, -1, 1, 1, -1, -1], [MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3]], [-MPLft[4], -MPLft[4], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[4], -MPLft[4]]], [[1, -1, -1, -1], [-MPLb[4], -MPLb[4], MPLb[1], MPLb[3]], [-MPLft[2], -MPLft[4], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1], [MPLb[1], -MPLb[5], MPLb[1], -MPLb[5], MPLb[1], MPLb[1], MPLb[3]], [-MPLft[4], -MPLft[4], -MPLft[3], -MPLft[3], -MPLft[4], -MPLft[3], -MPLft[3]]]], [[[1, -1, -1, -1, -1], [0, 0, MPLb[1], MPLb[3], MPLb[6]], [-MPLft[2], MPLft[1], -MPLft[2], -MPLft[2], -MPLft[2]]], [[1, -1, 1, -1, -1, -1], [MPLb[1], MPLb[1], MPLb[1], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[3], MPLft[1], MPLft[1], -MPLft[3], -MPLft[3], -MPLft[3]]], [[1, -1, -1], [-MPLb[2], -MPLb[2], MPLb[1]], [-MPLft[2], -MPLft[3], -MPLft[2]]], [[1, 1, -1, -1, 1, 1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[4], -MPLft[4], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, -1, -1, -1], [-MPLb[4], -MPLb[4], MPLb[1], MPLb[3]], [-MPLft[2], -MPLft[4], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1], [MPLb[1], -MPLb[5], MPLb[1], -MPLb[5], MPLb[1], MPLb[1], MPLb[3]], [-MPLft[4], -MPLft[4], -MPLft[3], -MPLft[3], -MPLft[4], -MPLft[3], -MPLft[3]]], [[1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[5], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[5], -MPLft[5], -MPLft[5]]], [[1, -1, -1, -1, -1], [-MPLb[7], -MPLb[7], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[2], -MPLft[5], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1], [MPLb[1], -MPLb[8], MPLb[1], -MPLb[8], MPLb[1], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4]]]], [[[1, -1, -1, -1, -1, -1], [0, 0, MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[2], MPLft[1], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[1, -1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[1], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[3], MPLft[1], MPLft[1], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[1, -1, -1], [-MPLb[2], -MPLb[2], MPLb[1]], [-MPLft[2], -MPLft[3], -MPLft[2]]], [[1, 1, -1, -1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[4], -MPLft[4], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, -1, -1, -1], [-MPLb[4], -MPLb[4], MPLb[1], MPLb[3]], [-MPLft[2], -MPLft[4], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1], [MPLb[1], -MPLb[5], MPLb[1], -MPLb[5], MPLb[1], MPLb[1], MPLb[3]], [-MPLft[4], -MPLft[4], -MPLft[3], -MPLft[3], -MPLft[4], -MPLft[3], -MPLft[3]]], [[1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[5], -MPLft[5], -MPLft[5], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[1, -1, -1, -1, -1], [-MPLb[7], -MPLb[7], 
MPLb[1], MPLb[3], MPLb[6]], [-MPLft[2], -MPLft[5], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1], [MPLb[1], -MPLb[8], MPLb[1], -MPLb[8], MPLb[1], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[1, -1, -1, -1, -1, -1], [-MPLb[11], -MPLb[11], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[2], -MPLft[6], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], -MPLb[12], MPLb[1], -MPLb[12], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[3], -MPLft[3], -MPLft[6],
 -MPLft[3], -MPLft[3], -MPLft[3], -
MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[13], MPLb[1], MPLb[3], -MPLb[13], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[6], -MPLft[6], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[14], MPLb[1], MPLb[3], MPLb[6], -MPLb[14], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]]], [[[1, -1, -1, -1, -1, -1, -1], [0, 0, MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[2], MPLft[1], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[1, -1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[1], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[3], MPLft[1], MPLft[1], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[1, -1, -1], [-MPLb[2], -MPLb[2], MPLb[1]], [-MPLft[2], -MPLft[3], -MPLft[2]]], [[1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[4], -MPLft[4], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, -1, -1, -1], [-MPLb[4], -MPLb[4], MPLb[1], MPLb[3]], [-MPLft[2], -MPLft[4], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1], [MPLb[1], -MPLb[5], MPLb[1], -MPLb[5], MPLb[1], MPLb[1], MPLb[3]], [-MPLft[4], -MPLft[4], -MPLft[3], -MPLft[3], -MPLft[4], -MPLft[3], -MPLft[3]]], [[1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[5], -MPLft[5], -MPLft[5], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[1, -1, -1, -1, -1], [-MPLb[7], -MPLb[7], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[2], -MPLft[5], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1], [MPLb[1], -MPLb[8], MPLb[1], -MPLb[8], MPLb[1], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[1, -1, -1, -1, -1, -1], [-MPLb[11], -MPLb[11], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[2], -MPLft[6], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], -MPLb[12], MPLb[1], -MPLb[12], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[3], -MPLft[3], -MPLft[6], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[13], MPLb[1], MPLb[3], -MPLb[13], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[6], -MPLft[6], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[14], MPLb[1], MPLb[3], MPLb[6], -MPLb[14], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1,
 -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[1, -1, -1, -1, -1, -1, -1], [-MPLb[16], -MPLb[16], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[2], -MPLft[7], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[17], MPLb[1], -MPLb[17], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[3], -MPLft[3], -MPLft[7], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[18], MPLb[1], MPLb[3], -MPLb[18], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[7], -MPLft[7], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[19], MPLb[1], MPLb[3], MPLb[6]
, -MPLb[19], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[20], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[20], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]]], [[[1, -1, -1, -1, -1, -1, -1, -1], [0, 0, MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[2], MPLft[1], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[1, -1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[1], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[3], MPLft[1], MPLft[1], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[1, -1, -1], [-MPLb[2], -MPLb[2], MPLb[1]], [-MPLft[2], -MPLft[3], -MPLft[2]]], [[1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[4], -MPLft[4], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, -1, -1, -1], [-MPLb[4], -MPLb[4], MPLb[1], MPLb[3]], [-MPLft[2], -MPLft[4], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1], [MPLb[1], -MPLb[5], MPLb[1], -MPLb[5], MPLb[1], MPLb[1], MPLb[3]], [-MPLft[4], -MPLft[4], -MPLft[3], -MPLft[3], -MPLft[4], -MPLft[3], -MPLft[3]]], [[1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[5], -MPLft[5], -MPLft[5], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[1, -1, -1, -1, -1], [-MPLb[7], -MPLb[7], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[2], -MPLft[5], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1], [MPLb[1], -MPLb[8], MPLb[1], -MPLb[8], MPLb[1], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[1, -1, -1, -1, -1, -1], [-MPLb[11], -MPLb[11], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[2], -MPLft[6], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], -MPLb[12], MPLb[1], -MPLb[12], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[3], -MPLft[3], -MPLft[6], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[13], MPLb[1], MPLb[3], -MPLb[13], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[6], -MPLft[6], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[14], MPLb[1], MPLb[3], MPLb[6], -MPLb[14], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -
