Finiteness for Relative Equilibria of the Four-Body Problem

Introduction

This notebook contains computational algorithms and results which support the paper "Finiteness of relative equilibria of the four-body problem" by Marshall Hampton and Richard Moeckel.  The notebook is divided into sections explaining the different kinds of computations used to verify the results in the paper.  The reader can go through the notebook section by section, executing the cells in order to check the computations.

Some computations were done with the other programs such as Porta, Macaulay2, lrs and Mixvol.  As explained below, these results have simply been copied into this notebook so that further computations based on them can be illustrated.

Equations for Relative Equilibria

First we define some functions to automatically construct the Albouy-Chenciner equations for central configurations.  For the four-body problem, there are six equations for the six mutual distances.

(* 
      Define mutual distances and normalized variables Sij *) 
r[i_, i_] := 0
r[i_, j_] := r[j, i] /; j < i
S[i_, i_] :=  0
S[i_, j_]  := 1/r[i, j]^3 - 
        1

 (* 
        Carry out the sum in equation (10) of section 2.1 *) 
P[i_, j_, n_]  := 
      Plus @@ Table[
          m[k]*(S[i, k]*(r[j, k]^2 - r[i, k]^2 - r[i, j]^2) + 
                S[j, k]*(r[i, k]^2 - r[j, k]^2 - r[i, j]^2)), {k, 1, 
            n}]

   
ACeqs[
        n_]  :=  Table[P[i, j, n], {j, 2, n}, {i, 1, j - 1}] // 
            Flatten // Factor // Numerator

Here are the equations written out with the array variables replaced by ordinary ones.

varsub  =  {r[1, 2] -> r12, r[1, 3] -> r13, 
          r[2, 3] -> r23, r[1, 4] -> r14, r[2, 4] -> r24, 
          r[3, 4] -> r34, m[1] -> m1, m[2] -> m2, 
          m[3] -> m3, 
          m[4] -> m4};

aceqs  =  ACeqs[4] /. varsub

Next we enter in the three Dziobek equations.

dzeqs  =  {S[1, 2] S[3, 4] - 
                S[1, 4] S[2, 3], S[1, 2] S[3, 4] - S[1, 3] S[2, 4], 
              S[1, 3] S[2, 4] - S[1, 4] S[2, 3]} /. varsub // Factor // 
        Numerator

Our main system consists of these nine equations for the six mutual distances.

acdzeqs  =  aceqs~Join~dzeqs;

For constructing the upper bound we also use another system of 10 equations and 10 unknowns.  We begin by entering the system of 11 equations and unknowns (13) from section 2.2  The first five are geometrical equations arising from the "Cayley-Menger" matrix of squared mutual distances.

CM =  {{0, 1, 1, 1, 1}, 
{1, 0, r12^2, r13^2, 
            r14^2}, 
{1, r12^2, 0, r23^2, 
            r24^2}, 
{1, r13^2, r23^2, 0, 
            r34^2}, 
{1, r14^2, r24^2, r34^2, 
            0}};
geomeqs  =  CM . {k, m1*z1, m2*z2, m3*z3, m4*z4}

The other six are essentially due to Dziobek.

moredzeqs  =  Table[
                S[i, j] - z[i]*z[j], {j, 2, 4}, {i, 1, j - 1}] // Flatten // 
            Factor // Numerator;
varsub2  =  {z[1] -> z1, z[2] -> z2, z[3] -> z3, 
          z[4] -> z4};
moredzeqs  =  moredzeqs /. varsub /. varsub2

The system of 10 equations and ten unknowns is obtained by eliminating k.

geomeqsnok  =  {geomeqs[[1]], 
          geomeqs[[2]] - geomeqs[[5]], 
          geomeqs[[3]] - geomeqs[[5]], 
          geomeqs[[4]] - geomeqs[[5]]};
teneqs  =  geomeqsnok~Join~moredzeqs

Newton Polytopes

In this section we find show the Mathematica functions used to compute the Newton polytopes of our equations and their  Minkowski sums.   The Mathematica part just involves reading off all the exponent vectors and adding them.   For the real work of finding the convex hulls we used Porta 1.3.2.  The final result was verified using lrs 4.1.

Exponent Lists

First we have some simple functions based on Mathematica's built-in Exponent command.  Essentially a polynomial which has  been completely expanded is represented in Mathematica as a list of its terms (with a "Head" of "Plus" in front).  We also make use of a list of the variables whose exponents we want to read  off.  The first function below is intended to act on a single term of a  polynomials.  It applies Mathematica's Exponent command to the monomial for each variable in the  variable list thereby producing a list of the exponents for all the  variables. For a polynomial, we just to this for every term to get a list of  lists of exponents.  The Union command eliminates redundancies arising from  terms which involve the same powers of the variables with different   coefficients.

GetExponents[mon_, vars_]  :=  
      Map[Exponent[mon, #] &, vars]
GetAllExponents[poly_, 
        vars_] := 
Table[
          GetExponents[poly[[i]], vars], {i, 1, Length[poly]}] // 
        Union

Here is the exponent list for the Albouy-Chenciner-Dziobek system.

vars4bp  =  {r12, r13, r14, r23, r24, 
          r34};
explist9  =  Map[GetAllExponents[#, vars4bp] &, acdzeqs]

The Albouy-Chenciner equations have 14 essentially different monomials and the Dziobek equations have 6.  These will be the initial  numbers  of vertices in the initial Newton polytopes, but some of them may not be extreme points on the convex hull.

Map[Length, explist9]

In a similar way, we compute the exponent vectors for the auxiliary system of 10 equations and 10 unknowns.

tenvars  =  {r12, r13, r14, r23, r24, r34, z1, z2, z3, 
          z4};

explist10  =  
      Map[GetAllExponents[#, tenvars] &, 
        teneqs]

Map[Length, explist10]

At this point the exponent list explist10 was put into a data file and edited to conform with the syntax requirements of the program Mixvol.  The resulting file, called   teneqs.sites  was given as input to that program which computed the mixed volume of the 10 polytopes.  The result was 25380 as reported in section 6 of the paper.  After this we have no further need for the system of 10 equations or its exponent lists.

Partial Minkowski Sums

A key step in the method is to find the Minkowski sum of the 9 Newton polytopes of the Albouy-Chenciner-Dziobek system.  The naive way to find a Minkowski sum is just to take all possible sums of nine vertices, one from each of the Newton polytopes.  In practice, we had to  go through cycles of taking Minkowski sums of a few of the 9 Newton polytopes, finding a more efficient representation of the convex hull using Porta and then adding in more of the Newton polytopes.   In this way we could succeed in finding separate Minkowski sums for the six Albouy-Chenciner equations and for the three Dziobek equations.  To add these two together required some tricks which will be handled in the next subsection.

We begin with basic functios to add a single vertex to a list of vertices and to add two lists of vertices together.  The second function is a primitive Minkowski sum for two polytopes but the vertex list will be unnecessarily long.  One needs a program like Porta to find the true extreme points of the convex hull.

AddToAll[vect_, vlist_]  := 
      Map[( vect + #) &, vlist]
MinkSum[vlist_, 
        wlist_]  :=  Map[AddToAll[#, wlist] &, vlist] // 
          Flatten[#, 1] & // Union

Here is the primitive Minkowski sum for the three Dziobek equations. We get a list of 132 vertices.

dzmink  =  
      MinkSum[MinkSum[explist9[[7]], explist9[[8]]], 
        explist9[[9]]]
Length[dzmink]

We put this list in a file named "dzmink.poi" and edited it to conform  with the syntax of the program Porta 1.3.2.  Running the command traf -l dzmink.poi produces a file called "dzmink.poi.ieq" containing a minimal list of  inequalities in six variables x1, ... , x6  defining the convex hull .  Running the command traf -l dzmink.poi.ieq produces yet another file "dzmink.poi.ieq.poi which contains the  true vertices of the Minkowski sum polytope.  To avoid having to deal with  these files here, we will just copy the results, showing the commands in  comments

\( (*\ Write\ the\ raw\ vertices\ to\ a\ file\ *) 
 (*\ 
      Put[dzmink, "dzmink.poi"]\ *) 

 (*\ 
      Read\ in\ the\ results\ from\ porta, \ 
      after\ editing\ the\ output\ files\ to\ Mathematica\ syntax\ *) 
 (*\ 
      dzconv\  = \ 
        ReadList["dzmink.poi.ieq.poi", {Number, Number, Number, Number, 
            Number, Number}]*)  (*\ 
      dzineq\  = \ 
        ReadList["dzmink.poi.ieq", 
          Expression]*) 

\(dzconv\  = \ {{3, 6, 0, 0, 6, 3}, {0, 3, 6, 6, 6, 0}, {3, 6, 0, 0, 6, 6}, {3, 6, 0, 6, 6, 
            6}, {6, 3, 0, 0, 6, 6}, {6, 3, 0, 6, 6, 6}, {0, 3, 6, 6, 3, 
            0}, {0, 6, 3, 3, 6, 0}, {0, 3, 6, 6, 6, 6}, {0, 6, 3, 6, 6, 
            0}, {0, 6, 3, 6, 6, 6}, {0, 6, 6, 3, 6, 0}, {0, 6, 6, 3, 6, 
            6}, {0, 6, 6, 6, 3, 0}, {6, 3, 6, 0, 6, 6}, {0, 3, 6, 6, 3, 
            6}, {0, 6, 3, 3, 6, 6}, {0, 6, 6, 6, 3, 6}, {6, 6, 0, 0, 3, 
            6}, {6, 6, 0, 6, 3, 6}, {6, 6, 6, 0, 3, 6}, {6, 0, 3, 3, 0, 
            6}, {6, 0, 3, 3, 6, 6}, {6, 0, 3, 6, 0, 6}, {6, 0, 3, 6, 6, 
            6}, {3, 0, 6, 6, 0, 3}, {3, 0, 6, 6, 6, 3}, {3, 0, 6, 6, 0, 
            6}, {3, 0, 6, 6, 6, 6}, {6, 0, 6, 3, 0, 6}, {6, 0, 6, 3, 6, 
            6}, {3, 6, 6, 6, 0, 3}, {3, 6, 6, 6, 0, 6}, {6, 6, 3, 3, 0, 
            6}, {6, 6, 3, 6, 0, 6}, {6, 6, 6, 3, 0, 6}, {6, 0, 6, 6, 0, 
            3}, {6, 0, 6, 6, 6, 3}, {6, 6, 0, 0, 6, 3}, {6, 6, 0, 6, 6, 
            3}, {6, 6, 6, 6, 0, 3}, {6, 3, 6, 6, 6, 0}, {6, 3, 6, 6, 3, 
            0}, {6, 6, 3, 3, 6, 0}, {3, 6, 6, 0, 6, 6}, {6, 6, 3, 6, 6, 
            0}, {6, 6, 6, 0, 6, 3}, {6, 6, 6, 3, 6, 0}, {3, 6, 0, 6, 6, 
            3}, {3, 6, 6, 0, 6, 3}, {6, 3, 0, 0, 3, 6}, {6, 3, 0, 6, 3, 
            6}, {6, 3, 6, 0, 3, 6}, {6, 6, 6, 6, 3, 
            0}};\)
\)
dzineq  =  {x1 + x2 + x5 + x6 ≤ 
            21, -x1 - x2 - x3 ≤ -9, -x1 - x2 - 
              x4 ≤ -9, 
          x3 ≤ 6, -x1 - x4 - x5 ≤ -9, 
          x4 ≤ 6, -x1 - x3 - x5 ≤ -9, 
          x6 ≤ 6, 
          x5 ≤ 6, -x6 ≤ 
            0, -x2 - x3 - x6 ≤ -9, -x2 - x4 - 
              x6 ≤ -9, -x3 - x5 - 
              x6 ≤ -9, -x4 - x5 - x6 ≤ -9, 
          x2 + x3 + x4 + x5 ≤ 21, -x1 ≤ 0, 
          x2 ≤ 6, -x2 ≤ 0, -x5 ≤ 0, 
          x1 + x3 + x4 + x6 ≤ 21, 
          x1 ≤ 6, -x3 ≤ 0, -x4 ≤ 0, 
          x1 + x2 + x3 + x4 + x5 + x6 ≤ 27};

This is the description of the polytope P2 in section 4.1 of the paper. It has 54 vertices and 24 facets.

Length[dzconv]
Length[dzineq]

A similar approach was used for the six Albouy-Chenciner equations.  This time it is not possible to add all six at once. Instead we had to add three of the polytopes, reduce the number of hull vertices with Porta, add in the fourth, reduces the hull, etc.   Here are the final results.  To save space, this cell has been kept closed.  Select it and open it to see the results.  In any case, the cell should be selected and executed at this time before continuing.

