This notebook is used for the calculations of extreme pathways.
Given an *.expa file, user can use the accompanying perl parser to create:
	a) initial matrix, InitialMtrx,  which is used to construct Initial Tableau, T0, by removing rows corresponding to the Free exchange fluxes; and
	b) list of indicies of Free metabolites FreeMet
These then have to be 'evaluated' appropriately so that all other cells can be evaluated sequencially.
The above two inputs are the minimal set of information required for the calculations of extreme pathways. Other additional information can be extracted from the initial tableau.

Three examples are provide here - the E.coli core model, Red Blood Cell, and a small test file, the latter two available with the expa program by Steve Bell. Each example is highlighted by a yellow text bar for easy identification. Please scroll to the end of the notebook to reveal the E.coli input. This is because the matrix is too latge for demonstration purposes and calculation time is in the regions of days.

Until it can be shown that is it possible to accelerate extreme pathway calculations process, this notebook should only be used for demonstrative / educational purposes.

Important:
This notebook was developed using Mathematica 4. From version 5 onwards, matrices can be stored as SparseArray[]. Feel free to adjust the code accordingly.

Please address comment and question (with appropriate subject title) to: myeung@be-research.ucsd.edu

Input:	- Initial Tableau
	- List if Free metabolites (in terms of indicies)

Red Blood Cell

InputMtrx = {{-1, -1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
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            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            0, 0, 0, 0}, {0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
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            0, 0, 0, 0}, {0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
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            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
            1}};
FreeMet = {19, 20, 37, 32, 33, 4, 2, 10, 13, 21, 23, 11, 26, 5, 34, 
          16};

Test File

InputMtrx = {{-1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0}, {0, -1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 
          1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 
          0, -1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 
          1, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, -1, 
          0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, -1, 1, 
          0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, -1, 0, 0, 0}, {0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 1, 0, 0}, {0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          1, 0}, {0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}}; 
    FreeMet = {2, 6};

Firstly, Find:	- Number of Reactions rxn
		- Number of Metabolites met
		- Number of Exchange Fluxes exch

So we now have:
	- T0 Initial Tableau (constructed below with rows corresponding to Free metabolites removed)
	- met Number of Metabolites
	- rxn Number os Reactions (including exchange fluxes)
	- ExMet List of Exchange Metabolites
	- FreeMet List of Free Metabolites
	- exch Number of Exchange Metabolites
So we should be able to rock and roll!

rxn = Dimensions[
            InputMtrx][[1]];
met = Dimensions[InputMtrx][[2]] - Dimensions[
              InputMtrx][[1]];
ExMet = {};
For[i = 1,  
        i ≤ 
          rxn, 
{counter = 0, 
For[j = 1, 
            j ≤ met, 
If[
              InputMtrx[[i, j]] ≠ 
                0, 
{counter++, 
                If[counter == 1, 
                  isHere = 
                    j]}
]; 
j++], 
If[
            counter == 1, 
ExMet = 
              Append[ExMet, 
                isHere]
]}; 
i++];
exch = Dimensions[ExMet][[1]];


T0 = {};
For[i = 1, 
        i ≤ Dimensions[InputMtrx][[1]] - 
            exch, 
T0 = 
          Append[T0, 
            InputMtrx[[i]]]; 
i++];
For[i = Dimensions[InputMtrx][[1]] - exch + 1,  
          i ≤ Dimensions[
                InputMtrx][[1]], 
For[j = 1, 
            j ≤ met, 
If[
              InputMtrx[[i, j]] ≠ 
                0, 
{If[(! MemberQ[FreeMet, 
                        j]), {T0 = Append[T0, InputMtrx[[i]]]}], 
                Break[]}
]; 
j++]; 
i++];


DoneList = {};   
Timing[For[j = 1,j ≤ met + 1,
{
  
\(If[
                    j < met + 
                        1, {
combo = {}, 
place = {}, 
For[i = 1, 
                        i ≤ 
                          met, {
If[\(! MemberQ[DoneList, 
                                i]\), {
combo = 
                                Append[
                                  combo, \((Count[Normal[T0[\([All, i]\)]], 
                                        0] + 
                                      Count[
                                        Normal[T0[\([All, i]\)]], _?Positive]*
                                        Count[
                                        Normal[T0[\([All, i]\)]], _?
                                        Negative])\)], 
place = Append[place, 
                                  i]
}]
}; \(i++\)], 
DoneList = 
                        Append[DoneList, 
                          place[\([\(Flatten[
                                  Position[combo, 
                                    Min[combo]]]\)[\([1]\)]]\)]], 
 (*\ \(Print[
                          combo]\)\(,\)\ *) 
 (*\ \(Print[
                          place[\([\(Flatten[
                                  Position[combo, 
                                    Min[combo]]]\)[\([1]\)]]\)]]\)\(,\)*) 
Print["Iteration: ", j, ", Metabolite: ", 
                        DoneList[\([j]\)], ", Zeros+Pos*Neg: ", 
                        Min[combo\ ], ", Number of Rows in Current Tableau: ", \(Dimensions[T0]\)[\([1]\)]]
}]\)
  

,

If[(j < 
                            met + 1) ∧ (! MemberQ[FreeMet, 
                              DoneList[[j]]]),
{T1 = {},

  
For[i = 1, 
                            i ≤ Dimensions[
                                  T0][[1]], 
{If[
                                T0[[i, DoneList[[j]]]] == 
                                  0, 
{T1 = 
                                    Append[T1, 
                                      T0[[i]]], 
T0 = 
                                    Delete[T0, i], 
i = 
                                    i - 1}]}; 
i++]
  