MPLft[6], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[1, -1, -1, -1, -1, -1, -1], [-MPLb[16], -MPLb[16], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[2], -MPLft[7], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[17], MPLb[1], -MPLb[17], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[3], -MPLft[3], -MPLft[7], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[18], MPLb[1], MPLb[3], -MPLb[18], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[7], -MPLft[7]
, -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[19], MPLb[1], MPLb[3], MPLb[6], -MPLb[19], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[20], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[20], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[22], -MPLb[22], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[2], -MPLft[8], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[23], MPLb[1], -MPLb[23], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[3], -MPLft[3], -MPLft[8], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[24], MPLb[1], MPLb[3], -MPLb[24], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[8], -MPLft[8], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[25], MPLb[1], MPLb[3], MPLb[6], -MPLb[25], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[26], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[26], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[27], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[27], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]]], [[[1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[2], MPLft[1], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[1, -1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[1], MPLb[1], MPLb[1], MPLb[3], MPLb[6], 
MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[3], MPLft[1], MPLft[1], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[1, -1, -1], [-MPLb[2], -MPLb[2], MPLb[1]], [-MPLft[2], -MPLft[3], -MPLft[2]]], [[1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[4], -MPLft[4], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, -1, -1, -1], [-MPLb[4], -MPLb[4], MPLb[1], MPLb[3]], [-MPLft[2], -MPLft[4], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1], [MPLb[1], -MPLb[5], MPLb[1], -MPLb[5], MPLb[1], MPLb[1], MPLb[3]], [-MPLft[4], -MPLft[4], -MPLft[3], -MPLft[3], -MPLft[4], -MPLft[3], -MPLft[3]]], [[1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[5], -MPLft[5], -MPLft[5], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[1, -1, -1, -1, -1], [-MPLb[7], -MPLb[7], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[2], -MPLft[5], -MPLft[2], -
MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1], [MPLb[1], -MPLb[8], MPLb[1], -MPLb[8], MPLb[1], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[1, -1, -1, -1, -1, -1], [-MPLb[11], -MPLb[11], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[2], -MPLft[6], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], -MPLb[12], MPLb[1], -MPLb[12], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[3], -MPLft[3], -MPLft[6], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[13], MPLb[1], MPLb[3], -MPLb[13], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[6], -MPLft[6], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[14], MPLb[1], MPLb[3], MPLb[6], -MPLb[14], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[1, -1, -1, -1, -1, -1, -1], [-MPLb[16], -MPLb[16], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[2], -MPLft[7], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[17], MPLb[1], -MPLb[17], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[3], -MPLft[3], -MPLft[7], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[18], MPLb[1], MPLb[3], -MPLb[18], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[7], -MPLft[7], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[19], MPLb[1], MPLb[3], MPLb[6], -MPLb[19], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[20], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[20], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[6], -MPLft[6], -MPLft[
6], -MPLft[6], -MPLft[6]]], [[1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[22], -MPLb[22], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[2], -MPLft[8], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[23], MPLb[1], -MPLb[23], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[3], -MPLft[3], -MPLft[8], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[24], MPLb[1], MPLb[3], -MPLb[24], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -
MPLft[8], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[8], -MPLft[8], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[25], MPLb[1], MPLb[3], MPLb[6], -MPLb[25], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[26], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[26], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[27], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[27], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[29], -MPLb[29], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[2], -MPLft[9], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[30], MPLb[1], -MPLb[30], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[3], -MPLft[3], -MPLft[9], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[31], MPLb[1], MPLb[3], -MPLb[31], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[9], -MPLft[9], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[32], MPLb[1], MPLb[3], MPLb[6], -MPLb[32], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[33], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[33], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -
MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[34], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[34], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[35], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[35], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]]], [[[1, -1, -1, -1, -1, -1, -1, -1, -1, -1],