acconv = {{0, 13, 13, 17, 17, 15}, {0, 13, 13, 19, 14, 13}, {0, 10, 
            15, 17, 17, 13}, {0, 10, 13, 17, 17, 15}, {0, 13, 17, 17, 13, 
            15}, {0, 13, 17, 19, 10, 13}, {0, 10, 19, 17, 13, 13}, {0, 10, 
            17, 17, 13, 15}, {0, 13, 17, 17, 10, 15}, {0, 13, 10, 17, 17, 
            15}, {0, 13, 13, 14, 19, 13}, {0, 13, 13, 17, 17, 12}, {0, 15, 
            10, 17, 17, 13}, {0, 17, 17, 13, 13, 15}, {0, 17, 17, 15, 10, 
            13}, {0, 14, 19, 13, 13, 13}, {0, 17, 17, 13, 10, 15}, {0, 17, 
            13, 13, 17, 15}, {0, 17, 10, 13, 17, 15}, {0, 17, 13, 10, 19, 
            13}, {0, 19, 10, 13, 17, 13}, {0, 17, 17, 10, 13, 15}, {0, 17, 
            13, 10, 17, 15}, {0, 17, 17, 10, 15, 13}, {0, 19, 14, 13, 13, 
            13}, {0, 17, 17, 13, 13, 12}, {0, 17, 13, 13, 17, 12}, {0, 13, 
            17, 17, 13, 12}, {1, 10, 13, 19, 17, 15}, {1, 10, 13, 21, 14, 
            13}, {1, 7, 15, 19, 17, 13}, {1, 7, 13, 19, 17, 15}, {1, 10, 17, 
            19, 13, 15}, {1, 10, 17, 21, 10, 13}, {1, 7, 19, 19, 13, 13}, {1, 
            7, 17, 19, 13, 15}, {1, 10, 17, 19, 10, 15}, {1, 10, 10, 19, 17, 
            15}, {1, 13, 10, 17, 19, 15}, {1, 10, 12, 17, 19, 13}, {1, 10, 
            10, 17, 19, 15}, {1, 13, 10, 14, 21, 13}, {1, 10, 13, 16, 19, 
            13}, {1, 13, 10, 17, 19, 12}, {1, 13, 7, 17, 19, 15}, {1, 10, 13, 
            19, 17, 12}, {1, 12, 10, 19, 17, 13}, {1, 15, 7, 17, 19, 13}, {1, 
            13, 19, 17, 10, 15}, {1, 13, 19, 19, 7, 13}, {1, 10, 21, 17, 10, 
            13}, {1, 10, 19, 17, 10, 15}, {1, 13, 19, 17, 7, 15}, {1, 10, 17, 
            19, 13, 12}, {1, 17, 10, 10, 21, 13}, {1, 17, 10, 13, 19, 
            15}, {1, 17, 7, 13, 19, 15}, {1, 17, 10, 10, 19, 15}, {1, 13, 10, 
            19, 16, 13}, {3, 13, 13, 15, 19, 12}, {3, 10, 15, 15, 19, 
            10}, {3, 13, 13, 12, 21, 10}, {3, 13, 13, 15, 19, 9}, {6, 13, 15, 
            13, 19, 6}, {4, 10, 13, 17, 19, 12}, {4, 7, 15, 17, 19, 10}, {4, 
            13, 10, 15, 21, 12}, {4, 10, 12, 15, 21, 10}, {4, 13, 10, 12, 23, 
            10}, {4, 13, 10, 15, 21, 9}, {4, 10, 13, 17, 19, 9}, {1, 17, 19, 
            13, 10, 15}, {1, 14, 21, 13, 10, 13}, {1, 17, 19, 13, 7, 15}, {1, 
            17, 19, 10, 10, 15}, {1, 17, 19, 15, 7, 13}, {1, 17, 19, 13, 10, 
            12}, {1, 13, 19, 17, 10, 12}, {1, 17, 19, 10, 12, 13}, {1, 19, 
            17, 10, 13, 15}, {1, 16, 19, 10, 13, 13}, {1, 19, 17, 7, 13, 
            15}, {1, 19, 17, 7, 15, 13}, {1, 19, 7, 13, 19, 13}, {1, 17, 10, 
            13, 19, 12}, {3, 13, 13, 19, 15, 12}, {3, 13, 13, 21, 12, 
            10}, {3, 13, 13, 19, 15, 9}, {3, 15, 10, 19, 15, 10}, {6, 15, 13, 
            19, 13, 6}, {4, 10, 13, 21, 15, 12}, {4, 10, 13, 23, 12, 10}, {4, 
            13, 10, 19, 17, 9}, {4, 13, 10, 19, 17, 12}, {4, 10, 13, 21, 15, 
            9}, {4, 12, 10, 21, 15, 10}, {4, 15, 7, 19, 17, 10}, {3, 15, 19, 
            13, 13, 12}, {3, 12, 21, 13, 13, 10}, {3, 15, 19, 10, 15, 
            10}, {3, 15, 19, 13, 13, 9}, {6, 13, 19, 13, 15, 6}, {4, 15, 21, 
            13, 10, 12}, {4, 12, 23, 13, 10, 10}, {4, 15, 21, 13, 10, 9}, {4, 
            15, 21, 10, 12, 10}, {4, 17, 19, 10, 13, 12}, {4, 17, 19, 7, 15, 
            10}, {1, 19, 13, 7, 17, 15}, {1, 21, 10, 10, 17, 13}, {1, 19, 13, 
            10, 17, 15}, {1, 19, 10, 10, 17, 15}, {1, 19, 13, 7, 19, 13}, {1, 
            19, 17, 12, 10, 13}, {1, 19, 17, 10, 10, 15}, {1, 19, 17, 10, 13, 
            12}, {4, 17, 19, 10, 13, 9}, {1, 19, 16, 13, 10, 13}, {1, 21, 14, 
            10, 13, 13}, {1, 19, 13, 10, 17, 12}, {3, 19, 15, 13, 13, 
            12}, {3, 19, 15, 15, 10, 10}, {3, 21, 12, 13, 13, 10}, {3, 19, 
            15, 13, 13, 9}, {4, 19, 17, 13, 10, 12}, {4, 19, 17, 15, 7, 
            10}, {4, 19, 17, 13, 10, 9}, {4, 21, 15, 10, 13, 12}, {6, 19, 13, 
            15, 13, 6}, {4, 21, 15, 12, 10, 10}, {4, 21, 15, 10, 13, 9}, {4, 
            23, 12, 10, 13, 10}, {3, 10, 13, 17, 15, 17}, {3, 7, 13, 17, 15, 
            17}, {3, 10, 15, 17, 13, 17}, {3, 7, 15, 17, 13, 17}, {3, 10, 15, 
            17, 10, 17}, {3, 10, 10, 17, 15, 17}, {4, 7, 13, 19, 15, 17}, {4, 
            4, 13, 19, 15, 17}, {4, 7, 15, 19, 13, 17}, {4, 4, 15, 19, 13, 
            17}, {4, 7, 15, 19, 10, 17}, {4, 7, 10, 19, 15, 17}, {3, 13, 10, 
            15, 17, 17}, {3, 10, 10, 15, 17, 17}, {3, 13, 7, 15, 17, 17}, {3, 
            15, 10, 13, 17, 17}, {3, 15, 7, 13, 17, 17}, {3, 15, 10, 10, 17, 
            17}, {4, 13, 7, 15, 19, 17}, {4, 10, 7, 15, 19, 17}, {4, 13, 4, 
            15, 19, 17}, {4, 15, 7, 10, 19, 17}, {4, 15, 7, 13, 19, 17}, {4, 
            15, 4, 13, 19, 17}, {6, 10, 10, 15, 15, 19}, {6, 7, 10, 15, 15, 
            19}, {6, 10, 7, 15, 15, 19}, {6, 7, 13, 14, 13, 19}, {3, 13, 17, 
            15, 10, 17}, {3, 10, 17, 15, 10, 17}, {3, 13, 17, 15, 7, 17}, {3, 
            15, 17, 13, 10, 17}, {3, 15, 17, 13, 7, 17}, {3, 15, 17, 10, 10, 
            17}, {4, 10, 19, 15, 7, 17}, {4, 13, 19, 15, 7, 17}, {4, 13, 19, 
            15, 4, 17}, {4, 15, 19, 13, 7, 17}, {4, 15, 19, 13, 4, 17}, {4, 
            15, 19, 10, 7, 17}, {6, 10, 15, 15, 10, 19}, {6, 7, 15, 15, 10, 
            19}, {6, 10, 15, 15, 7, 19}, {3, 13, 19, 15, 13, 9}, {4, 13, 21, 
            15, 10, 12}, {4, 10, 23, 15, 10, 10}, {4, 13, 21, 15, 10, 9}, {6, 
            13, 7, 13, 14, 19}, {3, 15, 13, 13, 19, 9}, {4, 15, 10, 10, 23, 
            10}, {4, 15, 10, 13, 21, 12}, {4, 15, 10, 13, 21, 9}, {3, 13, 15, 
            19, 13, 9}, {4, 10, 15, 21, 13, 12}, {4, 10, 15, 23, 10, 10}, {4, 
            10, 15, 21, 13, 9}, {6, 13, 14, 13, 7, 19}, {3, 17, 15, 10, 13, 
            17}, {3, 17, 15, 10, 10, 17}, {3, 17, 13, 10, 15, 17}, {3, 17, 
            10, 10, 15, 17}, {3, 17, 15, 7, 13, 17}, {3, 17, 13, 7, 15, 
            17}, {4, 19, 15, 4, 13, 17}, {4, 19, 15, 7, 13, 17}, {4, 19, 13, 
            4, 15, 17}, {4, 19, 13, 7, 15, 17}, {4, 19, 10, 7, 15, 17}, {4, 
            19, 15, 7, 10, 17}, {6, 15, 10, 10, 15, 19}, {6, 15, 7, 10, 15, 
            19}, {6, 15, 10, 7, 15, 19}, {6, 15, 15, 10, 10, 19}, {6, 15, 15, 
            10, 7, 19}, {6, 15, 15, 7, 10, 19}, {6, 14, 13, 7, 13, 19}, {3, 
            19, 13, 13, 15, 9}, {4, 23, 10, 10, 15, 10}, {4, 21, 13, 10, 15, 
            12}, {4, 21, 13, 10, 15, 9}, {4, 7, 13, 21, 12, 15}, {4, 7, 15, 
            21, 10, 15}, {7, 4, 13, 16, 13, 19}, {4, 4, 13, 19, 17, 15}, {4, 
            7, 10, 17, 19, 15}, {4, 10, 10, 15, 21, 12}, {7, 1, 13, 19, 15, 
            17}, {4, 7, 15, 21, 15, 10}, {4, 7, 13, 21, 15, 12}, {4, 10, 10, 
            21, 15, 12}, {7, 4, 13, 21, 15, 12}, {6, 13, 15, 10, 21, 7}, {6, 
            10, 21, 13, 15, 7}, {3, 10, 21, 15, 13, 10}, {3, 15, 13, 10, 21, 
            10}, {4, 7, 13, 16, 19, 13}, {4, 4, 15, 19, 17, 13}, {7, 4, 15, 
            21, 15, 10}, {4, 13, 7, 12, 21, 15}, {4, 15, 7, 10, 21, 15}, {7, 
            7, 7, 15, 19, 17}, {4, 10, 13, 14, 21, 10}, {4, 10, 10, 14, 21, 
            13}, {6, 10, 13, 14, 13, 19}, {12, 10, 10, 10, 10, 23}, {7, 7, 
            13, 16, 13, 19}, {7, 7, 13, 23, 10, 12}, {4, 7, 17, 21, 13, 
            10}, {4, 10, 21, 15, 7, 15}, {4, 12, 21, 13, 7, 15}, {4, 14, 21, 
            10, 13, 10}, {10, 1, 17, 21, 13, 10}, {4, 13, 7, 15, 21, 12}, {4, 
            15, 7, 15, 21, 10}, {4, 10, 10, 21, 14, 13}, {4, 10, 7, 19, 17, 
            15}, {4, 13, 4, 17, 19, 15}, {7, 7, 7, 19, 15, 17}, {7, 7, 10, 
            21, 12, 15}, {7, 13, 1, 15, 19, 17}, {7, 10, 7, 12, 21, 15}, {3, 
            13, 15, 21, 10, 10}, {4, 13, 7, 19, 16, 13}, {3, 13, 15, 19, 13, 
            12}, {4, 13, 17, 21, 7, 10}, {6, 15, 13, 21, 10, 7}, {3, 13, 19, 
            15, 13, 12}, {7, 10, 23, 13, 7, 12}, {4, 15, 21, 13, 7, 12}, {4, 
            15, 21, 10, 10, 12}, {4, 15, 21, 15, 7, 10}, {4, 13, 21, 17, 7, 
            10}, {4, 7, 21, 17, 13, 10}, {4, 17, 19, 7, 10, 15}, {4, 14, 21, 
            10, 10, 13}, {4, 16, 19, 7, 13, 13}, {4, 19, 17, 4, 13, 15}, {4, 
            19, 17, 4, 15, 13}, {7, 15, 19, 7, 7, 17}, {7, 12, 21, 10, 7, 
            15}, {7, 13, 4, 13, 16, 19}, {7, 13, 4, 15, 21, 12}, {4, 13, 10, 
            21, 14, 10}, {6, 21, 10, 15, 13, 7}, {3, 21, 10, 13, 15, 10}, {4, 
            15, 4, 17, 19, 13}, {4, 17, 7, 13, 21, 10}, {7, 15, 4, 15, 21, 
            10}, {3, 15, 13, 13, 19, 12}, {7, 13, 16, 13, 4, 19}, {6, 13, 14, 
            13, 10, 19}, {7, 13, 16, 13, 7, 19}, {7, 13, 7, 10, 23, 12}, {6, 
            13, 10, 13, 14, 19}, {7, 13, 7, 13, 16, 19}, {4, 21, 10, 7, 15, 
            15}, {4, 21, 12, 7, 13, 15}, {4, 17, 13, 7, 21, 10}, {10, 17, 1, 
            13, 21, 10}, {7, 19, 15, 1, 13, 17}, {4, 17, 19, 13, 4, 15}, {4, 
            17, 19, 15, 4, 13}, {4, 19, 17, 10, 7, 15}, {4, 21, 15, 10, 10, 
            12}, {4, 19, 16, 13, 7, 13}, {7, 15, 19, 13, 1, 17}, {7, 19, 15, 
            7, 7, 17}, {7, 15, 21, 13, 4, 12}, {7, 15, 21, 15, 4, 10}, {10, 
            13, 21, 17, 1, 10}, {4, 21, 14, 13, 10, 10}, {4, 21, 14, 10, 10, 
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            10}, {10, 23, 10, 4, 15, 10}, {10, 23, 4, 10, 15, 10}, {10, 17, 
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            10}, {7, 17, 7, 19, 15, 7}, {10, 17, 7, 19, 15, 4}, {10, 17, 7, 
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            7}, {7, 21, 12, 15, 10, 7}, {7, 21, 7, 15, 15, 7}, {10, 19, 15, 
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            19}, {13, 15, 17, 10, 7, 19}, {13, 15, 17, 10, 1, 19}, {13, 15, 
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            12}, {7, 19, 15, 15, 6, 10}, {7, 21, 13, 12, 9, 10}, {7, 23, 10, 
            10, 12, 10}, {7, 21, 12, 10, 9, 13}, {7, 17, 17, 13, 3, 15}, {7, 
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            13}, {10, 15, 17, 13, 0, 17}, {7, 21, 12, 13, 9, 10}, {13, 15, 
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            12}, {10, 19, 15, 15, 6, 7}, {10, 19, 15, 15, 6, 10}, {10, 21, 
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            15}, {10, 21, 13, 7, 9, 12}, {13, 15, 17, 10, 0, 17}, {10, 15, 
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            13}, {7, 21, 14, 10, 13, 13}, {7, 23, 12, 10, 13, 10}, {7, 19, 
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            13}, {10, 21, 12, 10, 15, 13}, {10, 23, 10, 10, 12, 10}, {10, 21, 
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            10}, {15, 15, 15, 10, 10, 19}, {9, 17, 17, 15, 10, 13}, {9, 19, 
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            13}, {9, 19, 14, 13, 13, 13}, {9, 21, 12, 13, 13, 10}, {12, 19, 
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            17}, {7, 19, 15, 1, 17, 13}, {10, 17, 15, 0, 17, 13}, {10, 19, 
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            15}, {10, 23, 10, 7, 13, 12}, {12, 21, 10, 15, 13, 7}, {10, 21, 
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            7}, {10, 21, 13, 1, 13, 14}, {10, 21, 12, 4, 10, 15}, {7, 21, 12, 
            4, 13, 15}, {10, 23, 10, 4, 13, 12}, {10, 21, 12, 4, 13, 15}, {7, 
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            4}, {10, 23, 10, 7, 12, 10}, {10, 23, 10, 10, 12, 7}, {10, 23, 
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            14}, {10, 4, 10, 21, 13, 14}, {10, 7, 10, 21, 13, 14}, {10, 3, 
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            13}, {10, 6, 21, 13, 7, 15}, {10, 9, 21, 13, 4, 15}, {10, 7, 9, 
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            10}, {13, 1, 19, 17, 15, 10}, {13, 1, 19, 17, 15, 7}, {13, 4, 19, 
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            7}, {10, 7, 21, 15, 15, 4}, {10, 7, 23, 13, 12, 7}, {15, 10, 19, 
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            14}, {10, 10, 4, 13, 21, 14}, {10, 9, 7, 12, 21, 13}, {10, 13, 7, 
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            15}, {10, 9, 15, 17, 17, 13}, {10, 12, 13, 15, 19, 12}, {10, 9, 
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            13}, {13, 12, 15, 17, 15, 15}, {10, 12, 13, 14, 19, 13}, {10, 12, 
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            13}, {12, 12, 15, 13, 19, 10}, {15, 12, 17, 15, 15, 13}, {15, 15, 
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            4}, {10, 10, 14, 13, 21, 7}, {10, 9, 13, 12, 21, 7}, {10, 10, 15, 
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            21}, {10, 7, 10, 15, 12, 21}, {9, 7, 10, 13, 12, 21}, {10, 4, 10, 
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            21}, {10, 4, 12, 15, 10, 21}, {10, 7, 12, 15, 7, 21}, {9, 12, 7, 
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            21}, {10, 12, 4, 10, 15, 21}, {9, 12, 13, 10, 7, 21}, {9, 10, 13, 
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            21}, {12, 7, 10, 21, 7, 15}, {10, 7, 13, 21, 6, 15}, {10, 4, 13, 
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            15}, {10, 10, 15, 21, 3, 13}, {10, 4, 15, 21, 12, 13}, {10, 4, 
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            10}, {10, 10, 12, 23, 7, 10}, {12, 10, 9, 21, 7, 13}, {12, 10, 9, 
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            13}, {12, 7, 21, 10, 7, 15}, {12, 4, 23, 13, 10, 10}, {10, 7, 23, 
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            15}, {12, 7, 21, 9, 13, 10}, {12, 7, 21, 10, 15, 7}, {12, 3, 21, 
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            10}, {15, 4, 19, 13, 17, 4}, {15, 4, 19, 13, 17, 7}, {12, 4, 21, 
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            13}, {10, 13, 12, 17, 17, 15}, {10, 15, 9, 17, 17, 13}, {10, 13, 
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            10}, {13, 13, 9, 15, 17, 17}, {10, 13, 12, 19, 14, 13}, {10, 13, 
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            17}, {13, 15, 12, 15, 17, 15}, {13, 17, 9, 15, 17, 13}, {15, 17, 
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            10}, {10, 15, 10, 7, 12, 21}, {10, 15, 7, 7, 12, 21}, {10, 15, 
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            21}, {13, 7, 10, 15, 12, 21}, {9, 13, 10, 7, 12, 21}, {9, 13, 12, 
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            21}, {10, 13, 17, 21, 7, 4}, {10, 12, 13, 23, 7, 7}, {13, 13, 19, 
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            4}, {13, 17, 15, 19, 7, 7}, {13, 17, 15, 19, 4, 7}, {15, 17, 13, 
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            4}, {15, 10, 19, 13, 17, 1}, {10, 13, 21, 10, 4, 14}, {10, 13, 
            21, 10, 7, 14}, {10, 12, 21, 9, 7, 13}, {12, 10, 21, 10, 7, 
            15}, {12, 10, 21, 9, 10, 13}, {12, 10, 21, 9, 7, 13}, {10, 13, 
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            12}, {10, 17, 17, 12, 13, 15}, {10, 14, 19, 12, 13, 13}, {10, 17, 
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            10}, {12, 15, 17, 12, 15, 13}, {13, 17, 15, 9, 13, 17}, {13, 17, 
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            17}, {12, 10, 21, 9, 13, 10}, {10, 13, 21, 13, 7, 14}, {10, 12, 
            21, 10, 15, 4}, {10, 13, 21, 10, 14, 4}, {10, 13, 21, 10, 14, 
            7}, {10, 12, 21, 9, 13, 7}, {12, 10, 21, 10, 15, 4}, {12, 10, 21, 