,
TmpT1 = Dimensions[
                                T1][[1]]
,
  

For[i = 1, 
                            i ≤ Dimensions[T0][[1]] - 
                                1, {
For[k = i + 1, 
                                k ≤ Dimensions[
                                      T0][[1]], {
If[
                                    T0[[i, DoneList[[j]]]]/
                                        T0[[k, DoneList[[j]]]] < 
                                      0, 
{tt = ((Abs[T0[[i, DoneList[[j]]]]]*T0[[k]] + Abs[T0[[k, DoneList[[j]]]]]*T0[[i]])/GCD)[T0[[i, DoneList[[j]]]], T0[[k, DoneList[[j]]]]], 
T1 = 
                                        Append[T1, 
                                        tt]}]
}; k++]
}; i++]
  
,
  
  

For[i = TmpT1, 
                            i ≤ Dimensions[T1][[1]] - 
                                1, {
SubFlag = 
                                0, 
IndRow1 = {}, 
IndRow1 = Flatten[
                                  Position[Normal[T1[[i]]], 
                                    0]], 
For[k = i + 1, 
                                  k ≤ Dimensions[
                                        T1][[1]], {
IndRow2 = {}, 
IndRow2 = 
                                      Flatten[
                                        Position[Normal[T1[[k]]], 
                                        0]], 
α = 
                                      Length[
                                        Intersection[IndRow1, 
                                        IndRow2]], 
β = Length[IndRow1], 
γ = 
                                      Length[
                                        IndRow2], 
If[(α ≠ 
                                        0) ∧ ((α == β) ∨ (α == γ)), {
If[β ≠ γ, {
If[α == β, SubFlag = 
                                        1], 
If[α == γ, {T1 = Delete[T1, k], k = k - 
                                        1}]
}]
 (*,If[(β == γ) ∧ ((α == β) ∨ (α == γ)), {T1 = 
                                        Delete[T1, k], 
                                        k = k - 
                                        1} ]*) 
}, 
                                      SubFlag = 0], 
If[
                                      SubFlag == 1, 
                                      Break[]]
}; k++]
If[SubFlag == 1, {T1 = Delete[T1, i], 
                                    i = i - 
                                        1}]
}; i++]
,
  

For[i = 1, 
                            i ≤ Dimensions[T1][[1]] - 
                                TmpT1, {
SubFlag = 
                                0, 
IndRow1 = {}, 
IndRow1 = Flatten[
                                  Position[Normal[T1[[i]]], 
                                    0]], 
For[k = TmpT1, 
                                  k ≤ Dimensions[
                                        T1][[1]], {
IndRow2 = {}, 
IndRow2 = 
                                      Flatten[
                                        Position[Normal[T1[[k]]], 
                                        0]], 
α = 
                                      Length[
                                        Intersection[IndRow1, 
                                        IndRow2]], 
β = Length[IndRow1], 
γ = 
                                      Length[
                                        IndRow2], 
If[(α ≠ 
                                        0) ∧ ((α == β) ∨ (α == γ)), {
If[β ≠ γ, {
If[α == β, SubFlag = 
                                        1], 
If[α == γ, {T1 = Delete[T1, k], k = k - 
                                        1}]
}]
 (*,If[(β == γ) ∧ ((α == β) ∨ (α == γ)), {T1 = 
                                        Delete[T1, k], 
                                        k = k - 
                                        1} ]*) 
}, 
                                      SubFlag = 0], 
If[
                                      SubFlag == 1, 
                                      Break[]]
}; k++]
If[SubFlag == 1, {T1 = Delete[T1, i], i = i - 1, 
                                    TmpT1 = 
                                      TmpT1 - 
                                        1}]
}; i++]
  
,
T0 = T1
}]   
,

  
If[
                    j == met + 1, 
For[k = 1, 
                      k ≤ met, 
If[
                        MemberQ[FreeMet, 
                          k], 
{
isHere = Flatten[Position[ExMet, k]][[1]], 
 (*For[l = 1, 
                              l ≤ 
                                exch, 
{isHere = 
                                  0, 
If[
                                  k == ExMet[[l]], {isHere = l, 
                                    Break[]}]}; 
l++]*) 
T0[[All, met + rxn - exch + isHere]] = 
                            T0[[All, k]], 
T0[[All, 
                                k]] = 
                            0
}]; 
k++]
]
  

};j++]]

Assuming that there were no blocked reactions, remove nullified part of tableau that was previously the transposed stoihiometrix matrix to reveal Extreme Pathway Matrix P

P = Transpose[T0];
For[i = 1, 
        i ≤ met, 
P = 
          Delete[P, 
            1]
; i++];
P = Transpose[P];
P // MatrixForm

Finally, export Extreme Pathway Matrix P to external text file for further analysis.
The full path has to be specified, as demonstrated below, otherwise default location is used.

Export["C:\pathways.txt", Normal[P], "Text"]

E.coli Core

InputMtrx = {{-1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0}, {1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0}, {-1, 0, 0, 0, 0, 0, -1, 1, 1, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -2, 0, 
          0, -1, 1, 1, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 2, 
          0, 0, 1, -1, -1, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 
          2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 
          0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 1, 0, -1, 1, 1, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0}, {0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 
          0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 
          0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
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    FreeMet = {22, 9, 53, 61};