 [0, 0, MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[2], MPLft[1], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[1], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[3], MPLft[1], MPLft[1], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[1, -1, -1], [-MPLb[2], -MPLb[2], MPLb[1]], [-MPLft[2], -MPLft[3], -MPLft[2]]], [[1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[4], -MPLft[4], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, -1, -1, -1], [-MPLb[4], -MPLb[4], MPLb[1], MPLb[3]], [-MPLft[2], -MPLft[4], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1], [MPLb[1], -MPLb[5], MPLb[1], -MPLb[5], MPLb[1], MPLb[1], MPLb[3]], [-MPLft[4], -MPLft[4], -MPLft[3], -MPLft[3], -MPLft[4], -MPLft[3], -MPLft[3]]], [[1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[5], -MPLft[5], -MPLft[5], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[1, -1, -1, -1, -1], [-MPLb[7], -MPLb[7], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[2], -MPLft[5], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1], [MPLb[1], -MPLb[8], MPLb[1], -MPLb[8], MPLb[1], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[1, -1, -1, -1, -1, -1], [-MPLb[11], -MPLb[11], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[2], -MPLft[6], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], -MPLb[12], MPLb[1], -MPLb[12], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[3], -MPLft[3], -MPLft[6], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[13], MPLb[1], MPLb[3], -MPLb[13], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[6], -MPLft[6], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[14], MPLb[1], MPLb[3], MPLb[6], -MPLb[14], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], MPLft[1], MPLft[1], MPLft[1], 
MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[1, -1, -1, -1, -1, -1, -1], [-MPLb[16], -MPLb[16], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[2], -MPLft[7], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[17], MPLb[1], -MPLb[17], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[3], -MPLft[3], -MPLft[7], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[18], MPLb[1], MPLb[3], -MPLb[18], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[7], -MPLft[7], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[19], MPLb[1], MPLb[3], MPLb[6], -MPLb[19], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, 
-1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[20], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[20], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[22], -MPLb[22], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[2], -MPLft[8], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[23], MPLb[1], -MPLb[23], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[3], -MPLft[3], -MPLft[8], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[24], MPLb[1], MPLb[3], -MPLb[24], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[8], -MPLft[8], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[25], MPLb[1], MPLb[3], MPLb[6], -MPLb[25], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[26], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[26], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[27], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[27], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1], [-
MPLb[29], -MPLb[29], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[2], -MPLft[9], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[30], MPLb[1], -MPLb[30], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[3], -MPLft[3], -MPLft[9], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[31], MPLb[1], MPLb[3], -MPLb[31], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[9], -MPLft[9], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[32], MPLb[1], MPLb[3], MPLb[6], -MPLb[32], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[33], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[33], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[34], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[34], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[35], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[35], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[37], -MPLb[37], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[2], -MPLft[10], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[38], MPLb[1], -MPLb[38], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[3], -MPLft[3], -MPLft[10], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[39], MPLb[1], MPLb[3], -MPLb[39], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[10], -MPLft[10], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[40], MPLb[1], MPLb[3], MPLb[6], -MPLb[40], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[
10], -MPLb[41], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[41], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[42], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[42], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[43], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[43], MPLb[
1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[44], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[44], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]]], [[[1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[2], MPLft[1], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[1], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[3], MPLft[1], MPLft[1], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[1, -1, -1], [-MPLb[2], -MPLb[2], MPLb[1]], [-MPLft[2], -MPLft[3], -MPLft[2]]], [[1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[4], -MPLft[4], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, -1, -1, -1], [-MPLb[4], -MPLb[4], MPLb[1], MPLb[3]], [-MPLft[2], -MPLft[4], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1], [MPLb[1], -MPLb[5], MPLb[1], -MPLb[5], MPLb[1], MPLb[1], MPLb[3]], [-MPLft[4], -MPLft[4], -MPLft[3], -MPLft[3], -MPLft[4], -MPLft[3], -MPLft[3]]], [[1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[5], -MPLft[5], -MPLft[5], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[1, -1, -1, -1, -1], [-MPLb[7], -MPLb[7], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[2], -MPLft[5], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1], [MPLb[1], -MPLb[8], MPLb[1], -MPLb[8], MPLb[1], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[1, -1, -1, -1, -1, -1], [-MPLb[11], -
MPLb[11], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[2], -MPLft[6], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], -MPLb[12], MPLb[1], -MPLb[12], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[3], -MPLft[3], -MPLft[6], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[13], MPLb[1], MPLb[3], -MPLb[13], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[6], -MPLft[6], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[14], MPLb[1], MPLb[3], MPLb[6], -MPLb[14], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[
45]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[1, -1, -1, -1, -1, -1, -1], [-MPLb[16], -MPLb[16], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[2], -MPLft[7], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[17], MPLb[1], -MPLb[17], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[3], -MPLft[3], -MPLft[7], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[18], MPLb[1], MPLb[3], -MPLb[18], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[7], -MPLft[7], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[19], MPLb[1], MPLb[3], MPLb[6], -MPLb[19], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[20], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[20], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[22], -MPLb[22], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[2], -MPLft[8], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[23], MPLb[1], -MPLb[23], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[3], -MPLft[3], -MPLft[8], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[24], MPLb[1], MPLb[3], -MPLb[24], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[8], -MPLft[8], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[25], MPLb[1], MPLb[3], MPLb[6], -MPLb[25], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[26], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[26], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[6], -
MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[27], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[27], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -
MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[29], -MPLb[29], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[2], -MPLft[9], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[30], MPLb[1], -MPLb[30], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[3], -MPLft[3], -MPLft[9], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[31], MPLb[1], MPLb[3], -MPLb[31], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[9], -MPLft[9], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[32], MPLb[1], MPLb[3], MPLb[6], -MPLb[32], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[33], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[33], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[34], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[34], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[35], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[35], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[37], -MPLb[37], MPLb[1], MPLb[3], 
MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[2], -MPLft[10], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[38], MPLb[1], -MPLb[38], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[3], -MPLft[3], -MPLft[10], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[39], MPLb[1], MPLb[3], -MPLb[39], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[10], -MPLft[10], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[40], MPLb[1], MPLb[3], MPLb[6], -MPLb[40], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[5], -MPLft[5], -MPLft[
5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[41], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[41], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[42], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[42], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[43], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[43], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[44], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[44], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[46], -MPLb[46], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[2], -MPLft[11], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[47], MPLb[1], -MPLb[47], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[3], -
MPLft[3], -MPLft[11], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[48], MPLb[1], MPLb[3], -MPLb[48], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[11], -MPLft[11], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[49], MPLb[1], MPLb[3], MPLb[6], -MPLb[49], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[50], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[50], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6]
, MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[51], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[51], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[52], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[52], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[53], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[53], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[-1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], -MPLb[54], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], -MPLb[54], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10]]]], [[[1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[2], MPLft[1], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[1], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[3], MPLft[1], MPLft[1], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[1, -1, -1], [-MPLb[2], -MPLb[2], MPLb[1]], [-MPLft[2], -MPLft[3], -MPLft[2]]], [[1, 1, -1, -
1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[4], -MPLft[4], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, -1, -1, -1], [-MPLb[4], -MPLb[4], MPLb[1], MPLb[3]], [-MPLft[2], -MPLft[4], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1], [MPLb[1], -MPLb[5], MPLb[1], -MPLb[5], MPLb[1], MPLb[1], MPLb[3]], [-MPLft[4], -MPLft[4], -MPLft[3], -MPLft[3], -MPLft[4], -MPLft[3], -MPLft[3]]], [[1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[5], -MPLft[5], -MPLft[5], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[1, -1, -1, -1, -1], [-MPLb[7], -MPLb[7], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[2], -MPLft[5], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1], [MPLb[1], -
MPLb[8], MPLb[1], -MPLb[8], MPLb[1], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[1, -1, -1, -1, -1, -1], [-MPLb[11], -MPLb[11], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[2], -MPLft[6], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], -MPLb[12], MPLb[1], -MPLb[12], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[3], -MPLft[3], -MPLft[6], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[13], MPLb[1], MPLb[3], -MPLb[13], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[6], -MPLft[6], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[14], MPLb[1], MPLb[3], MPLb[6], -MPLb[14], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[1, -1, -1, -1, -1, -1, -1], [-MPLb[16], -MPLb[16], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[2], -MPLft[7], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[17], MPLb[1], -MPLb[17], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[3], -MPLft[3], -MPLft[7], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[18], MPLb[1], MPLb[3], -MPLb[18], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[7], -MPLft[7], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[19], MPLb[1], MPLb[3], MPLb[6], -MPLb[19], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[20], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[20], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], 
-MPLft[6], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[22], -MPLb[22], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[2], -MPLft[8], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[23], MPLb[1], -MPLb[23], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[3], -MPLft[3], -MPLft[8], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -
1], [MPLb[1], MPLb[3], -MPLb[24], MPLb[1], MPLb[3], -MPLb[24], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[8], -MPLft[8], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[25], MPLb[1], MPLb[3], MPLb[6], -MPLb[25], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[26], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[26], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[27], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[27], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[29], -MPLb[29], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[2], -MPLft[9], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[30], MPLb[1], -MPLb[30], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[3], -MPLft[3], -MPLft[9], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[31], MPLb[1], MPLb[3], -MPLb[31], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[9], -MPLft[9], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[32], MPLb[1], MPLb[3], MPLb[6], -MPLb[32], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[33], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[33], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[