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            4}, {12, 13, 19, 10, 17, 4}, {12, 10, 7, 7, 21, 15}, {12, 10, 7, 
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            13}, {10, 15, 4, 9, 21, 13}, {12, 13, 10, 3, 21, 13}, {12, 13, 
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            10}, {12, 15, 10, 21, 7, 7}, {10, 14, 10, 21, 13, 4}, {10, 14, 
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            4}, {12, 13, 9, 21, 10, 7}, {12, 15, 10, 21, 10, 4}, {12, 15, 10, 
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            7}, {10, 13, 12, 7, 23, 7}, {12, 10, 15, 10, 21, 4}, {10, 15, 15, 
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            15, 15, 4, 21, 7}, {10, 15, 15, 7, 21, 4}, {13, 15, 17, 4, 19, 
            7}, {13, 15, 17, 7, 19, 7}, {13, 19, 13, 7, 19, 1}, {13, 15, 17, 
            4, 19, 4}, {13, 15, 17, 7, 19, 1}, {13, 19, 13, 7, 19, 7}, {13, 
            17, 15, 1, 19, 10}, {13, 17, 15, 7, 19, 10}, {13, 17, 15, 1, 19, 
            7}, {14, 13, 13, 1, 21, 10}, {14, 10, 13, 4, 21, 10}, {12, 13, 
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            4}, {10, 13, 12, 13, 21, 3}, {9, 15, 13, 10, 21, 4}, {12, 15, 13, 
            10, 21, 4}, {12, 13, 15, 7, 21, 4}, {15, 13, 17, 7, 19, 1}, {9, 
            13, 15, 21, 10, 4}, {9, 15, 13, 21, 10, 4}, {10, 12, 13, 21, 13, 
            3}, {12, 13, 15, 21, 10, 4}, {12, 15, 13, 21, 10, 4}, {14, 13, 
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            10}, {10, 15, 10, 19, 15, 3}, {9, 17, 10, 19, 13, 4}, {12, 17, 
            10, 19, 13, 4}, {12, 15, 13, 21, 7, 4}, {13, 15, 17, 13, 9, 
            17}, {15, 15, 15, 13, 12, 17}, {10, 17, 17, 13, 12, 15}, {13, 15, 
            17, 15, 12, 15}, {10, 17, 17, 15, 9, 13}, {10, 19, 15, 13, 12, 
            12}, {10, 19, 15, 15, 9, 10}, {10, 21, 13, 12, 12, 10}, {13, 15, 
            17, 17, 9, 13}, {15, 19, 10, 15, 15, 10}, {10, 19, 14, 13, 12, 
            13}, {10, 21, 12, 13, 12, 10}, {12, 17, 15, 15, 12, 13}, {12, 19, 
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            14}, {10, 21, 13, 7, 10, 14}, {10, 21, 12, 7, 9, 13}, {9, 21, 10, 
            13, 15, 4}, {9, 21, 10, 15, 13, 4}, {10, 21, 13, 12, 13, 3}, {12, 
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            4}, {10, 21, 13, 14, 10, 7}, {10, 21, 12, 15, 10, 4}, {10, 21, 
            12, 13, 9, 7}, {15, 17, 13, 19, 4, 4}, {15, 17, 13, 19, 4, 
            7}, {15, 19, 10, 17, 13, 7}, {9, 19, 13, 17, 10, 4}, {10, 19, 15, 
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            1}, {15, 17, 13, 19, 7, 1}, {12, 21, 10, 15, 13, 4}, {12, 19, 13, 
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            15}, {13, 19, 1, 13, 19, 7}, {10, 21, 4, 15, 15, 7}, {10, 21, 7, 
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            10}, {13, 19, 1, 15, 17, 7}, {13, 19, 4, 17, 15, 4}, {13, 19, 4, 
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            21, 7, 15, 15, 7}, {10, 23, 7, 12, 13, 7}, {12, 21, 10, 13, 15, 
            4}, {12, 21, 7, 7, 10, 15}, {12, 23, 4, 10, 13, 10}, {12, 21, 10, 
            7, 10, 15}, {12, 21, 10, 4, 10, 15}, {12, 21, 3, 10, 13, 
            13}, {14, 21, 1, 13, 13, 10}, {12, 21, 7, 15, 10, 7}, {12, 21, 
            10, 15, 10, 7}, {12, 21, 10, 15, 10, 4}, {12, 21, 4, 15, 13, 
            7}, {15, 19, 7, 17, 13, 1}, {15, 19, 4, 17, 13, 4}, {15, 19, 4, 
            17, 13, 7}, {12, 21, 7, 15, 13, 4}, {10, 23, 7, 10, 12, 10}, {12, 
            21, 7, 10, 9, 13}, {12, 21, 10, 10, 9, 13}, {12, 21, 10, 7, 9, 
            13}, {14, 21, 4, 10, 10, 13}, {12, 21, 7, 13, 9, 10}, {12, 21, 
            10, 13, 9, 10}, {12, 21, 10, 13, 9, 7}, {14, 21, 4, 13, 10, 
            10}, {10, 1, 17, 19, 12, 13}, {10, 1, 13, 19, 12, 17}, {12, 1, 
            10, 19, 13, 17}, {13, 0, 13, 14, 13, 19}, {10, 1, 12, 17, 13, 
            19}, {10, 0, 15, 17, 13, 17}, {13, 0, 13, 17, 12, 17}, {13, 0, 
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            14}, {13, 0, 17, 17, 12, 13}, {10, 3, 15, 15, 10, 19}, {10, 6, 
            17, 13, 7, 19}, {13, 3, 13, 12, 10, 21}, {13, 6, 15, 10, 7, 
            21}, {13, 4, 10, 15, 12, 21}, {10, 9, 15, 15, 10, 19}, {10, 12, 
            17, 13, 7, 19}, {13, 9, 13, 12, 10, 21}, {10, 9, 19, 17, 13, 
            13}, {10, 12, 17, 17, 13, 15}, {10, 9, 15, 17, 13, 17}, {13, 9, 
            13, 14, 13, 19}, {12, 12, 15, 13, 10, 19}, {12, 12, 15, 15, 13, 
            17}, {10, 12, 13, 21, 13, 9}, {15, 0, 10, 17, 13, 17}, {10, 7, 
            13, 17, 12, 19}, {10, 4, 13, 17, 12, 19}, {13, 7, 10, 14, 13, 
            21}, {13, 3, 13, 15, 12, 19}, {13, 9, 13, 15, 12, 19}, {10, 4, 
            13, 17, 9, 19}, {10, 7, 13, 17, 6, 19}, {13, 4, 10, 15, 9, 
            21}, {13, 7, 10, 15, 6, 21}, {13, 1, 10, 17, 12, 19}, {13, 3, 13, 
            15, 9, 19}, {15, 1, 7, 17, 13, 19}, {10, 1, 19, 17, 15, 10}, {10, 
            4, 19, 15, 17, 7}, {15, 4, 19, 10, 17, 7}, {12, 10, 13, 23, 7, 
            10}, {13, 7, 7, 10, 12, 23}, {13, 10, 7, 7, 12, 23}, {13, 7, 12, 
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            7, 10, 12, 7, 23}, {13, 12, 7, 7, 10, 23}, {13, 12, 10, 7, 7, 
            23}, {12, 7, 13, 23, 7, 10}, {12, 10, 13, 23, 7, 7}, {10, 13, 12, 
            13, 21, 9}, {10, 12, 17, 13, 4, 19}, {10, 9, 17, 13, 4, 19}, {10, 
            12, 19, 13, 1, 17}, {13, 12, 15, 10, 4, 21}, {13, 10, 4, 12, 15, 
            21}, {12, 10, 13, 21, 9, 13}, {14, 10, 10, 21, 7, 13}, {12, 10, 
            12, 21, 10, 13}, {13, 9, 15, 10, 4, 21}, {10, 10, 15, 15, 19, 
            9}, {14, 7, 19, 6, 13, 13}, {14, 10, 19, 6, 13, 13}, {12, 13, 10, 
            7, 23, 10}, {12, 13, 7, 7, 23, 10}, {12, 13, 10, 7, 23, 7}, {14, 
            6, 13, 7, 19, 13}, {14, 6, 13, 10, 19, 13}, {14, 10, 10, 7, 21, 
            13}, {14, 13, 13, 7, 21, 10}, {14, 10, 13, 7, 21, 10}, {12, 10, 
            13, 15, 12, 19}, {15, 12, 13, 13, 12, 19}, {10, 13, 17, 15, 0, 
            17}, {10, 13, 17, 19, 0, 13}, {10, 10, 15, 15, 3, 19}, {13, 10, 
            12, 13, 3, 21}, {13, 13, 14, 13, 0, 19}, {13, 12, 15, 13, 3, 
            19}, {13, 9, 15, 13, 3, 19}, {13, 12, 17, 13, 0, 17}, {10, 10, 
            15, 15, 9, 19}, {13, 10, 12, 13, 9, 21}, {10, 13, 17, 15, 9, 
            17}, {10, 13, 17, 19, 9, 13}, {10, 13, 17, 17, 12, 15}, {12, 13, 
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            12}, {17, 17, 9, 13, 15, 10}, {21, 10, 13, 1, 10, 17}, {21, 10, 
            13, 7, 10, 17}, {19, 13, 13, 0, 14, 13}, {17, 15, 13, 9, 17, 
            10}, {19, 12, 13, 1, 17, 10}, {21, 12, 10, 4, 15, 10}, {19, 13, 
            13, 1, 16, 10}, {21, 10, 13, 1, 14, 13}, {19, 13, 13, 10, 14, 
            6}, {19, 13, 13, 7, 14, 6}, {19, 13, 13, 4, 16, 7}, {21, 13, 10, 
            4, 14, 10}, {23, 10, 10, 4, 12, 13}, {17, 15, 13, 10, 17, 
            9}, {19, 15, 10, 10, 15, 9}, {19, 13, 12, 10, 15, 12}, {19, 13, 
            13, 7, 16, 10}, {19, 13, 13, 7, 16, 7}, {21, 13, 10, 7, 14, 
            10}, {19, 13, 13, 9, 14, 13}, {19, 13, 13, 10, 14, 12}, {17, 15, 
            13, 12, 15, 12}, {19, 15, 10, 12, 13, 12}, {21, 13, 10, 10, 1, 
            17}, {17, 13, 15, 17, 10, 9}, {17, 13, 15, 15, 12, 12}, {17, 13, 
            15, 17, 9, 10}, {19, 10, 15, 13, 12, 12}, {19, 10, 15, 15, 10, 
            9}, {19, 12, 13, 15, 10, 12}, {19, 13, 13, 14, 0, 13}, {19, 13, 
            13, 14, 9, 13}, {21, 10, 12, 15, 4, 10}, {19, 13, 12, 17, 1, 
            10}, {19, 15, 10, 17, 1, 10}, {19, 13, 13, 14, 10, 6}, {19, 13, 
            13, 14, 7, 6}, {19, 13, 13, 14, 10, 12}, {21, 10, 12, 13, 10, 
            12}, {19, 13, 13, 16, 7, 10}, {21, 13, 10, 14, 1, 13}, {19, 13, 
            13, 16, 1, 10}, {23, 10, 10, 12, 4, 13}, {19, 13, 13, 16, 7, 
            7}, {19, 13, 13, 16, 4, 7}, {19, 14, 0, 13, 13, 13}, {19, 14, 9, 
            13, 13, 13}, {17, 17, 10, 15, 13, 3}, {17, 17, 10, 13, 15, 
            3}, {17, 17, 7, 13, 15, 3}, {17, 17, 7, 15, 13, 3}, {19, 14, 10, 
            13, 13, 6}, {19, 14, 7, 13, 13, 6}, {19, 15, 10, 10, 15, 6}, {19, 
            15, 7, 10, 15, 6}, {19, 15, 10, 15, 10, 6}, {19, 15, 7, 15, 10, 
            6}, {23, 10, 10, 10, 10, 12}, {17, 17, 10, 10, 15, 3}, {17, 17, 
            10, 15, 10, 3}, {19, 15, 10, 7, 15, 6}, {19, 15, 10, 15, 7, 
            6}, {17, 17, 10, 10, 3, 15}, {17, 17, 10, 15, 3, 10}, {19, 17, 7, 
            10, 4, 15}, {19, 15, 10, 10, 1, 17}, {19, 17, 7, 15, 4, 10}, {19, 
            14, 10, 13, 13, 12}, {21, 13, 10, 10, 12, 12}, {19, 16, 7, 13, 
            13, 10}, {21, 13, 10, 10, 7, 17}, {21, 14, 7, 10, 13, 10}, {21, 
            12, 10, 10, 13, 12}, {21, 10, 13, 14, 7, 10}, {21, 10, 13, 12, 
            10, 12}, {21, 10, 13, 14, 4, 10}, {21, 15, 4, 10, 12, 10}, {19, 
            17, 1, 13, 12, 10}, {19, 16, 1, 13, 13, 10}, {21, 14, 1, 13, 10, 
            13}, {19, 16, 7, 13, 13, 7}, {19, 16, 4, 13, 13, 7}, {23, 12, 4, 
            10, 10, 13}, {21, 14, 4, 10, 13, 10}, {21, 4, 10, 7, 15, 
            15}, {19, 7, 17, 10, 15, 7}, {19, 4, 17, 10, 15, 7}, {19, 7, 17, 
            7, 15, 7}, {19, 10, 15, 7, 17, 7}, {19, 10, 15, 4, 17, 7}, {19, 
            7, 15, 7, 17, 7}, {21, 4, 12, 7, 15, 13}, {21, 7, 14, 10, 13, 
            13}, {21, 14, 7, 13, 10, 13}, {23, 7, 12, 10, 10, 13}, {21, 10, 
            12, 10, 13, 9}, {21, 7, 12, 10, 13, 9}, {21, 10, 12, 13, 10, 
            9}, {21, 7, 12, 13, 10, 9}, {21, 12, 10, 10, 13, 9}, {21, 12, 7, 
            10, 13, 9}, {21, 12, 10, 13, 10, 9}, {21, 12, 7, 13, 10, 9}, {21, 
            7, 14, 10, 13, 10}, {21, 4, 14, 10, 13, 10}, {21, 7, 15, 10, 12, 
            13}, {19, 9, 15, 13, 12, 13}, {21, 12, 10, 15, 4, 13}, {19, 12, 
            13, 15, 9, 13}, {19, 12, 13, 15, 3, 13}, {19, 12, 13, 13, 3, 
            15}, {21, 12, 10, 15, 7, 13}, {19, 3, 13, 13, 12, 15}, {19, 3, 
            15, 13, 12, 13}, {21, 3, 10, 13, 10, 15}, {19, 3, 13, 13, 9, 
            15}, {19, 3, 15, 13, 9, 13}, {19, 9, 13, 15, 3, 13}, {19, 9, 13, 
            13, 3, 15}, {19, 6, 13, 15, 9, 13}, {19, 6, 13, 15, 6, 13}, {21, 
            4, 15, 10, 12, 13}, {19, 6, 15, 13, 6, 13}, {19, 9, 15, 13, 6, 
            13}, {21, 10, 13, 10, 3, 15}, {21, 4, 13, 10, 12, 15}, {21, 7, 
            15, 10, 6, 13}, {21, 6, 10, 15, 7, 13}, {23, 4, 10, 10, 10, 
            15}, {21, 4, 15, 10, 9, 13}, {21, 3, 12, 13, 10, 13}, {21, 9, 12, 
            13, 10, 13}, {21, 9, 10, 15, 4, 13}, {23, 10, 10, 10, 4, 
            15}, {21, 10, 13, 12, 3, 13}, {21, 10, 13, 12, 9, 13}, {23, 10, 
            10, 12, 7, 13}, {19, 12, 13, 17, 4, 10}, {19, 6, 13, 17, 7, 
            10}, {19, 12, 13, 17, 7, 10}, {19, 4, 17, 13, 12, 10}, {19, 7, 
            17, 13, 12, 10}, {19, 7, 17, 13, 6, 10}, {19, 4, 17, 13, 9, 
            10}, {19, 9, 13, 17, 4, 10}, {19, 3, 15, 15, 10, 10}, {19, 10, 
            15, 15, 3, 10}, {19, 9, 15, 15, 10, 10}, {19, 10, 15, 15, 9, 
            10}, {19, 1, 13, 10, 12, 17}, {21, 4, 13, 10, 9, 15}, {23, 7, 10, 
            10, 10, 12}, {21, 4, 15, 10, 12, 10}, {21, 7, 15, 4, 10, 
            15}, {21, 7, 15, 4, 12, 13}, {21, 12, 10, 13, 4, 15}, {21, 10, 4, 
            15, 7, 15}, {19, 15, 3, 12, 13, 13}, {19, 13, 12, 9, 15, 
            13}, {21, 10, 12, 4, 15, 13}, {19, 13, 3, 12, 13, 15}, {19, 15, 
            9, 12, 13, 13}, {21, 10, 3, 10, 13, 15}, {19, 13, 9, 3, 13, 
            15}, {19, 13, 12, 3, 13, 15}, {19, 13, 12, 3, 15, 13}, {21, 10, 
            12, 7, 15, 13}, {19, 15, 3, 9, 13, 13}, {19, 13, 9, 3, 15, 
            13}, {19, 13, 3, 9, 13, 15}, {21, 15, 7, 12, 10, 13}, {19, 13, 6, 
            9, 15, 13}, {19, 13, 6, 6, 15, 13}, {21, 13, 10, 3, 10, 15}, {19, 
            15, 6, 6, 13, 13}, {19, 15, 9, 6, 13, 13}, {21, 15, 4, 12, 10, 
            13}, {21, 10, 12, 4, 13, 15}, {21, 13, 4, 12, 10, 15}, {21, 10, 
            6, 7, 15, 13}, {21, 15, 7, 6, 10, 13}, {21, 10, 9, 4, 15, 
            13}, {23, 10, 4, 10, 10, 15}, {21, 15, 4, 9, 10, 13}, {21, 12, 9, 
            10, 13, 13}, {23, 10, 10, 4, 10, 15}, {21, 13, 10, 3, 12, 
            13}, {23, 10, 10, 7, 12, 13}, {21, 13, 10, 9, 12, 13}, {21, 12, 
            3, 10, 13, 13}, {19, 17, 7, 12, 13, 10}, {19, 13, 12, 4, 17, 
            10}, {19, 17, 4, 12, 13, 10}, {19, 13, 6, 7, 17, 10}, {19, 13, 
            12, 7, 17, 10}, {19, 17, 7, 6, 13, 10}, {19, 13, 9, 4, 17, 
            10}, {19, 17, 4, 9, 13, 10}, {19, 15, 10, 3, 15, 10}, {19, 15, 3, 
            10, 15, 10}, {19, 15, 9, 10, 15, 10}, {19, 15, 10, 9, 15, 
            10}, {19, 10, 12, 1, 13, 17}, {21, 10, 9, 4, 13, 15}, {21, 10, 
            12, 4, 15, 10}, {19, 15, 10, 17, 4, 7}, {19, 15, 10, 17, 7, 
            7}, {19, 15, 7, 17, 7, 7}, {19, 17, 7, 15, 10, 7}, {19, 17, 4, 
            15, 10, 7}, {19, 17, 7, 15, 7, 7}, {21, 14, 4, 13, 10, 10}, {21, 
            14, 7, 13, 10, 10}, {21, 12, 4, 15, 7, 13}, {23, 10, 7, 10, 10, 
            12}, {19, 13, 1, 12, 10, 17}, {21, 13, 4, 9, 10, 15}, {21, 13, 
            10, 14, 7, 13}, {21, 10, 13, 7, 14, 13}, {21, 10, 13, 7, 12, 
            9}, {21, 10, 13, 12, 7, 9}, {21, 10, 13, 10, 12, 9}, {21, 10, 13, 
            12, 10, 9}, {21, 13, 10, 10, 12, 9}, {21, 13, 10, 12, 10, 
            9}, {21, 13, 10, 7, 12, 9}, {21, 13, 10, 12, 7, 9}, {21, 10, 13, 
            7, 14, 10}, {21, 10, 13, 4, 14, 10}, {21, 13, 10, 14, 4, 
            10}, {21, 13, 10, 14, 7, 10}, {23, 10, 10, 7, 10, 12}, {23, 10, 
            10, 10, 7, 12}, {19, 12, 10, 13, 1, 17}, {21, 9, 10, 13, 4, 
            15}, {21, 15, 7, 10, 4, 15}, {21, 15, 7, 12, 4, 13}, {21, 12, 10, 
            15, 4, 10}, {21, 15, 4, 12, 10, 10}, {21, 10, 7, 15, 7, 15}, {21, 
            4, 7, 13, 10, 17}, {21, 7, 7, 15, 7, 15}, {21, 7, 12, 15, 7, 
            10}, {21, 10, 12, 15, 7, 10}, {21, 12, 10, 15, 7, 10}, {21, 12, 
            7, 15, 7, 10}, {21, 10, 7, 15, 4, 15}, {21, 10, 7, 13, 4, 
            17}, {23, 7, 10, 12, 7, 13}, {21, 7, 4, 10, 13, 17}, {21, 7, 10, 
            7, 15, 15}, {21, 7, 7, 7, 15, 15}, {21, 12, 7, 7, 15, 10}, {21, 
            12, 10, 7, 15, 10}, {21, 10, 12, 7, 15, 10}, {21, 7, 12, 7, 15, 
            10}, {21, 7, 15, 7, 10, 15}, {21, 4, 15, 7, 10, 15}, {21, 7, 15, 
            7, 7, 15}, {21, 10, 13, 7, 4, 17}, {21, 4, 13, 7, 10, 17}, {21, 
            7, 10, 4, 15, 15}, {21, 7, 10, 4, 13, 17}, {23, 7, 10, 7, 12, 
            13}, {23, 10, 7, 7, 12, 13}, {23, 10, 7, 12, 7, 13}, {21, 4, 15, 
            7, 12, 13}, {21, 7, 15, 12, 7, 10}, {21, 7, 15, 12, 10, 10}, {21, 
            7, 15, 10, 12, 10}, {21, 7, 15, 7, 12, 10}, {21, 7, 13, 10, 12, 
            9}, {21, 7, 13, 12, 10, 9}, {21, 7, 12, 4, 15, 13}, {21, 10, 12, 
            7, 13, 9}, {21, 12, 10, 7, 13, 9}, {21, 10, 12, 13, 7, 9}, {21, 
            12, 10, 13, 7, 9}, {21, 12, 7, 15, 4, 13}, {23, 7, 12, 10, 7, 
            13}, {23, 7, 12, 7, 10, 13}, {21, 13, 10, 4, 7, 17}, {21, 15, 7, 
            10, 7, 15}, {21, 15, 4, 10, 7, 15}, {21, 15, 7, 7, 7, 15}, {21, 
            13, 4, 10, 7, 17}, {21, 13, 7, 12, 10, 9}, {21, 15, 7, 7, 12, 
            10}, {21, 15, 7, 10, 12, 10}, {21, 13, 7, 10, 12, 9}, {21, 15, 7, 
            12, 10, 10}, {21, 15, 7, 12, 7, 10}, {23, 12, 7, 7, 10, 13}, {23, 
            12, 7, 10, 7, 13}, {21, 15, 4, 12, 7, 13}, {23, 12, 7, 10, 10, 
            13}};