10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[34], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[34], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[35], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[35], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -
MPLft[8], -MPLft[8], -MPLft[8], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[37], -MPLb[37], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[2], -MPLft[10], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[38], MPLb[1], -MPLb[38], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[3], -MPLft[3], -MPLft[10], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[39], MPLb[1], MPLb[3], -MPLb[39], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[10], -MPLft[10], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[40], MPLb[1], MPLb[3], MPLb[6], -MPLb[40], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[41], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[41], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[42], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[42], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[43], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[43], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[
10], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[44], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[44], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[
15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[46], -MPLb[46], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[2], -MPLft[11], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[47], MPLb[1], -MPLb[47], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[3], -MPLft[3], -MPLft[11], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[48], MPLb[1], MPLb[3], -MPLb[48], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[11], -MPLft[11], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[49], MPLb[1], MPLb[3], MPLb[6], -MPLb[49], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[50], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[50], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[51], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[51], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[52], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[52], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[
8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[53], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[53], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[-1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], -MPLb[54], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], -MPLb[54], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-
MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10]]], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[56], -MPLb[56], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[2], -MPLft[12], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[57], MPLb[1], -MPLb[57], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[3], -MPLft[3], -MPLft[12], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[58], MPLb[1], MPLb[3], -MPLb[58], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[12], -MPLft[12], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[59], MPLb[1], MPLb[3], MPLb[6], -MPLb[59], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[60], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[60], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[61], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[61], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -
MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[62], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[62], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[63], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[63], MPLb[1], MPLb[3], MPLb[6], 
MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[-1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], -MPLb[64], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], -MPLb[64], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10]]], [[-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], -MPLb[65], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], -MPLb[65], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11]]]], [[[1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[2], MPLft[1], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[1], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[3], MPLft[1], MPLft[1], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[1, -1, -1], [-MPLb[2], -MPLb[2], MPLb[1]], [-MPLft[2], -MPLft[3], -MPLft[2]]], [[1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[4], -MPLft[4], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, -1, -1, -1], [-MPLb[4], -MPLb[4], MPLb[1], MPLb[3]], [-MPLft[2], -MPLft[4], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1], [MPLb[1], -MPLb[5], MPLb[1], -MPLb[5], MPLb[1], MPLb[1], MPLb[3]], [-MPLft[4], -MPLft[4], -MPLft[3], -MPLft[3], -MPLft[4], -MPLft[3], -MPLft[3]]], [[1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], 
MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[5], -MPLft[5], -MPLft[5], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[1, -1, -1, -1, -1], [-MPLb[7], -MPLb[7], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[2], -MPLft[5], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1], [MPLb[1], -MPLb[8], MPLb[1], -MPLb[8], MPLb[1], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[6], -MPLft[6],
 -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[1, -1, -1, -1, -1, -1], [-MPLb[11], -MPLb[11], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[2], -MPLft[6], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], -MPLb[12], MPLb[1], -MPLb[12], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[3], -MPLft[3], -MPLft[6], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[13], MPLb[1], MPLb[3], -MPLb[13], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[6], -MPLft[6], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[14], MPLb[1], MPLb[3], MPLb[6], -MPLb[14], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[1, -1, -1, -1, -1, -1, -1], [-MPLb[16], -MPLb[16], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[2], -MPLft[7], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[17], MPLb[1], -MPLb[17], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[3], -MPLft[3], -MPLft[7], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[18], MPLb[1], MPLb[3], -MPLb[18], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[7], -MPLft[7], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[19], MPLb[1], MPLb[3], MPLb[6], -MPLb[19], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[20], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[20], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[1, -1, -1, -1, -