acineq  =  {-x1 ≤ 0, 
          (x3/45) + (x5/45) + (x6/45) ≤ 
            1, -(x1/72) - (x2/72) - (x3/72) - (x4/72) - (x5/72) - 
              (x6/72) ≤ -1, -((2 x1)/35) + ((2 x3)/175) + (x4/35) + ((2 x5)/175) + ((2 x6)/175) ≤ 
            1, -(x1/16) + (x4/32) + (x6/32) ≤ 
            1, -((6 x1)/85) + ((3 x4)/85) + ((2 x5)/85) ≤ 
            1, -((6 x1)/385) + ((4 x2)/385) + ((6 x3)/385) + ((9 x4)/385) + ((6 x5)/385) ≤ 
            1, -((2 x1)/49) + (x3/49) + (x4/49) + (x6/49) ≤ 
            
            1, -((6 x1)/85) + ((2 x4)/85) + ((3 x5)/85) ≤ 1, -(x1/16) + (x5/32) + (x6/32) ≤ 
            1, -((4 x1)/175) + ((2 x3)/175) + ((2 x4)/175) + 
              (x5/35) + ((2 x6)/175) ≤ 1, 
          (x3/61) + ((3 x5)/122) + ((3 x6)/122) ≤ 
            1, -(x1/17) + (x4/34) + (x5/34) ≤ 
            1, -(x1/16) + (x3/32) + (x6/32) ≤ 
            1, ((3 x3)/122) + (x5/61) + ((3 x6)/122) ≤ 
            1, -((6 x1)/385) + ((6 x2)/385) + ((9 x3)/385) + ((6 x4)/385) + ((4 x5)/385) ≤ 
            1, -((2 x1)/35) + ((2 x2)/175) + 
              (x3/35) + ((2 x4)/175) + ((2 x6)/175) ≤ 1, 
          (x2/77) + ((3 x3)/154) + ((3 x4)/154) + (x5/77) ≤ 
            1, -((2 x1)/35) + ((2 x2)/175) + ((2 x4)/175) + 
              (x5/35) + ((2 x6)/175) ≤ 1, 
          (x2/45) + (x4/45) + (x6/45) ≤ 1, 
          (x2/61) + ((3 x4)/122) + ((3 x6)/122) ≤ 
            1, -((4 x1)/175) + ((2 x2)/175) + 
              (x4/35) + ((2 x5)/175) + ((2 x6)/175) ≤ 
            1, -((6 x1)/385) + ((6 x2)/385) + ((4 x3)/385) + ((6 x4)/385) + ((9 x5)/385) ≤ 
            1, -((6 x1)/85) + ((2 x2)/85) + ((3 x3)/85) ≤ 
            1, -((4 x1)/175) + ((2 x2)/175) + 
              (x3/35) + ((2 x5)/175) + ((2 x6)/175) ≤ 
            1, -((2 x1)/49) + (x2/49) + (x5/49) + (x6/49) ≤ 
            1, -(x1/16) + (x2/32) + (x6/32) ≤ 
            1, ((3 x2)/122) + (x4/61) + ((3 x6)/122) ≤ 
            1, -((2 x1)/35) + 
              (x2/35) + ((2 x3)/175) + ((2 x5)/175) + ((2 x6)/175) ≤ 
            1, -((6 x1)/385) + ((9 x2)/385) + ((6 x3)/385) + ((4 x4)/385) + ((6 x5)/385) ≤ 
            1, ((3 x2)/154) + (x3/77) + (x4/77) + ((3 x5)/154) ≤ 
            1, -((6 x1)/85) + ((3 x2)/85) + ((2 x3)/85) ≤ 1, -(x1/17) + (x2/34) + (x3/34) ≤ 
            1, -((4 x1)/175) + 
              (x2/35) + ((2 x3)/175) + ((2 x4)/175) + ((2 x6)/175) ≤ 1, -((2 x1)/45) + (x6/15) ≤ 
            1, -(x1/31) + (x4/62) + ((3 x6)/62) ≤ 
            1, -(x1/47) + (x4/94) + (x5/94) + ((2 x6)/47) ≤ 
            1, -(x1/47) + (x3/94) + (x4/94) + ((2 x6)/47) ≤ 
            1, -(x1/31) + (x5/62) + ((3 x6)/62) ≤ 
            1, -(x1/225) + (x2/75) + (x3/50) + (x4/75) + 
              (x5/50) ≤ 
            1, ((2 x2)/167) + ((3 x3)/167) + ((3 x4)/167) + ((3 x5)/167) ≤ 
            1, -((2 x1)/419) + ((4 x2)/419) + ((6 x3)/419) + ((7 x4)/419) + ((10 x5)/419) ≤ 
            1, -((18 x1)/3335) + ((32 x2)/3335) + ((48 x3)/3335) + ((54 x4)/3335) + ((81 x5)/3335) ≤ 
            1, -((4 x1)/945) + ((8 x2)/945) + ((2 x3)/135) + ((2 x4)/135) + ((23 x5)/945) + ((2 x6)/945) ≤ 
            1, -(x1/31) + (x3/62) + ((3 x6)/62) ≤ 
            1, -((6 x1)/1207) + ((18 x2)/1207) + ((27 x3)/1207) + ((18 x4)/1207) + ((16 x5)/1207) ≤ 
            1, -((18 x1)/3335) + ((54 x2)/3335) + ((81 x3)/3335) + ((32 x4)/3335) + ((48 x5)/3335) ≤ 
            1, -((4 x1)/945) + ((2 x2)/135) + ((23 x3)/945) + ((8 x4)/945) + ((2 x5)/135) + ((2 x6)/945) ≤ 
            1, -((6 x1)/1207) + ((18 x2)/1207) + ((16 x3)/1207) + ((18 x4)/1207) + ((27 x5)/1207) ≤ 
            1, ((3 x2)/167) + ((2 x3)/167) + ((3 x4)/167) + ((3 x5)/167) ≤ 
            1, -(x1/225) + (x2/50) + (x3/75) + (x4/50) + 
              (x5/75) ≤ 
            1, -((18 x1)/3335) + ((48 x2)/3335) + ((32 x3)/3335) + ((81 x4)/3335) + ((54 x5)/3335) ≤ 
            1, -((6 x1)/1207) + ((16 x2)/1207) + ((18 x3)/1207) + ((27 x4)/1207) + ((18 x5)/1207) ≤ 
            1, -((2 x1)/419) + ((6 x2)/419) + ((4 x3)/419) + ((10 x4)/419) + ((7 x5)/419) ≤ 1, 
          (x2/60) + (x3/60) + (x4/60) + (x5/60) ≤ 1, 
          (x2/77) + (x3/77) + ((3 x4)/154) + ((3 x5)/154) ≤ 
            1, -((4 x1)/945) + ((2 x2)/135) + ((8 x3)/945) + ((23 x4)/945) + ((2 x5)/135) + ((2 x6)/945) ≤ 
            1, ((3 x2)/167) + ((3 x3)/167) + ((3 x4)/167) + ((2 x5)/167) ≤ 
            1, -(x1/47) + (x2/94) + (x5/94) + ((2 x6)/47) ≤ 
            1, ((3 x2)/167) + ((3 x3)/167) + ((2 x4)/167) + ((3 x5)/167) ≤ 
            1, -(x1/47) + (x2/94) + (x3/94) + ((2 x6)/47) ≤ 
            1, -((2 x1)/419) + ((7 x2)/419) + ((10 x3)/419) + ((4 x4)/419) + ((6 x5)/419) ≤ 
            1, -(x1/31) + (x2/62) + ((3 x6)/62) ≤ 
            1, -((6 x1)/1207) + ((27 x2)/1207) + ((18 x3)/1207) + ((16 x4)/1207) + ((18 x5)/1207) ≤ 
            1, -((2 x1)/419) + ((10 x2)/419) + ((7 x3)/419) + ((6 x4)/419) + ((4 x5)/419) ≤ 
            1, -((18 x1)/3335) + ((81 x2)/3335) + ((54 x3)/3335) + ((48 x4)/3335) + ((32 x5)/3335) ≤ 
            1, ((3 x2)/154) + ((3 x3)/154) + (x4/77) + (x5/77) ≤ 
            1, -((4 x1)/945) + ((23 x2)/945) + ((2 x3)/135) + ((2 x4)/135) + ((8 x5)/945) + ((2 x6)/945) ≤ 
            1, ((2 x3)/185) + 
              (x4/37) + ((2 x5)/185) + ((2 x6)/185) ≤ 
            1, -(x1/50) + ((3 x4)/100) + ((3 x6)/100) ≤ 
            1, ((2 x3)/179) + ((2 x4)/179) + ((5 x5)/179) + ((2 x6)/179) ≤ 1, (x4/36) + (x5/36) ≤ 1, 
          (x4/51) + (x5/51) + (x6/51) ≤ 
            1, ((5 x4)/159) + ((2 x5)/159) + ((2 x6)/159) ≤ 
            1, (x3/51) + (x4/51) + (x6/51) ≤ 
            1, -((2 x1)/271) + ((9 x4)/271) + ((6 x5)/271) ≤ 
            1, -((2 x1)/389) + ((4 x2)/389) + ((6 x3)/389) + ((9 x4)/389) + ((6 x5)/389) ≤ 
            1, -(x1/50) + ((3 x5)/100) + ((3 x6)/100) ≤ 
            1, ((2 x4)/159) + ((5 x5)/159) + ((2 x6)/159) ≤ 
            1, ((2 x2)/179) + ((5 x4)/179) + ((2 x5)/179) + ((2 x6)/179) ≤ 
            1, -((2 x1)/271) + ((6 x4)/271) + ((9 x5)/271) ≤ 
            1, ((4 x2)/391) + ((6 x3)/391) + ((6 x4)/391) + ((9 x5)/391) ≤ 
            1, -(x1/50) + ((3 x3)/100) + ((3 x6)/100) ≤ 
            1, ((2 x2)/185) + 
              (x3/37) + ((2 x4)/185) + ((2 x6)/185) ≤ 
            1, -((2 x1)/389) + ((6 x2)/389) + ((9 x3)/389) + ((6 x4)/389) + ((4 x5)/389) ≤ 
            1, -((2 x1)/271) + ((6 x2)/271) + ((9 x3)/271) ≤ 
            1, ((2 x2)/179) + ((5 x3)/179) + ((2 x5)/179) + ((2 x6)/179) ≤ 
            1, ((2 x2)/159) + ((5 x3)/159) + ((2 x6)/159) ≤ 
            1, ((2 x2)/185) + ((2 x4)/185) + 
              (x5/37) + ((2 x6)/185) ≤ 
            1, -((2 x1)/389) + ((6 x2)/389) + ((4 x3)/389) + ((6 x4)/389) + ((9 x5)/389) ≤ 
            1, ((6 x2)/391) + ((4 x3)/391) + ((9 x4)/391) + ((6 x5)/391) ≤ 
            1, ((6 x2)/391) + ((9 x3)/391) + ((4 x4)/391) + ((6 x5)/391) ≤ 1, (x2/51) + (x5/51) + (x6/51) ≤ 1, 
          (x2/36) + (x3/36) ≤ 1, 
          (x2/51) + (x3/51) + (x6/51) ≤ 
            1, ((5 x2)/179) + ((2 x3)/179) + ((2 x4)/179) + ((2 x6)/179) ≤ 
            1, -(x1/50) + ((3 x2)/100) + ((3 x6)/100) ≤ 
            1, (x2/37) + ((2 x3)/185) + ((2 x5)/185) + ((2 x6)/185) ≤ 1, ((5 x2)/159) + ((2 x3)/159) + ((2 x6)/159) ≤ 
            1, -((2 x1)/389) + ((9 x2)/389) + ((6 x3)/389) + ((4 x4)/389) + ((6 x5)/389) ≤ 
            1, -((2 x1)/271) + ((9 x2)/271) + ((6 x3)/271) ≤ 
            1, ((9 x2)/391) + ((6 x3)/391) + ((6 x4)/391) + ((4 x5)/391) ≤ 
            1, -((2 x1)/79) + (x4/79) + ((4 x6)/79) ≤ 
            1, -((2 x1)/79) + (x5/79) + ((4 x6)/79) ≤ 
            1, -((4 x1)/265) + ((2 x3)/265) + ((2 x4)/265) + ((2 x5)/265) + ((11 x6)/265) ≤ 
            1, -((2 x1)/79) + (x3/79) + ((4 x6)/79) ≤ 
            1, ((2 x2)/139) + ((3 x3)/139) + ((2 x4)/139) + ((2 x5)/139) ≤ 
            1, -((4 x1)/265) + ((2 x2)/265) + ((2 x4)/265) + ((2 x5)/265) + ((11 x6)/265) ≤ 
            1, ((2 x2)/139) + ((2 x3)/139) + ((2 x4)/139) + ((3 x5)/139) ≤ 
            1, ((2 x2)/139) + ((2 x3)/139) + ((3 x4)/139) + ((2 x5)/139) ≤ 
            1, -((4 x1)/265) + ((2 x2)/265) + ((2 x3)/265) + ((2 x4)/265) + ((11 x6)/265) ≤ 
            1, -((2 x1)/79) + (x2/79) + ((4 x6)/79) ≤ 
            1, -((4 x1)/265) + ((2 x2)/265) + ((2 x3)/265) + ((2 x5)/265) + ((11 x6)/265) ≤ 
            1, ((3 x2)/139) + ((2 x3)/139) + ((2 x4)/139) + ((2 x5)/139) ≤ 1, 
          (x4/36) + (x6/36) ≤ 
            1, ((2 x3)/179) + ((2 x4)/179) + ((2 x5)/179) + ((5 x6)/179) ≤ 
            1, -((4 x2)/265) + ((2 x3)/265) + ((2 x4)/265) + ((11 x5)/265) + ((2 x6)/265) ≤ 
            1, -(x2/31) + (x4/62) + ((3 x5)/62) ≤ 
            1, -(x2/47) + (x4/94) + ((2 x5)/47) + (x6/94) ≤ 
            1, -((2 x2)/79) + (x4/79) + ((4 x5)/79) ≤ 
            1, (x4/31) + ((2 x5)/93) ≤ 
            1, -(x2/50) + ((3 x4)/100) + ((3 x5)/100) ≤ 
            1, ((3 x3)/122) + ((3 x5)/122) + (x6/61) ≤ 1, 
          (x3/51) + (x4/51) + (x5/51) ≤ 
            1, -(x2/47) + (x3/94) + (x4/94) + ((2 x5)/47) ≤ 
            1, (x5/36) + (x6/36) ≤ 
            1, -((4 x2)/245) + ((2 x4)/245) + ((11 x5)/245) + ((2 x6)/245) ≤ 
            1, ((2 x3)/109) + ((3 x5)/109) + ((2 x6)/109) ≤ 
            
            1, -((4 x2)/245) + ((2 x3)/245) + ((2 x4)/245) + ((11 x5)/245) ≤ 
            1, ((4 x2)/655) + ((12 x3)/655) + ((6 x4)/655) + ((3 x5)/131) + ((6 x6)/655) ≤ 
            1, ((4 x2)/565) + ((6 x3)/565) + ((6 x4)/565) + ((6 x5)/565) + ((3 x6)/113) ≤ 
            1, ((4 x2)/307) + ((9 x4)/307) + ((6 x6)/307) ≤ 
            1, (x4/31) + ((2 x6)/93) ≤ 
            1, ((2 x3)/165) + (x4/33) + ((2 x6)/165) ≤ 
            1, ((4 x2)/397) + ((6 x3)/397) + ((9 x4)/397) + ((6 x5)/397) ≤ 
            1, ((2 x3)/165) + (x4/33) + ((2 x5)/165) ≤ 1, 
          (x3/36) + (x6/36) ≤ 
            1, ((3 x3)/109) + ((2 x5)/109) + ((2 x6)/109) ≤ 
            1, (x3/38) + (x4/38) ≤ 
            1, ((2 x4)/93) + (x5/31) ≤ 
            1, ((2 x2)/265) - ((4 x3)/265) + ((11 x4)/265) + ((2 x5)/265) + ((2 x6)/265) ≤ 
            1, -((4 x3)/245) + ((11 x4)/245) + ((2 x5)/245) + ((2 x6)/245) ≤ 
            1, -((2 x3)/79) + ((4 x4)/79) + (x5/79) ≤ 
            1, -(x3/47) + ((2 x4)/47) + (x5/94) + (x6/94) ≤ 
            1, ((4 x3)/307) + ((9 x5)/307) + ((6 x6)/307) ≤ 
            1, -((4 x2)/179) + ((2 x4)/179) + ((9 x5)/179) ≤ 1, ((2 x2)/109) + ((3 x4)/109) + ((2 x6)/109) ≤ 
            1, -((4 x3)/179) + ((9 x4)/179) + ((2 x5)/179) ≤ 1, ((6 x3)/307) + ((9 x5)/307) + ((4 x6)/307) ≤ 
            1, ((4 x2)/629) + ((10 x3)/629) + ((6 x4)/629) + ((15 x5)/629) + ((6 x6)/629) ≤ 
            1, ((2 x2)/131) + ((6 x3)/655) + ((3 x4)/131) + ((6 x5)/655) + ((6 x6)/655) ≤ 
            1, ((10 x2)/629) + ((4 x3)/629) + ((15 x4)/629) + ((6 x5)/629) + ((6 x6)/629) ≤ 1, 
          (x4/23) ≤ 
            1, ((6 x2)/307) + ((9 x4)/307) + ((4 x6)/307) ≤ 
            1, ((2 x2)/245) - ((4 x3)/245) + ((11 x4)/245) + ((2 x5)/245) ≤ 
            1, ((9 x3)/307) + ((4 x5)/307) + ((6 x6)/307) ≤ 
            1, (x3/33) + ((2 x4)/165) + ((2 x6)/165) ≤ 
            1, ((6 x2)/655) + ((3 x3)/131) + ((6 x4)/655) + ((2 x5)/131) + ((6 x6)/655) ≤ 1, 
          (x3/31) + ((2 x6)/93) ≤ 
            1, ((2 x2)/93) + (x3/31) ≤ 
            1, ((6 x2)/397) + ((9 x3)/397) + ((6 x4)/397) + ((4 x5)/397) ≤ 
            1, ((9 x3)/307) + ((6 x5)/307) + ((4 x6)/307) ≤ 
            1, ((2 x2)/265) + ((11 x3)/265) - ((4 x4)/265) + ((2 x5)/265) + ((2 x6)/265) ≤ 
            1, ((2 x2)/245) + ((11 x3)/245) - ((4 x4)/245) + ((2 x6)/245) ≤ 1, 
          (x3/23) ≤ 
            1, ((2 x2)/245) + ((11 x3)/245) - ((4 x4)/245) + ((2 x5)/245) ≤ 
            1, ((2 x2)/179) + ((9 x3)/179) - ((4 x4)/179) ≤ 
            1, ((2 x2)/165) + (x3/33) + ((2 x4)/165) ≤ 
            1, ((6 x2)/629) + ((15 x3)/629) + ((4 x4)/629) + ((10 x5)/629) + ((6 x6)/629) ≤ 
            1, ((2 x2)/179) + ((2 x4)/179) + ((2 x5)/179) + ((5 x6)/179) ≤ 
            1, -(x3/50) + ((3 x4)/100) + ((3 x5)/100) ≤ 
            1, -(x3/31) + ((3 x4)/62) + (x5/62) ≤ 
            1, ((3 x2)/122) + ((3 x4)/122) + (x6/61) ≤ 
            1, ((6 x2)/397) + ((4 x3)/397) + ((6 x4)/397) + ((9 x5)/397) ≤ 1, 
          (x5/23) ≤ 
            1, ((2 x2)/165) + ((2 x4)/165) + (x5/33) ≤ 
            1, ((6 x2)/655) + ((2 x3)/131) + ((6 x4)/655) + ((3 x5)/131) + ((6 x6)/655) ≤ 
            1, ((12 x2)/655) + ((4 x3)/655) + ((3 x4)/131) + ((6 x5)/655) + ((6 x6)/655) ≤ 
            1, ((2 x2)/179) + ((2 x3)/179) + ((2 x4)/179) + ((5 x6)/179) ≤ 
            1, ((6 x2)/565) + ((6 x3)/565) + ((6 x4)/565) + ((4 x5)/565) + ((3 x6)/113) ≤ 1, 
          (x2/51) + (x3/51) + (x4/51) ≤ 
            1, ((6 x2)/655) + ((3 x3)/131) + ((4 x4)/655) + ((12 x5)/655) + ((6 x6)/655) ≤ 1, 
          (x2/51) + (x4/51) + (x5/51) ≤ 1, 
          (x5/31) + ((2 x6)/93) ≤ 
            1, ((2 x2)/165) + (x5/33) + ((2 x6)/165) ≤ 
            1, ((6 x2)/565) + ((4 x3)/565) + ((6 x4)/565) + ((6 x5)/565) + ((3 x6)/113) ≤ 1, 
          (x2/79) + ((4 x3)/79) - ((2 x4)/79) ≤ 1, 
          (x2/94) - (x3/47) + ((2 x4)/47) + (x5/94) ≤ 1, 
          (x2/36) + (x6/36) ≤ 1, (x2/38) + (x5/38) ≤ 1, 
          (x2/94) + ((2 x3)/47) - (x4/47) + (x6/94) ≤ 1, 
          (x2/51) + (x3/51) + (x5/51) ≤ 1, 
          (x2/94) + ((2 x3)/47) - (x4/47) + (x5/94) ≤ 
            1, ((11 x2)/265) + ((2 x3)/265) + ((2 x4)/265) - ((4 x5)/265) + ((2 x6)/265) ≤ 
            1, ((3 x2)/62) + (x3/62) - (x5/31) ≤ 
            1, ((2 x2)/47) + (x3/94) - (x5/47) + (x6/94) ≤ 
            1, ((3 x2)/100) + ((3 x3)/100) - (x5/50) ≤ 
            1, ((4 x2)/79) + (x3/79) - ((2 x5)/79) ≤ 
            1, ((3 x2)/131) + ((6 x3)/655) + ((12 x4)/655) + ((4 x5)/655) + ((6 x6)/655) ≤ 
            1, ((15 x2)/629) + ((6 x3)/629) + ((10 x4)/629) + ((4 x5)/629) + ((6 x6)/629) ≤ 
            1, ((2 x2)/47) + (x3/94) + (x4/94) - (x5/47) ≤ 
            1, ((3 x2)/109) + ((2 x4)/109) + ((2 x6)/109) ≤ 
            1, ((2 x2)/179) + ((2 x3)/179) + ((2 x5)/179) + ((5 x6)/179) ≤ 
            1, ((6 x2)/565) + ((6 x3)/565) + ((4 x4)/565) + ((6 x5)/565) + ((3 x6)/113) ≤ 
            1, ((3 x2)/131) + ((6 x3)/655) + ((2 x4)/131) + ((6 x5)/655) + ((6 x6)/655) ≤ 1, 
          (x2/62) + ((3 x3)/62) - (x4/31) ≤ 
            1, ((11 x2)/245) + ((2 x3)/245) - ((4 x5)/245) + ((2 x6)/245) ≤ 
            1, ((11 x2)/245) + ((2 x3)/245) + ((2 x4)/245) - ((4 x5)/245) ≤ 
            1, ((9 x2)/307) + ((4 x4)/307) + ((6 x6)/307) ≤ 
            1, (x2/33) + ((2 x5)/165) + ((2 x6)/165) ≤ 
            1, ((9 x2)/307) + ((6 x4)/307) + ((4 x6)/307) ≤ 
            1, (x2/31) + ((2 x3)/93) ≤ 
            1, ((3 x2)/100) + ((3 x3)/100) - (x4/50) ≤ 
            1, ((9 x2)/397) + ((6 x3)/397) + ((4 x4)/397) + ((6 x5)/397) ≤ 1, 
          (x2/33) + ((2 x3)/165) + ((2 x5)/165) ≤ 
            1, ((9 x2)/179) + ((2 x3)/179) - ((4 x5)/179) ≤ 
            1, (x2/31) + ((2 x6)/93) ≤ 1, 
          (x2/23) ≤ 
            1, -((4 x1)/245) + ((2 x4)/245) + ((2 x5)/245) + ((11 x6)/245) ≤ 
            1, -((4 x1)/245) + ((2 x3)/245) + ((2 x4)/245) + ((11 x6)/245) ≤ 
            1, ((2 x3)/109) + ((2 x5)/109) + ((3 x6)/109) ≤ 
            1, ((2 x2)/195) + ((2 x3)/195) + ((2 x4)/195) + ((2 x5)/195) + (x6/39) ≤ 
            1, ((4 x2)/545) + ((6 x3)/545) + ((6 x4)/545) + ((4 x5)/545) + ((3 x6)/109) ≤ 1, 
          (x2/120) + (x3/48) + (x4/120) + (x5/48) + (x6/120) ≤ 1, 
          (x2/77) + ((3 x3)/154) + (x4/77) + ((3 x5)/154) ≤ 
            1, -((4 x1)/245) + ((2 x2)/245) + ((2 x5)/245) + ((11 x6)/245) ≤ 
            1, -((4 x1)/245) + ((2 x2)/245) + ((2 x3)/245) + ((11 x6)/245) ≤ 
            1, ((2 x2)/109) + ((2 x4)/109) + ((3 x6)/109) ≤ 
            1, (x2/48) + (x3/120) + (x4/48) + (x5/120) + (x6/120) ≤ 1, 
          (x2/75) + (x3/75) + (x4/50) + (x5/50) - (x6/225) ≤ 
            1, ((6 x2)/545) + ((4 x3)/545) + ((4 x4)/545) + ((6 x5)/545) + ((3 x6)/109) ≤ 
            1, ((3 x2)/154) + (x3/77) + ((3 x4)/154) + (x5/77) ≤ 
            1, (x2/50) + (x3/50) + (x4/75) + (x5/75) - (x6/225) ≤ 
            1, ((2 x1)/167) + ((3 x3)/167) + ((3 x4)/167) + ((3 x6)/167) ≤ 1, 
          (x1/61) + ((3 x4)/122) + ((3 x5)/122) ≤ 
            1, -(x2/17) + (x4/34) + (x6/34) ≤ 
            1, -((4 x2)/175) + ((2 x3)/175) + ((2 x4)/175) + ((2 x5)/175) + (x6/35) ≤ 
            1, ((8 x1)/945) - ((4 x2)/945) + ((2 x3)/135) + ((2 x4)/135) + ((2 x5)/945) + ((23 x6)/945) ≤ 
            1, ((4 x1)/419) - ((2 x2)/419) + ((6 x3)/419) + ((7 x4)/419) + ((10 x6)/419) ≤ 
            1, ((4 x1)/655) + ((12 x3)/655) + ((6 x4)/655) + ((6 x5)/655) + ((3 x6)/131) ≤ 
            1, -((2 x2)/35) + ((2 x3)/175) + 
              (x4/35) + ((2 x5)/175) + ((2 x6)/175) ≤ 
            1, ((4 x1)/307) + ((9 x4)/307) + ((6 x5)/307) ≤ 
            1, -((2 x2)/271) + ((9 x4)/271) + ((6 x6)/271) ≤ 1, -(x2/16) + (x4/32) + (x5/32) ≤ 
            1, ((4 x1)/385) - ((6 x2)/385) + ((6 x3)/385) + ((9 x4)/385) + ((6 x6)/385) ≤ 
            1, ((4 x1)/389) - ((2 x2)/389) + ((6 x3)/389) + ((9 x4)/389) + ((6 x6)/389) ≤ 
            1, -((6 x2)/85) + ((3 x4)/85) + ((2 x6)/85) ≤ 1, 
          (x1/77) + ((3 x3)/154) + ((3 x4)/154) + (x6/77) ≤ 
            1, -((2 x2)/49) + (x3/49) + (x4/49) + (x5/49) ≤ 
            1, -((2 x2)/45) + (x5/15) ≤ 
            1, ((4 x1)/565) + ((6 x3)/565) + ((6 x4)/565) + ((3 x5)/113) + ((6 x6)/565) ≤ 
            1, ((2 x4)/159) + ((2 x5)/159) + ((5 x6)/159) ≤ 
            1, ((4 x1)/391) + ((6 x3)/391) + ((6 x4)/391) + ((9 x6)/391) ≤ 
            1, ((4 x1)/397) + ((6 x3)/397) + ((9 x4)/397) + ((6 x6)/397) ≤ 
            1, ((4 x1)/397) + ((9 x3)/397) + ((6 x4)/397) + ((6 x6)/397) ≤ 
            1, -((2 x2)/79) + ((4 x5)/79) + (x6/79) ≤ 
            1, -((2 x2)/79) + (x3/79) + ((4 x5)/79) ≤ 
            1, ((4 x1)/545) + ((4 x3)/545) + ((6 x4)/545) + ((3 x5)/109) + ((6 x6)/545) ≤ 
            1, -((2 x3)/79) + ((4 x4)/79) + (x6/79) ≤ 
            1, ((4 x1)/777) + ((4 x2)/777) + ((10 x3)/777) + ((10 x4)/777) + ((4 x5)/777) + ((19 x6)/777) ≤ 
            1, -((4 x3)/179) + ((9 x4)/179) + ((2 x6)/179) ≤ 1, (x3/36) + (x5/36) ≤ 1, 
          (x1/135) + (x2/135) + (x3/54) + (x4/54) + (x5/135) + 
              (x6/135) ≤ 
            1, ((4 x2)/397) + ((9 x3)/397) + ((6 x4)/397) + ((6 x5)/397) ≤ 1, (x3/31) + ((2 x5)/93) ≤ 1, 
          (x3/33) + ((2 x4)/165) + ((2 x5)/165) ≤ 
            1, ((4 x1)/307) + ((6 x4)/307) + ((9 x5)/307) ≤ 
            1, (x1/180) + (x2/180) + (x3/72) + (x4/72) + (x5/180) + 
              (x6/45) ≤ 
            1, ((4 x1)/1041) + ((4 x2)/1041) + ((16 x3)/1041) + ((10 x4)/1041) + ((10 x5)/1041) + ((25 x6)/1041) ≤ 1, 
          (x1/180) + (x2/180) + (x3/72) + (x4/72) + (x5/45) + (x6/180) ≤ 
            1, ((4 x1)/777) + ((4 x2)/777) + ((10 x3)/777) + ((10 x4)/777) + ((19 x5)/777) + ((4 x6)/777) ≤ 
            1, ((4 x1)/545) + ((6 x3)/545) + ((6 x4)/545) + ((3 x5)/109) + ((4 x6)/545) ≤ 
            1, ((4 x1)/1041) + ((4 x2)/1041) + ((16 x3)/1041) + ((10 x4)/1041) + ((25 x5)/1041) + ((10 x6)/1041) ≤ 
            1, -((2 x3)/45) + (x4/15) ≤ 
            1, ((4 x1)/545) + ((4 x2)/545) + ((3 x4)/109) + ((6 x5)/545) + ((6 x6)/545) ≤ 
            1, ((4 x1)/565) + ((6 x2)/565) + ((3 x4)/113) + ((6 x5)/565) + ((6 x6)/565) ≤ 
            1, ((2 x2)/179) - ((4 x3)/179) + ((9 x4)/179) ≤ 
            1, ((2 x3)/93) + (x5/31) ≤ 1, 
          (x1/120) + (x2/120) + (x3/120) + (x4/48) + (x5/48) ≤ 
            1, ((4 x1)/1015) + ((2 x2)/145) + ((4 x3)/1015) + ((5 x4)/203) + ((2 x5)/203) + ((2 x6)/203) ≤ 
            1, ((4 x1)/777) + ((10 x2)/777) + ((4 x3)/777) + ((19 x4)/777) + ((10 x5)/777) + ((4 x6)/777) ≤ 
            1, ((6 x2)/397) + ((6 x3)/397) + ((9 x4)/397) + ((4 x5)/397) ≤ 
            1, ((2 x2)/165) + ((2 x3)/165) + (x4/33) ≤ 
            1, ((4 x1)/307) + ((6 x2)/307) + ((9 x3)/307) ≤ 
            1, (x3/15) - ((2 x4)/45) ≤ 
            1, ((9 x3)/179) - ((4 x4)/179) + ((2 x6)/179) ≤ 
            1, ((9 x3)/179) - ((4 x4)/179) + ((2 x5)/179) ≤ 
            1, ((4 x1)/565) + ((6 x2)/565) + ((3 x3)/113) + ((6 x5)/565) + ((6 x6)/565) ≤ 
            1, ((4 x1)/545) + ((6 x2)/545) + ((3 x3)/109) + ((4 x5)/545) + ((6 x6)/545) ≤ 
            1, ((4 x1)/777) + ((10 x2)/777) + ((19 x3)/777) + ((4 x4)/777) + ((10 x5)/777) + ((4 x6)/777) ≤ 
            1, ((4 x1)/545) + ((6 x2)/545) + ((3 x3)/109) + ((6 x5)/545) + ((4 x6)/545) ≤ 
            1, ((4 x1)/1015) + ((2 x2)/203) + ((5 x3)/203) + ((4 x4)/1015) + ((2 x5)/145) + ((2 x6)/203) ≤ 
            1, -((4 x2)/179) + ((9 x5)/179) + ((2 x6)/179) ≤ 
            1, -((4 x2)/179) + ((2 x3)/179) + ((9 x5)/179) ≤ 
            1, ((4 x1)/1015) + ((4 x2)/1015) + ((2 x3)/145) + ((2 x4)/203) + ((5 x5)/203) + ((2 x6)/203) ≤ 
            1, ((2 x1)/315) + ((2 x2)/315) + ((2 x3)/315) + (x4/63) + 
              (x5/63) + (x6/63) ≤ 
            1, ((2 x2)/93) + (x4/31) ≤ 
            1, ((4 x1)/545) + ((6 x2)/545) + ((3 x4)/109) + ((6 x5)/545) + ((4 x6)/545) ≤ 
            1, ((4 x1)/419) + ((7 x3)/419) + ((6 x4)/419) - ((2 x5)/419) + ((10 x6)/419) ≤ 
            1, ((8 x1)/945) + ((2 x2)/945) + ((2 x3)/135) + ((2 x4)/135) - ((4 x5)/945) + ((23 x6)/945) ≤ 
            1, ((4 x1)/655) + ((6 x2)/655) + ((6 x3)/655) + ((12 x4)/655) + ((3 x6)/131) ≤ 
            1, ((4 x1)/1041) + ((10 x2)/1041) + ((10 x3)/1041) + ((16 x4)/1041) + ((4 x5)/1041) + ((25 x6)/1041) ≤ 
            1, ((4 x3)/79) - ((2 x4)/79) + (x6/79) ≤ 
            1, ((4 x3)/79) - ((2 x4)/79) + (x5/79) ≤ 
            1, ((4 x1)/1041) + ((10 x2)/1041) + ((25 x3)/1041) + ((4 x4)/1041) + ((16 x5)/1041) + ((10 x6)/1041) ≤ 
            1, ((9 x3)/271) - ((2 x5)/271) + ((6 x6)/271) ≤ 
            1, ((4 x1)/389) + ((9 x3)/389) + ((6 x4)/389) - ((2 x5)/389) + ((6 x6)/389) ≤ 
            1, ((2 x1)/167) + ((3 x2)/167) + ((3 x5)/167) + ((3 x6)/167) ≤ 1, -(x3/17) + (x5/34) + (x6/34) ≤ 
            1, ((2 x2)/175) - ((4 x3)/175) + ((2 x4)/175) + ((2 x5)/175) + (x6/35) ≤ 
            1, ((2 x2)/175) - ((2 x3)/35) + ((2 x4)/175) + 
              (x5/35) + ((2 x6)/175) ≤ 
            1, -((2 x3)/271) + ((9 x5)/271) + ((6 x6)/271) ≤ 1, -(x3/16) + (x4/32) + (x5/32) ≤ 
            1, -((6 x3)/85) + ((3 x5)/85) + ((2 x6)/85) ≤ 
            1, ((4 x1)/389) + ((6 x2)/389) - ((2 x3)/389) + ((9 x5)/389) + ((6 x6)/389) ≤ 
            1, ((4 x1)/391) + ((6 x2)/391) + ((6 x5)/391) + ((9 x6)/391) ≤ 
            1, ((4 x1)/397) + ((6 x2)/397) + ((9 x5)/397) + ((6 x6)/397) ≤ 
            1, ((4 x1)/777) + ((10 x2)/777) + ((4 x3)/777) + ((4 x4)/777) + ((10 x5)/777) + ((19 x6)/777) ≤ 
            1, ((6 x2)/397) + ((6 x3)/397) + ((4 x4)/397) + ((9 x5)/397) ≤ 
            1, ((2 x2)/165) + ((2 x3)/165) + (x5/33) ≤ 
            1, ((4 x1)/1041) + ((16 x2)/1041) + ((4 x3)/1041) + ((25 x4)/1041) + ((10 x5)/1041) + ((10 x6)/1041) ≤ 1, 
          (x1/61) + ((3 x2)/122) + ((3 x3)/122) ≤ 1, 
          (x1/120) + (x2/48) + (x3/48) + (x4/120) + (x5/120) ≤ 
            1, ((4 x1)/385) + ((6 x2)/385) - ((6 x3)/385) + ((9 x5)/385) + ((6 x6)/385) ≤ 
            1, ((4 x1)/419) + ((6 x2)/419) - ((2 x3)/419) + ((7 x5)/419) + ((10 x6)/419) ≤ 
            1, ((8 x1)/945) + ((2 x2)/135) - ((4 x3)/945) + ((2 x4)/945) + ((2 x5)/135) + ((23 x6)/945) ≤ 
            1, ((4 x1)/655) + ((12 x2)/655) + ((6 x4)/655) + ((6 x5)/655) + ((3 x6)/131) ≤ 1, 
          (x1/77) + ((3 x2)/154) + ((3 x5)/154) + (x6/77) ≤ 1, 
          (x2/79) - ((2 x3)/79) + ((4 x4)/79) ≤ 1, 
          (x1/180) + (x2/72) + (x3/180) + (x4/180) + (x5/72) + (x6/45) ≤ 
            1, ((4 x1)/1041) + ((16 x2)/1041) + ((4 x3)/1041) + ((10 x4)/1041) + ((10 x5)/1041) + ((25 x6)/1041) ≤ 1, 
          (x1/135) + (x2/54) + (x3/135) + (x4/135) + (x5/54) + 
              (x6/135) ≤ 1, 
          (x1/180) + (x2/72) + (x3/180) + (x4/45) + (x5/72) + (x6/180) ≤ 
            1, (x2/36) + (x4/36) ≤ 
            1, ((2 x2)/159) + ((2 x3)/159) + ((5 x6)/159) ≤ 
            1, (x1/180) + (x2/72) + (x3/45) + (x4/180) + (x5/72) + 
              (x6/180) ≤ 
            1, ((2 x2)/175) + 
              (x3/35) + ((2 x4)/175) - ((2 x5)/35) + ((2 x6)/175) ≤ 1, 
          (x3/34) - (x5/17) + (x6/34) ≤ 
            1, ((2 x2)/175) + ((2 x3)/175) + ((2 x4)/175) - ((4 x5)/175) + (x6/35) ≤ 
            1, ((4 x1)/385) + ((9 x3)/385) + ((6 x4)/385) - ((6 x5)/385) + ((6 x6)/385) ≤ 
            1, ((3 x3)/85) - ((6 x5)/85) + ((2 x6)/85) ≤ 1, 
          (x2/32) + (x3/32) - (x5/16) ≤ 1, 
          (x2/49) + (x3/49) + (x4/49) - ((2 x5)/49) ≤ 1, 
          (x2/49) - ((2 x3)/49) + (x4/49) + (x5/49) ≤ 
            1, ((8 x1)/945) + ((2 x2)/135) + ((2 x3)/945) - ((4 x4)/945) + ((2 x5)/135) + ((23 x6)/945) ≤ 
            1, ((4 x1)/419) + ((7 x2)/419) - ((2 x4)/419) + ((6 x5)/419) + ((10 x6)/419) ≤ 
            1, ((4 x1)/655) + ((6 x2)/655) + ((6 x3)/655) + ((12 x5)/655) + ((3 x6)/131) ≤ 
            1, ((4 x1)/1041) + ((10 x2)/1041) + ((10 x3)/1041) + ((4 x4)/1041) + ((16 x5)/1041) + ((25 x6)/1041) ≤ 1, 
          (x2/15) - ((2 x5)/45) ≤ 
            1, ((4 x1)/565) + ((3 x2)/113) + ((6 x3)/565) + ((6 x4)/565) + ((6 x6)/565) ≤ 
            1, ((2 x1)/315) + (x2/63) + 
              (x3/63) + ((2 x4)/315) + ((2 x5)/315) + (x6/63) ≤ 
            1, 
          (x1/180) + (x2/45) + (x3/72) + (x4/72) + (x5/180) + (x6/180) ≤ 
            1, ((4 x1)/1041) + ((25 x2)/1041) + ((10 x3)/1041) + ((16 x4)/1041) + ((4 x5)/1041) + ((10 x6)/1041) ≤ 
            1, ((4 x1)/1015) + ((5 x2)/203) + ((2 x3)/203) + ((2 x4)/145) + ((4 x5)/1015) + ((2 x6)/203) ≤ 
            1, ((2 x2)/175) + ((2 x3)/175) - ((4 x4)/175) + ((2 x5)/175) + (x6/35) ≤ 1, (x2/34) - (x4/17) + (x6/34) ≤ 1, 
          (x2/49) + (x3/49) - ((2 x4)/49) + (x5/49) ≤ 
            1, ((4 x2)/79) - ((2 x5)/79) + (x6/79) ≤ 
            1, ((4 x1)/545) + ((3 x2)/109) + ((6 x3)/545) + ((4 x4)/545) + ((6 x6)/545) ≤ 
            1, ((4 x1)/777) + ((19 x2)/777) + ((10 x3)/777) + ((10 x4)/777) + ((4 x5)/777) + ((4 x6)/777) ≤ 
            1, ((4 x2)/79) + (x4/79) - ((2 x5)/79) ≤ 
            1, ((4 x1)/545) + ((3 x2)/109) + ((6 x3)/545) + ((6 x4)/545) + ((4 x6)/545) ≤ 
            1, ((9 x2)/397) + ((4 x3)/397) + ((6 x4)/397) + ((6 x5)/397) ≤ 1, 
          (x2/33) + ((2 x4)/165) + ((2 x5)/165) ≤ 1, 
          (x2/31) + ((2 x4)/93) ≤ 1, 
          (x2/35) + ((2 x3)/175) - ((2 x4)/35) + ((2 x5)/175) + ((2 x6)/175) ≤ 
            1, ((9 x2)/271) - ((2 x4)/271) + ((6 x6)/271) ≤ 
            1, ((4 x1)/389) + ((9 x2)/389) - ((2 x4)/389) + ((6 x5)/389) + ((6 x6)/389) ≤ 1, 
          (x2/32) + (x3/32) - (x4/16) ≤ 
            1, ((4 x1)/307) + ((9 x2)/307) + ((6 x3)/307) ≤ 
            1, ((4 x1)/385) + ((9 x2)/385) - ((6 x4)/385) + ((6 x5)/385) + ((6 x6)/385) ≤ 
            1, ((3 x2)/85) - ((6 x4)/85) + ((2 x6)/85) ≤ 
            1, ((4 x1)/397) + ((9 x2)/397) + ((6 x5)/397) + ((6 x6)/397) ≤ 
            1, ((9 x2)/179) - ((4 x5)/179) + ((2 x6)/179) ≤ 
            1, ((9 x2)/179) + ((2 x4)/179) - ((4 x5)/179) ≤ 
            1, ((2 x1)/179) + ((5 x4)/179) + ((2 x5)/179) + ((2 x6)/179) ≤ 
            1, ((2 x1)/139) + ((3 x3)/139) + ((2 x4)/139) + ((2 x6)/139) ≤ 
            1, ((2 x1)/265) - ((4 x3)/265) + ((11 x4)/265) + ((2 x5)/265) + ((2 x6)/265) ≤ 
            1, ((2 x1)/185) + 
              (x3/37) + ((2 x4)/185) + ((2 x5)/185) ≤ 
            1, ((2 x1)/265) - ((4 x2)/265) + ((2 x4)/265) + ((11 x5)/265) + ((2 x6)/265) ≤ 
            1, ((6 x1)/565) + ((4 x3)/565) + ((6 x4)/565) + ((3 x5)/113) + ((6 x6)/565) ≤ 
            1, ((2 x1)/195) + ((2 x3)/195) + ((2 x4)/195) + 
              (x5/39) + ((2 x6)/195) ≤ 
            1, ((2 x1)/265) - ((4 x2)/265) + ((2 x3)/265) + ((2 x4)/265) + ((11 x5)/265) ≤ 
            1, ((6 x1)/565) + ((6 x3)/565) + ((6 x4)/565) + ((3 x5)/113) + ((4 x6)/565) ≤ 
            1, ((2 x1)/179) + ((2 x4)/179) + ((5 x5)/179) + ((2 x6)/179) ≤ 
            1, ((6 x1)/565) + ((4 x2)/565) + ((3 x4)/113) + ((6 x5)/565) + ((6 x6)/565) ≤ 
            1, ((4 x3)/307) + ((6 x5)/307) + ((9 x6)/307) ≤ 
            1, ((6 x3)/307) + ((4 x5)/307) + ((9 x6)/307) ≤ 
            1, -((4 x1)/179) + ((2 x4)/179) + ((9 x6)/179) ≤ 
            1, -((4 x1)/179) + ((2 x5)/179) + ((9 x6)/179) ≤ 
            1, -((4 x1)/179) + ((2 x3)/179) + ((9 x6)/179) ≤ 
            1, ((6 x1)/391) + ((4 x3)/391) + ((9 x4)/391) + ((6 x6)/391) ≤ 
            1, ((2 x1)/139) + ((2 x3)/139) + ((3 x4)/139) + ((2 x6)/139) ≤ 
            1, ((2 x1)/245) - ((4 x3)/245) + ((11 x4)/245) + ((2 x6)/245) ≤ 
            1, ((2 x1)/245) + ((11 x3)/245) - ((4 x4)/245) + ((2 x6)/245) ≤ 
            1, ((2 x1)/245) + ((11 x3)/245) - ((4 x4)/245) + ((2 x5)/245) ≤ 
            1, ((6 x1)/391) + ((9 x3)/391) + ((4 x4)/391) + ((6 x6)/391) ≤ 
            1, ((2 x1)/159) + ((5 x3)/159) + ((2 x5)/159) ≤ 
            1, ((2 x1)/195) + ((2 x2)/195) + 
              (x4/39) + ((2 x5)/195) + ((2 x6)/195) ≤ 
            1, ((6 x2)/307) + ((4 x4)/307) + ((9 x6)/307) ≤ 
            1, ((4 x2)/307) + ((6 x4)/307) + ((9 x6)/307) ≤ 
            1, -((4 x1)/179) + ((2 x2)/179) + ((9 x6)/179) ≤ 
            1, ((2 x1)/185) + ((2 x2)/185) + ((2 x3)/185) + 
              (x4/37) ≤ 
            1, ((2 x1)/179) + ((2 x3)/179) + ((2 x4)/179) + ((5 x5)/179) ≤ 
            1, ((4 x2)/419) + ((7 x3)/419) + ((6 x4)/419) + ((10 x5)/419) - ((2 x6)/419) ≤ 
            1, ((2 x1)/265) + ((2 x2)/265) + ((11 x3)/265) - ((4 x4)/265) + ((2 x6)/265) ≤ 
            1, ((2 x1)/195) + ((2 x2)/195) + 
              (x3/39) + ((2 x5)/195) + ((2 x6)/195) ≤ 
            1, ((6 x1)/565) + ((6 x2)/565) + ((3 x3)/113) + ((4 x5)/565) + ((6 x6)/565) ≤ 
            1, ((2 x1)/265) + ((2 x2)/265) + ((11 x3)/265) - ((4 x4)/265) + ((2 x5)/265) ≤ 
            1, ((6 x1)/565) + ((6 x2)/565) + ((3 x3)/113) + ((6 x5)/565) + ((4 x6)/565) ≤ 
            1, ((2 x1)/179) + ((2 x2)/179) + ((5 x3)/179) + ((2 x6)/179) ≤ 
            1, ((48 x2)/3335) + ((81 x3)/3335) + ((32 x4)/3335) + ((54 x5)/3335) - ((18 x6)/3335) ≤ 
            1, ((6 x2)/419) + ((10 x3)/419) + ((4 x4)/419) + ((7 x5)/419) - ((2 x6)/419) ≤ 
            1, ((16 x2)/1207) + ((27 x3)/1207) + ((18 x4)/1207) + ((18 x5)/1207) - ((6 x6)/1207) ≤ 
            1, ((4 x2)/389) + ((9 x3)/389) + ((6 x4)/389) + ((6 x5)/389) - ((2 x6)/389) ≤ 
            1, ((9 x3)/271) + ((6 x5)/271) - ((2 x6)/271) ≤ 
            1, ((2 x1)/179) + ((2 x2)/179) + ((5 x3)/179) + ((2 x5)/179) ≤ 
            1, ((6 x1)/391) + ((4 x2)/391) + ((9 x5)/391) + ((6 x6)/391) ≤ 
            1, ((2 x1)/139) + ((2 x2)/139) + ((3 x5)/139) + ((2 x6)/139) ≤ 
            