1, -1, -1, -1], [-MPLb[22], -MPLb[22], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[2], -MPLft[8], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[23], MPLb[1], -MPLb[23], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[3], -MPLft[3], -MPLft[8], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[24], MPLb[1], MPLb[3], -MPLb[24], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[8], -MPLft[8], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[25], MPLb[1], MPLb[3], MPLb[6], -MPLb[25], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 
[MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[26], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[26], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[27], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[27], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[29], -MPLb[29], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[2], -MPLft[9], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[30], MPLb[1], -MPLb[30], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[3], -MPLft[3], -MPLft[9], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[31], MPLb[1], MPLb[3], -MPLb[31], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[9], -MPLft[9], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[32], MPLb[1], MPLb[3], MPLb[6], -MPLb[32], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[33], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[33], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[34], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[34], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[
9], -MPLft[9], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[35], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[35], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], MPLft[1], MPLft[1], MPLft[
1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[37], -MPLb[37], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[2], -MPLft[10], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[38], MPLb[1], -MPLb[38], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[3], -MPLft[3], -MPLft[10], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[39], MPLb[1], MPLb[3], -MPLb[39], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[10], -MPLft[10], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[40], MPLb[1], MPLb[3], MPLb[6], -MPLb[40], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[41], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[41], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[42], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[42], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[43], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[43], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[44], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[44], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], 
-MPLft[10], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[46], -MPLb[46], MPLb[1], MPLb[3], MPLb[6],
 MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[2], -MPLft[11], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[47], MPLb[1], -MPLb[47], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[3], -MPLft[3], -MPLft[11], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[48], MPLb[1], MPLb[3], -MPLb[48], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[11], -MPLft[11], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[49], MPLb[1], MPLb[3], MPLb[6], -MPLb[49], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[50], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[50], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[51], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[51], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[52], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[52], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[53], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[53], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -
MPLft[11], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[-1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], -MPLb[54], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], -MPLb[54], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10]]], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[1], MPLb[3]
, MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[56], -MPLb[56], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[2], -MPLft[12], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[57], MPLb[1], -MPLb[57], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[3], -MPLft[3], -MPLft[12], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[58], MPLb[1], MPLb[3], -MPLb[58], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[12], -MPLft[12], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[59], MPLb[1], MPLb[3], MPLb[6], -MPLb[59], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[60], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[60], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[61], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[61], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[62], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[62], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[
12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[63], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[63], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[-1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], 
MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], -MPLb[64], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], -MPLb[64], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10]]], [[-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], -MPLb[65], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], -MPLb[65], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11]]], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[67], -MPLb[67], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[2], -MPLft[13], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[68], MPLb[1], -MPLb[68], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[13], -MPLft[13], -MPLft[3], -MPLft[3], -MPLft[13], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[69], MPLb[1], MPLb[3], -MPLb[69], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[13], -MPLft[13], -MPLft[13], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[13], -MPLft[13], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -
1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[70], MPLb[1], MPLb[3], MPLb[6], -MPLb[70], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[71], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[71], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[72], MPLb[1], MPLb[3],
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11]]], [[-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], -MPLb[77], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], -MPLb[77], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12]]]], [[[1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[