            1, ((2 x1)/245) - ((4 x2)/245) + ((11 x5)/245) + ((2 x6)/245) ≤ 
            1, ((2 x1)/245) + ((2 x2)/245) - ((4 x3)/245) + ((11 x4)/245) ≤ 
            1, ((2 x1)/265) + ((2 x2)/265) - ((4 x3)/265) + ((11 x4)/265) + ((2 x5)/265) ≤ 
            1, ((6 x1)/565) + ((6 x2)/565) + ((3 x4)/113) + ((6 x5)/565) + ((4 x6)/565) ≤ 
            1, ((2 x1)/245) - ((4 x2)/245) + ((2 x3)/245) + ((11 x5)/245) ≤ 
            1, ((2 x1)/185) + ((2 x2)/185) + ((2 x3)/185) + 
              (x5/37) ≤ 
            1, ((2 x1)/159) + ((2 x3)/159) + ((5 x5)/159) ≤ 
            1, ((32 x2)/3335) + ((54 x3)/3335) + ((48 x4)/3335) + ((81 x5)/3335) - ((18 x6)/3335) ≤ 
            1, ((18 x2)/1207) + ((18 x3)/1207) + ((16 x4)/1207) + ((27 x5)/1207) - ((6 x6)/1207) ≤ 
            1, ((6 x3)/271) + ((9 x5)/271) - ((2 x6)/271) ≤ 
            1, ((6 x2)/389) + ((6 x3)/389) + ((4 x4)/389) + ((9 x5)/389) - ((2 x6)/389) ≤ 
            1, ((18 x2)/1207) + ((18 x3)/1207) + ((27 x4)/1207) + ((16 x5)/1207) - ((6 x6)/1207) ≤ 
            1, ((6 x2)/389) + ((6 x3)/389) + ((9 x4)/389) + ((4 x5)/389) - ((2 x6)/389) ≤ 
            1, ((2 x1)/159) + ((2 x2)/159) + ((5 x4)/159) ≤ 
            1, ((2 x1)/179) + ((2 x2)/179) + ((5 x4)/179) + ((2 x5)/179) ≤ 
            1, ((7 x2)/419) + ((4 x3)/419) + ((10 x4)/419) + ((6 x5)/419) - ((2 x6)/419) ≤ 
            1, ((54 x2)/3335) + ((32 x3)/3335) + ((81 x4)/3335) + ((48 x5)/3335) - ((18 x6)/3335) ≤ 
            1, ((6 x2)/271) + ((9 x4)/271) - ((2 x6)/271) ≤ 
            1, ((2 x1)/195) + 
              (x2/39) + ((2 x3)/195) + ((2 x4)/195) + ((2 x6)/195) ≤ 
            1, ((2 x1)/179) + ((5 x2)/179) + ((2 x3)/179) + ((2 x6)/179) ≤ 
            1, ((2 x1)/265) + ((11 x2)/265) + ((2 x3)/265) - ((4 x5)/265) + ((2 x6)/265) ≤ 
            
            1, ((6 x1)/565) + ((3 x2)/113) + ((6 x3)/565) + ((4 x4)/565) + ((6 x6)/565) ≤ 
            1, ((27 x2)/1207) + ((16 x3)/1207) + ((18 x4)/1207) + ((18 x5)/1207) - ((6 x6)/1207) ≤ 
            1, ((2 x1)/265) + ((11 x2)/265) + ((2 x3)/265) + ((2 x4)/265) - ((4 x5)/265) ≤ 
            1, ((6 x1)/565) + ((3 x2)/113) + ((6 x3)/565) + ((6 x4)/565) + ((4 x6)/565) ≤ 
            1, ((10 x2)/419) + ((6 x3)/419) + ((7 x4)/419) + ((4 x5)/419) - ((2 x6)/419) ≤ 
            1, ((81 x2)/3335) + ((48 x3)/3335) + ((54 x4)/3335) + ((32 x5)/3335) - ((18 x6)/3335) ≤ 
            1, ((2 x1)/179) + ((5 x2)/179) + ((2 x3)/179) + ((2 x4)/179) ≤ 
            1, ((2 x1)/139) + ((3 x2)/139) + ((2 x5)/139) + ((2 x6)/139) ≤ 
            1, ((2 x1)/185) + 
              (x2/37) + ((2 x4)/185) + ((2 x5)/185) ≤ 
            1, ((6 x1)/391) + ((9 x2)/391) + ((4 x5)/391) + ((6 x6)/391) ≤ 
            1, ((9 x2)/389) + ((4 x3)/389) + ((6 x4)/389) + ((6 x5)/389) - ((2 x6)/389) ≤ 
            1, ((9 x2)/271) + ((6 x4)/271) - ((2 x6)/271) ≤ 
            1, ((2 x1)/159) + ((5 x2)/159) + ((2 x4)/159) ≤ 
            1, ((2 x1)/245) + ((11 x2)/245) - ((4 x5)/245) + ((2 x6)/245) ≤ 
            1, ((2 x1)/245) + ((11 x2)/245) + ((2 x4)/245) - ((4 x5)/245) ≤ 
            1, ((16 x1)/1207) - ((6 x2)/1207) + ((18 x3)/1207) + ((27 x4)/1207) + ((18 x6)/1207) ≤ 
            1, ((48 x1)/3335) - ((18 x2)/3335) + ((32 x3)/3335) + ((81 x4)/3335) + ((54 x6)/3335) ≤ 
            1, -((6 x2)/85) + ((2 x4)/85) + ((3 x6)/85) ≤ 1, -x2 ≤ 0, 
          (x1/75) - (x2/225) + (x3/50) + (x4/75) + (x6/50) ≤ 
            1, ((32 x1)/3335) - ((18 x2)/3335) + ((48 x3)/3335) + ((54 x4)/3335) + ((81 x6)/3335) ≤ 1, 
          (x1/120) + (x3/48) + (x4/120) + (x5/120) + (x6/48) ≤ 
            
            1, ((2 x1)/131) + ((6 x3)/655) + ((3 x4)/131) + ((6 x5)/655) + ((6 x6)/655) ≤ 
            1, ((2 x1)/109) + ((3 x4)/109) + ((2 x5)/109) ≤ 
            1, ((18 x1)/1207) - ((6 x2)/1207) + ((27 x3)/1207) + ((18 x4)/1207) + ((16 x6)/1207) ≤ 
            1, ((6 x1)/655) + ((3 x3)/131) + ((6 x4)/655) + ((6 x5)/655) + ((2 x6)/131) ≤ 
            1, ((2 x1)/175) - ((4 x2)/175) + 
              (x4/35) + ((2 x5)/175) + ((2 x6)/175) ≤ 
            1, ((4 x1)/629) + ((10 x3)/629) + ((6 x4)/629) + ((6 x5)/629) + ((15 x6)/629) ≤ 1, 
          (x1/77) + (x3/77) + ((3 x4)/154) + ((3 x6)/154) ≤ 
            1, ((6 x1)/419) - ((2 x2)/419) + ((4 x3)/419) + ((10 x4)/419) + ((7 x6)/419) ≤ 
            1, -((2 x2)/271) + ((6 x4)/271) + ((9 x6)/271) ≤ 
            1, ((2 x1)/135) - ((4 x2)/945) + ((8 x3)/945) + ((23 x4)/945) + ((2 x5)/945) + ((2 x6)/135) ≤ 
            1, ((10 x1)/629) + ((4 x3)/629) + ((15 x4)/629) + ((6 x5)/629) + ((6 x6)/629) ≤ 
            1, -(x2/50) + ((3 x3)/100) + ((3 x5)/100) ≤ 
            1, ((6 x1)/389) - ((2 x2)/389) + ((9 x3)/389) + ((6 x4)/389) + ((4 x6)/389) ≤ 
            1, ((6 x1)/307) + ((9 x4)/307) + ((4 x5)/307) ≤ 
            1, (x6/23) ≤ 1, ((2 x4)/93) + (x6/31) ≤ 
            1, ((2 x1)/165) + ((2 x3)/165) + (x4/33) ≤ 
            1, ((6 x1)/397) + ((6 x3)/397) + ((9 x4)/397) + ((4 x6)/397) ≤ 
            1, ((2 x1)/165) + (x3/33) + ((2 x4)/165) ≤ 
            1, ((6 x1)/397) + ((9 x3)/397) + ((6 x4)/397) + ((4 x6)/397) ≤ 
            1, ((2 x1)/109) + ((2 x4)/109) + ((3 x5)/109) ≤ 
            1, (x1/77) + ((3 x3)/154) + (x4/77) + ((3 x6)/154) ≤ 
            1, ((2 x5)/93) + (x6/31) ≤ 
            1, ((2 x1)/179) - ((4 x3)/179) + ((9 x4)/179) ≤ 
            1, ((4 x2)/545) + ((4 x3)/545) + ((6 x4)/545) + ((6 x5)/545) + ((3 x6)/109) ≤ 
            1, ((10 x1)/777) + ((4 x2)/777) + ((4 x3)/777) + ((19 x4)/777) + ((4 x5)/777) + ((10 x6)/777) ≤ 
            1, ((6 x1)/545) + ((4 x2)/545) + ((3 x4)/109) + ((4 x5)/545) + ((6 x6)/545) ≤ 
            1, ((2 x3)/93) + (x6/31) ≤ 
            1, ((2 x1)/945) + ((8 x2)/945) + ((2 x3)/135) + ((2 x4)/135) + ((23 x5)/945) - ((4 x6)/945) ≤ 
            1, ((6 x1)/655) + ((4 x2)/655) + ((6 x3)/655) + ((12 x4)/655) + ((3 x5)/131) ≤ 
            1, ((10 x1)/1041) + ((4 x2)/1041) + ((10 x3)/1041) + ((16 x4)/1041) + ((25 x5)/1041) + ((4 x6)/1041) ≤ 
            1, ((2 x1)/265) + ((11 x3)/265) - ((4 x4)/265) + ((2 x5)/265) + ((2 x6)/265) ≤ 
            1, ((2 x1)/179) + ((9 x3)/179) - ((4 x4)/179) ≤ 
            1, ((6 x1)/307) + ((4 x4)/307) + ((9 x5)/307) ≤ 
            1, ((2 x1)/179) - ((4 x2)/179) + ((9 x5)/179) ≤ 
            1, ((2 x1)/265) - ((4 x2)/265) + ((2 x3)/265) + ((11 x5)/265) + ((2 x6)/265) ≤ 
            1, ((6 x1)/545) + ((4 x3)/545) + ((4 x4)/545) + ((3 x5)/109) + ((6 x6)/545) ≤ 
            1, ((6 x1)/565) + ((6 x3)/565) + ((4 x4)/565) + ((3 x5)/113) + ((6 x6)/565) ≤ 
            1, ((6 x1)/545) + ((6 x3)/545) + ((4 x4)/545) + ((3 x5)/109) + ((4 x6)/545) ≤ 
            1, ((4 x1)/1015) + ((4 x2)/1015) + ((2 x3)/145) + ((2 x4)/203) + ((2 x5)/203) + ((5 x6)/203) ≤ 1, 
          (x1/75) + (x3/75) + (x4/50) - (x5/225) + (x6/50) ≤ 1, 
          (x1/120) + (x2/120) + (x3/120) + (x4/48) + (x6/48) ≤ 
            1, ((2 x1)/145) + ((4 x2)/1015) + ((4 x3)/1015) + ((5 x4)/203) + ((2 x5)/203) + ((2 x6)/203) ≤ 
            1, ((48 x1)/3335) + ((81 x3)/3335) + ((32 x4)/3335) - ((18 x5)/3335) + ((54 x6)/3335) ≤ 
            1, ((6 x1)/419) + ((10 x3)/419) + ((4 x4)/419) - ((2 x5)/419) + ((7 x6)/419) ≤ 
            1, ((16 x1)/1207) + ((27 x3)/1207) + ((18 x4)/1207) - ((6 x5)/1207) + ((18 x6)/1207) ≤ 
            1, ((2 x1)/175) - ((4 x3)/175) + ((2 x4)/175) + 
              (x5/35) + ((2 x6)/175) ≤ 
            1, -((2 x3)/271) + ((6 x5)/271) + ((9 x6)/271) ≤ 
            1, -((6 x3)/85) + ((2 x5)/85) + ((3 x6)/85) ≤ 
            1, ((32 x1)/3335) + ((48 x2)/3335) - ((18 x3)/3335) + ((54 x5)/3335) + ((81 x6)/3335) ≤ 
            1, ((10 x1)/777) + ((4 x2)/777) + ((4 x3)/777) + ((4 x4)/777) + ((19 x5)/777) + ((10 x6)/777) ≤ 
            1, ((2 x1)/265) + ((2 x2)/265) - ((4 x3)/265) + ((11 x4)/265) + ((2 x6)/265) ≤ 
            1, ((6 x1)/565) + ((6 x2)/565) + ((3 x4)/113) + ((4 x5)/565) + ((6 x6)/565) ≤ 
            1, ((4 x1)/629) + ((6 x2)/629) + ((6 x3)/629) + ((10 x4)/629) + ((15 x6)/629) ≤ 
            1, ((4 x1)/1015) + ((2 x2)/203) + ((2 x3)/203) + ((2 x4)/145) + ((4 x5)/1015) + ((5 x6)/203) ≤ 
            1, ((6 x1)/629) + ((4 x2)/629) + ((6 x3)/629) + ((10 x4)/629) + ((15 x5)/629) ≤ 
            1, ((2 x1)/203) + ((4 x2)/1015) + ((2 x3)/203) + ((2 x4)/145) + ((5 x5)/203) + ((4 x6)/1015) ≤ 
            1, ((6 x1)/655) + ((6 x2)/655) + ((6 x3)/655) + ((3 x4)/131) + ((2 x5)/131) ≤ 
            1, ((6 x1)/307) + ((4 x2)/307) + ((9 x3)/307) ≤ 
            1, ((2 x1)/109) + ((2 x2)/109) + ((3 x3)/109) ≤ 
            1, ((6 x1)/565) + ((4 x2)/565) + ((3 x3)/113) + ((6 x5)/565) + ((6 x6)/565) ≤ 
            1, ((6 x1)/545) + ((4 x2)/545) + ((3 x3)/109) + ((4 x5)/545) + ((6 x6)/545) ≤ 
            1, ((6 x1)/545) + ((4 x2)/545) + ((3 x3)/109) + ((6 x5)/545) + ((4 x6)/545) ≤ 
            1, ((10 x1)/777) + ((4 x2)/777) + ((19 x3)/777) + ((4 x4)/777) + ((4 x5)/777) + ((10 x6)/777) ≤ 
            