2], MPLft[1], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[1], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[3], MPLft[1], MPLft[1], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[1, -1, -1], [-MPLb[2], -MPLb[2], MPLb[1]], [-MPLft[2], -MPLft[3], -MPLft[2]]], [[1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[4], -MPLft[4], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, -1, -1, -1], [-MPLb[4], -MPLb[4], MPLb[1], MPLb[3]], [-MPLft[2], -MPLft[4], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1], [MPLb[1], -MPLb[5], MPLb[1], -MPLb[5], MPLb[1], MPLb[1], MPLb[3]], [-MPLft[4], -MPLft[4], -MPLft[3], -MPLft[3], -MPLft[4], -MPLft[3], -MPLft[3]]], [[1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[5], -MPLft[5], -MPLft[5], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[1, -1, -1, -1, -1], [-MPLb[7], -MPLb[7], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[2], -MPLft[5], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1], [MPLb[1], -MPLb[8], MPLb[1], -MPLb[8], MPLb[1], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[5], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], -MPLb[9], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6]], [-MPLft[5], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[5], -MPLft[5], -MPLft[4], -MPLft[4], -MPLft[4]]], [[1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[1, -1, -1, -1, -1, -1], [-MPLb[11], -MPLb[11], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[2], -MPLft[6], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], -MPLb[12], MPLb[1], -MPLb[12], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[3], -MPLft[3], -MPLft[6], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[13], MPLb[1], MPLb[3], -MPLb[13], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[6], -MPLft[6], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[14], MPLb[1], MPLb[3], MPLb[6], -MPLb[14], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10]], [-MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 
1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[1, -1, -1, -1, -1, -1, -1], [-MPLb[16], -MPLb[16], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[2], -MPLft[7], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[17], MPLb[1], -MPLb[17], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[3], -MPLft[3], -MPLft[7], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[18], MPLb[1], MPLb[3], -MPLb[18], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[7], -MPLft[7], -MPLft[4], -
MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[19], MPLb[1], MPLb[3], MPLb[6], -MPLb[19], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[20], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[20], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15]], [-MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[22], -MPLb[22], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[2], -MPLft[8], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[23], MPLb[1], -MPLb[23], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[3], -MPLft[3], -MPLft[8], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[24], MPLb[1], MPLb[3], -MPLb[24], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[8], -MPLft[8], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[25], MPLb[1], MPLb[3], MPLb[6], -MPLb[25], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[26], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[26], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[27], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[27], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21]], [-MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], 
MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[29], -MPLb[29], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[2], -MPLft[9], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[30], MPLb[1], -MPLb[30], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[3], -MPLft[3], -MPLft[9], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[31], MPLb[1], MPLb[3], -MPLb[31], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[
15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[9], -MPLft[9], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[32], MPLb[1], MPLb[3], MPLb[6], -MPLb[32], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[33], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[33], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[34], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[34], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[35], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[35], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28]], [-MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[37], -MPLb[37], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[2], -MPLft[10], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[38], MPLb[1], -MPLb[38], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[3], -MPLft[3], -MPLft[10], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[39], MPLb[1], MPLb[3], -MPLb[39], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], 
-MPLft[10], -MPLft[10], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[10], -MPLft[10], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[40], MPLb[1], MPLb[3], MPLb[6], -MPLb[40], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[41], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[41], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[
1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[42], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[42], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[43], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[43], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[44], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[44], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]], [-MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[46], -MPLb[46], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[2], -MPLft[11], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[47], MPLb[1], -MPLb[47], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[3], -MPLft[3], -MPLft[11], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[48], MPLb[1], MPLb[3], -MPLb[48], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[11], -MPLft[11], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[
1], MPLb[3], MPLb[6], -MPLb[49], MPLb[1], MPLb[3], MPLb[6], -MPLb[49], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[50], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[50], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[51], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[51], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], 
MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[52], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[52], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[53], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[53], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[-1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], -MPLb[54], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], -MPLb[54], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45]], [-MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10]]], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[56], -MPLb[56], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[2], -MPLft[12], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -
1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[57], MPLb[1], -MPLb[57], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[3], -MPLft[3], -MPLft[12], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[58], MPLb[1], MPLb[3], -MPLb[58], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[12], -MPLft[12], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[59], MPLb[1], MPLb[3], MPLb[6], -MPLb[59], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -
MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[60], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[60], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[61], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[61], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[62], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[62], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[63], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[63], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[-1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], -MPLb[64], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], -MPLb[64], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10]]], [[-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], -MPLb[65], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36]
, MPLb[45], -MPLb[65], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55]], [-MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11]]], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[
78]], [-MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13]]], [[1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [-MPLb[67], -MPLb[67], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[2], -MPLft[13], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[68], MPLb[1], -MPLb[68], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[13], -MPLft[13], -MPLft[3], -MPLft[3], -MPLft[13], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[69], MPLb[1], MPLb[3], -MPLb[69], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[13], -MPLft[13], -MPLft[13], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[13], -MPLft[13], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[70], MPLb[1], MPLb[3], MPLb[6], -MPLb[70], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[71], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[71], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[72], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[72], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[73], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[73], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[8]
, -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[74], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[74], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[-1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6],
 MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], -MPLb[75], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], -MPLb[75], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10]]], [[-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], -MPLb[76], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], -MPLb[76], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11]]], [[-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], -MPLb[77], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], -MPLb[77], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66]], [-MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12]]], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], MPLft[1], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14]]], [[1, -1, -1, -1, -1, -1, -1,
 -1, -1, -1, -1, -1, -1, -1], [-MPLb[79], -MPLb[79], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[2], -MPLft[14], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2], -MPLft[2]]], [[-1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], -MPLb[80], MPLb[1], -MPLb[80], MPLb[1], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[14], -MPLft[14], -MPLft[3], -MPLft[3], -MPLft[14], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3], -MPLft[3]]], [[-1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], -MPLb[81], MPLb[1], MPLb[3], -MPLb[81], MPLb[1], MPLb[3], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[14], -MPLft[14], -MPLft[14], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[14], -MPLft[14], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4], -MPLft[4]]], [[-1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1,
 -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], -MPLb[82], MPLb[1], MPLb[3], MPLb[6], -MPLb[82], MPLb[1], MPLb[3], MPLb[6], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5], -MPLft[5]]], [[-1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[83], MPLb[1], MPLb[3], MPLb[6], MPLb[10], -MPLb[83], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6], -MPLft[6]]], [[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[84], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], -MPLb[84], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7], -MPLft[7]]], [[-1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[85], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], -MPLb[85], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8], -MPLft[8]]], [[-1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[86], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], -MPLb[86], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9], -MPLft[9]]], [[-1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], -MPLb[87], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], -MPLb[87], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[14], -
MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10], -MPLft[10]]], [[-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], -MPLb[88], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], -MPLb[88], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -
MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11], -MPLft[11]]], [[-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], -MPLb[89], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], -MPLb[89], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12], -MPLft[12]]], [[-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], -MPLb[90], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], -MPLb[90], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[1], MPLb[3], MPLb[6], MPLb[10], MPLb[15], MPLb[21], MPLb[28], MPLb[36], MPLb[45], MPLb[55], MPLb[66], MPLb[78]], [-MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[14], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13], -MPLft[13]]]]]:


# This list was created with the command: 

CreateLowestArnoldEquations:=proc(howmany)
local k, i, j, outp, NewRhs, NewEq:
outp:=[]:
for k from 0 to howmany do
 NewEq:=[]:
 MPLInitialize(u, k):
 for j from 2 to MPLnumberofvar+2 do
  for i from 1 to j-1 do
   NewRhs:=ArnoldCubical(MPLft[j], MPLft[i]):
   NewEq:=[op(NewEq), NewRhs]:
  end do:
 end do:
 outp:=[op(outp), NewEq]:
end do:
return outp:
end proc:





MPL_CoefflnZeroList:=[]:





defform(e=0):


# COMPATIBILITY_GRAPH is set true by default:

COMPATIBILITY_GRAPH:=true:
s:='s':




# The program MPL ends here.