            1, ((2 x1)/131) + ((6 x2)/655) + ((3 x3)/131) + ((6 x4)/655) + ((6 x6)/655) ≤ 
            1, ((10 x1)/629) + ((6 x2)/629) + ((15 x3)/629) + ((4 x4)/629) + ((6 x6)/629) ≤ 
            1, ((2 x1)/135) + ((2 x2)/945) + ((23 x3)/945) + ((8 x4)/945) - ((4 x5)/945) + ((2 x6)/135) ≤ 
            1, ((2 x1)/145) + ((2 x2)/203) + ((5 x3)/203) + ((4 x4)/1015) + ((4 x5)/1015) + ((2 x6)/203) ≤ 
            1, ((2 x1)/945) + ((2 x2)/135) + ((23 x3)/945) + ((8 x4)/945) + ((2 x5)/135) - ((4 x6)/945) ≤ 
            1, ((6 x1)/629) + ((10 x2)/629) + ((15 x3)/629) + ((4 x4)/629) + ((6 x5)/629) ≤ 
            1, ((6 x1)/655) + ((2 x2)/131) + ((3 x3)/131) + ((6 x4)/655) + ((6 x5)/655) ≤ 
            1, ((2 x1)/203) + ((2 x2)/145) + ((5 x3)/203) + ((4 x4)/1015) + ((2 x5)/203) + ((4 x6)/1015) ≤ 
            1, ((2 x1)/203) + ((4 x2)/1015) + ((5 x3)/203) + ((4 x4)/1015) + ((2 x5)/203) + ((2 x6)/145) ≤ 
            1, ((6 x1)/545) + ((6 x2)/545) + ((3 x4)/109) + ((4 x5)/545) + ((4 x6)/545) ≤ 
            1, ((4 x1)/629) + ((6 x2)/629) + ((6 x3)/629) + ((10 x5)/629) + ((15 x6)/629) ≤ 
            1, ((4 x1)/1015) + ((2 x2)/203) + ((2 x3)/203) + ((4 x4)/1015) + ((2 x5)/145) + ((5 x6)/203) ≤ 
            1, ((6 x3)/271) - ((2 x5)/271) + ((9 x6)/271) ≤ 
            1, ((32 x1)/3335) + ((54 x3)/3335) + ((48 x4)/3335) - ((18 x5)/3335) + ((81 x6)/3335) ≤ 
            1, ((6 x2)/545) + ((6 x3)/545) + ((4 x4)/545) + ((4 x5)/545) + ((3 x6)/109) ≤ 
            1, ((18 x1)/1207) + ((18 x3)/1207) + ((27 x4)/1207) - ((6 x5)/1207) + ((16 x6)/1207) ≤ 
            1, ((6 x1)/655) + ((6 x2)/655) + ((6 x3)/655) + ((3 x4)/131) + ((2 x6)/131) ≤ 
            1, ((10 x1)/1041) + ((10 x2)/1041) + ((4 x3)/1041) + ((25 x4)/1041) + ((4 x5)/1041) + ((16 x6)/1041) ≤ 
            1, ((2 x1)/203) + ((2 x2)/203) + ((4 x3)/1015) + ((5 x4)/203) + ((4 x5)/1015) + ((2 x6)/145) ≤ 
            1, ((2 x1)/203) + ((2 x2)/203) + ((4 x3)/1015) + ((5 x4)/203) + ((2 x5)/145) + ((4 x6)/1015) ≤ 
            1, ((10 x1)/1041) + ((10 x2)/1041) + ((4 x3)/1041) + ((25 x4)/1041) + ((16 x5)/1041) + ((4 x6)/1041) ≤ 
            1, ((6 x1)/389) + ((6 x3)/389) + ((9 x4)/389) - ((2 x5)/389) + ((4 x6)/389) ≤ 
            1, ((10 x1)/1041) + ((4 x2)/1041) + ((25 x3)/1041) + ((4 x4)/1041) + ((10 x5)/1041) + ((16 x6)/1041) ≤ 
            1, ((48 x1)/3335) + ((32 x2)/3335) - ((18 x3)/3335) + ((81 x5)/3335) + ((54 x6)/3335) ≤ 1, 
          (x1/77) + (x2/77) + ((3 x5)/154) + ((3 x6)/154) ≤ 
            1, ((6 x1)/419) + ((4 x2)/419) - ((2 x3)/419) + ((10 x5)/419) + ((7 x6)/419) ≤ 
            1, ((16 x1)/1207) + ((18 x2)/1207) - ((6 x3)/1207) + ((27 x5)/1207) + ((18 x6)/1207) ≤ 
            1, ((4 x1)/629) + ((10 x2)/629) + ((6 x4)/629) + ((6 x5)/629) + ((15 x6)/629) ≤ 
            1, ((2 x1)/131) + ((6 x2)/655) + ((6 x4)/655) + ((3 x5)/131) + ((6 x6)/655) ≤ 
            1, ((10 x1)/629) + ((4 x2)/629) + ((6 x4)/629) + ((15 x5)/629) + ((6 x6)/629) ≤ 
            1, ((2 x1)/135) + ((8 x2)/945) - ((4 x3)/945) + ((2 x4)/945) + ((23 x5)/945) + ((2 x6)/135) ≤ 
            1, -x3 ≤ 0, 
          (x1/75) + (x2/50) - (x3/225) + (x5/75) + (x6/50) ≤ 1, 
          (x1/120) + (x2/48) + (x4/120) + (x5/120) + (x6/48) ≤ 1, 
          (x1/75) + (x2/75) - (x4/225) + (x5/50) + (x6/50) ≤ 1, 
          (x1/120) + (x2/120) + (x3/120) + (x5/48) + (x6/48) ≤ 
            1, ((4 x1)/1015) + ((2 x2)/145) + ((4 x3)/1015) + ((2 x4)/203) + ((2 x5)/203) + ((5 x6)/203) ≤ 
            1, ((2 x1)/145) + ((4 x2)/1015) + ((4 x3)/1015) + ((2 x4)/203) + ((5 x5)/203) + ((2 x6)/203) ≤ 
            1, ((6 x1)/655) + ((6 x2)/655) + ((6 x3)/655) + ((2 x4)/131) + ((3 x5)/131) ≤ 
            1, ((6 x1)/655) + ((12 x2)/655) + ((3 x3)/131) + ((4 x4)/655) + ((6 x5)/655) ≤ 
            1, ((10 x1)/1041) + ((16 x2)/1041) + ((25 x3)/1041) + ((4 x4)/1041) + ((10 x5)/1041) + ((4 x6)/1041) ≤ 
            1, ((2 x1)/175) + ((2 x2)/175) + 
              (x3/35) - ((4 x5)/175) + ((2 x6)/175) ≤ 
            1, ((2 x1)/945) + ((2 x2)/135) + ((8 x3)/945) + ((23 x4)/945) + ((2 x5)/135) - ((4 x6)/945) ≤ 
            1, ((6 x1)/629) + ((6 x2)/629) + ((4 x3)/629) + ((15 x4)/629) + ((10 x5)/629) ≤ 
            1, ((6 x1)/655) + ((6 x2)/655) + ((4 x3)/655) + ((3 x4)/131) + ((12 x5)/655) ≤ 1, 
          (x1/77) + ((3 x2)/154) + (x5/77) + ((3 x6)/154) ≤ 
            1, ((2 x2)/93) + (x6/31) ≤ 
            1, ((32 x1)/3335) + ((54 x2)/3335) - ((18 x4)/3335) + ((48 x5)/3335) + ((81 x6)/3335) ≤ 
            1, ((18 x1)/1207) + ((18 x2)/1207) - ((6 x4)/1207) + ((27 x5)/1207) + ((16 x6)/1207) ≤ 
            1, ((6 x1)/655) + ((6 x2)/655) + ((6 x3)/655) + ((3 x5)/131) + ((2 x6)/131) ≤ 
            1, ((6 x2)/271) - ((2 x4)/271) + ((9 x6)/271) ≤ 
            1, ((2 x1)/203) + ((4 x2)/1015) + ((2 x3)/203) + ((4 x4)/1015) + ((5 x5)/203) + ((2 x6)/145) ≤ 
            1, ((10 x1)/1041) + ((4 x2)/1041) + ((10 x3)/1041) + ((4 x4)/1041) + ((25 x5)/1041) + ((16 x6)/1041) ≤ 
            1, ((3 x3)/100) - (x4/50) + ((3 x5)/100) ≤ 
            1, ((2 x3)/85) - ((6 x5)/85) + ((3 x6)/85) ≤ 
            1, -x5 ≤ 
            0, ((3 x2)/100) + ((3 x4)/100) - (x5/50) ≤ 
            1, ((18 x1)/1207) + ((27 x2)/1207) - ((6 x3)/1207) + ((18 x5)/1207) + ((16 x6)/1207) ≤ 
            1, ((6 x1)/655) + ((3 x2)/131) + ((6 x4)/655) + ((6 x5)/655) + ((2 x6)/131) ≤ 
            1, ((2 x1)/165) + ((2 x2)/165) + (x5/33) ≤ 
            1, ((6 x1)/397) + ((6 x2)/397) + ((9 x5)/397) + ((4 x6)/397) ≤ 
            1, ((6 x1)/389) + ((6 x2)/389) - ((2 x4)/389) + ((9 x5)/389) + ((4 x6)/389) ≤ 
            1, ((16 x1)/1207) + ((27 x2)/1207) - ((6 x4)/1207) + ((18 x5)/1207) + ((18 x6)/1207) ≤ 
            1, ((48 x1)/3335) + ((81 x2)/3335) - ((18 x4)/3335) + ((32 x5)/3335) + ((54 x6)/3335) ≤ 
            1, ((6 x1)/419) + ((10 x2)/419) - ((2 x4)/419) + ((4 x5)/419) + ((7 x6)/419) ≤ 1, -x4 ≤ 
            0, ((2 x2)/85) - ((6 x4)/85) + ((3 x6)/85) ≤ 
            1, ((2 x1)/131) + ((3 x2)/131) + ((6 x3)/655) + ((6 x5)/655) + ((6 x6)/655) ≤ 
            1, ((2 x1)/175) + 
              (x2/35) + ((2 x3)/175) - ((4 x4)/175) + ((2 x6)/175) ≤ 
            1, ((2 x1)/135) + ((23 x2)/945) + ((2 x3)/945) - ((4 x4)/945) + ((8 x5)/945) + ((2 x6)/135) ≤ 
            1, ((10 x1)/629) + ((15 x2)/629) + ((6 x3)/629) + ((4 x5)/629) + ((6 x6)/629) ≤ 
            1, ((2 x1)/145) + ((5 x2)/203) + ((2 x3)/203) + ((4 x4)/1015) + ((4 x5)/1015) + ((2 x6)/203) ≤ 
            1, ((10 x1)/1041) + ((25 x2)/1041) + ((16 x3)/1041) + ((10 x4)/1041) + ((4 x5)/1041) + ((4 x6)/1041) ≤ 
            1, ((2 x1)/945) + ((23 x2)/945) + ((2 x3)/135) + ((2 x4)/135) + ((8 x5)/945) - ((4 x6)/945) ≤ 
            1, ((6 x1)/655) + ((3 x2)/131) + ((12 x3)/655) + ((6 x4)/655) + ((4 x5)/655) ≤ 
            1, ((6 x1)/389) + ((9 x2)/389) - ((2 x3)/389) + ((6 x5)/389) + ((4 x6)/389) ≤ 
            1, ((3 x2)/100) - (x3/50) + ((3 x4)/100) ≤ 
            1, ((10 x1)/777) + ((19 x2)/777) + ((4 x3)/777) + ((4 x4)/777) + ((4 x5)/777) + ((10 x6)/777) ≤ 
            1, ((10 x1)/1041) + ((25 x2)/1041) + ((4 x3)/1041) + ((10 x4)/1041) + ((4 x5)/1041) + ((16 x6)/1041) ≤ 
            1, ((2 x1)/203) + ((5 x2)/203) + ((4 x3)/1015) + ((2 x4)/203) + ((4 x5)/1015) + ((2 x6)/145) ≤ 
            1, ((2 x1)/109) + ((3 x2)/109) + ((2 x3)/109) ≤ 
            1, ((6 x1)/655) + ((3 x2)/131) + ((2 x3)/131) + ((6 x4)/655) + ((6 x5)/655) ≤ 
            1, ((2 x1)/203) + ((5 x2)/203) + ((2 x3)/145) + ((2 x4)/203) + ((4 x5)/1015) + ((4 x6)/1015) ≤ 
            1, ((6 x1)/629) + ((15 x2)/629) + ((10 x3)/629) + ((6 x4)/629) + ((4 x5)/629) ≤ 
            1, ((2 x1)/165) + (x2/33) + ((2 x5)/165) ≤ 
            1, ((6 x1)/397) + ((9 x2)/397) + ((6 x5)/397) + ((4 x6)/397) ≤ 
            1, ((2 x1)/265) + ((11 x2)/265) + ((2 x4)/265) - ((4 x5)/265) + ((2 x6)/265) ≤ 
            1, ((2 x1)/179) + ((9 x2)/179) - ((4 x5)/179) ≤ 
            1, ((6 x1)/307) + ((9 x2)/307) + ((4 x3)/307) ≤ 
            1, ((6 x1)/545) + ((3 x2)/109) + ((4 x3)/545) + ((4 x4)/545) + ((6 x6)/545) ≤ 
            1, ((6 x1)/565) + ((3 x2)/113) + ((4 x3)/565) + ((6 x4)/565) + ((6 x6)/565) ≤ 
            1, ((6 x1)/545) + ((3 x2)/109) + ((4 x3)/545) + ((6 x4)/545) + ((4 x6)/545) ≤ 
            1, ((6 x1)/385) - ((6 x2)/385) + ((9 x3)/385) + ((6 x4)/385) + ((4 x6)/385) ≤ 
            1, -(x2/16) + (x3/32) + (x5/32) ≤ 
            1, ((2 x1)/175) - ((2 x2)/35) + 
              (x3/35) + ((2 x4)/175) + ((2 x5)/175) ≤ 
            1, ((2 x1)/175) + ((2 x2)/175) + ((2 x3)/175) - ((2 x4)/35) + (x5/35) ≤ 
            1, ((6 x1)/385) + ((6 x2)/385) - ((6 x4)/385) + ((9 x5)/385) + ((4 x6)/385) ≤ 1, 
          (x3/32) - (x4/16) + (x5/32) ≤ 
            1, ((6 x1)/385) + ((6 x3)/385) + ((9 x4)/385) - ((6 x5)/385) + ((4 x6)/385) ≤ 
            1, ((2 x1)/175) + ((2 x2)/175) + ((2 x3)/175) + 
              (x4/35) - ((2 x5)/35) ≤ 1, 
          (x2/32) + (x4/32) - (x5/16) ≤ 
            1, ((2 x1)/175) + 
              (x2/35) - ((2 x3)/35) + ((2 x4)/175) + ((2 x5)/175) ≤ 
            1, ((6 x1)/385) + ((9 x2)/385) - ((6 x3)/385) + ((6 x5)/385) + ((4 x6)/385) ≤ 1, 
          (x2/32) - (x3/16) + (x4/32) ≤ 
            1, ((3 x1)/122) + ((3 x4)/122) + (x5/61) ≤ 1, 
          (x1/48) + (x3/120) + (x4/48) + (x5/120) + (x6/120) ≤ 
            1, ((12 x1)/655) + ((4 x3)/655) + ((3 x4)/131) + ((6 x5)/655) + ((6 x6)/655) ≤ 1, 
          (x1/45) + (x4/45) + (x5/45) ≤ 1, 
          (x1/50) - (x2/225) + (x3/75) + (x4/50) + (x6/75) ≤ 
            1, ((3 x1)/167) + ((2 x3)/167) + ((3 x4)/167) + ((3 x6)/167) ≤ 
            1, ((2 x1)/185) + ((2 x4)/185) + ((2 x5)/185) + 
              (x6/37) ≤ 
            1, -(x2/31) + ((3 x5)/62) + (x6/62) ≤ 
            1, ((3 x1)/122) + (x4/61) + ((3 x5)/122) ≤ 
            1, ((6 x1)/655) + ((2 x3)/131) + ((6 x4)/655) + ((6 x5)/655) + ((3 x6)/131) ≤ 
            1, ((18 x1)/1207) - ((6 x2)/1207) + ((16 x3)/1207) + ((18 x4)/1207) + ((27 x6)/1207) ≤ 
            1, ((2 x1)/139) + ((2 x3)/139) + ((2 x4)/139) + ((3 x6)/139) ≤ 
            1, ((3 x1)/167) + ((3 x3)/167) + ((2 x4)/167) + ((3 x6)/167) ≤ 1, 
          (x1/60) + (x3/60) + (x4/60) + (x6/60) ≤ 
            1, ((3 x1)/167) + ((3 x3)/167) + ((3 x4)/167) + ((2 x6)/167) ≤ 
            1, -(x2/31) + (x3/62) + ((3 x5)/62) ≤ 
            1, ((2 x1)/135) - ((4 x2)/945) + ((23 x3)/945) + ((8 x4)/945) + ((2 x5)/945) + ((2 x6)/135) ≤ 
            1, ((54 x1)/3335) - ((18 x2)/3335) + ((81 x3)/3335) + ((32 x4)/3335) + ((48 x6)/3335) ≤ 
            1, ((6 x1)/655) + ((3 x3)/131) + ((4 x4)/655) + ((6 x5)/655) + ((12 x6)/655) ≤ 
            1, ((6 x1)/629) + ((15 x3)/629) + ((4 x4)/629) + ((6 x5)/629) + ((10 x6)/629) ≤ 
            1, -(x2/50) + ((3 x5)/100) + ((3 x6)/100) ≤ 
            1, -(x3/31) + ((3 x4)/62) + (x6/62) ≤ 
            1, -(x3/50) + ((3 x4)/100) + ((3 x6)/100) ≤ 
            1, ((6 x1)/397) + ((4 x3)/397) + ((6 x4)/397) + ((9 x6)/397) ≤ 
            1, ((2 x1)/165) + ((2 x5)/165) + (x6/33) ≤ 
            1, ((2 x1)/165) + ((2 x4)/165) + (x6/33) ≤ 
            1, ((6 x1)/389) - ((2 x2)/389) + ((4 x3)/389) + ((6 x4)/389) + ((9 x6)/389) ≤ 1, 
          (x1/51) + (x3/51) + (x4/51) ≤ 
            1, ((2 x1)/179) + ((5 x3)/179) + ((2 x5)/179) + ((2 x6)/179) ≤ 1, ((2 x1)/93) + (x3/31) ≤ 
            1, ((6 x1)/271) - ((2 x2)/271) + ((9 x3)/271) ≤ 
            1, (x1/50) + (x3/50) + (x4/75) - (x5/225) + (x6/75) ≤ 
            1, ((3 x1)/167) + ((2 x2)/167) + ((3 x5)/167) + ((3 x6)/167) ≤ 
            1, ((12 x1)/655) + ((4 x2)/655) + ((6 x4)/655) + ((3 x5)/131) + ((6 x6)/655) ≤ 
            1, ((16 x1)/1041) + ((4 x2)/1041) + ((4 x3)/1041) + ((10 x4)/1041) + ((25 x5)/1041) + ((10 x6)/1041) ≤ 
            1, ((16 x1)/1041) + ((4 x2)/1041) + ((4 x3)/1041) + ((25 x4)/1041) + ((10 x5)/1041) + ((10 x6)/1041) ≤ 1, 
          (x1/79) - ((2 x3)/79) + ((4 x4)/79) ≤ 
            1, ((2 x1)/93) + (x4/31) ≤ 
            1, ((2 x1)/165) + ((2 x3)/165) + (x6/33) ≤ 
            1, ((6 x1)/397) + ((6 x3)/397) + ((4 x4)/397) + ((9 x6)/397) ≤ 1, 
          (x1/79) + ((4 x3)/79) - ((2 x4)/79) ≤ 
            1, ((3 x1)/122) + (x2/61) + ((3 x3)/122) ≤ 1, 
          (x1/48) + (x2/120) + (x3/48) + (x4/120) + (x6/120) ≤ 
            1, ((18 x1)/1207) + ((18 x3)/1207) + ((16 x4)/1207) - ((6 x5)/1207) + ((27 x6)/1207) ≤ 1, 
          (x1/48) + (x2/120) + (x4/120) + (x5/48) + (x6/120) ≤ 1, 
          (x1/50) + (x2/75) - (x3/225) + (x5/50) + (x6/75) ≤ 
            1, ((18 x1)/1207) + ((16 x2)/1207) - ((6 x3)/1207) + ((18 x5)/1207) + ((27 x6)/1207) ≤ 
            1, ((2 x1)/139) + ((2 x2)/139) + ((2 x5)/139) + ((3 x6)/139) ≤ 
            1, ((6 x1)/389) + ((4 x2)/389) - ((2 x3)/389) + ((6 x5)/389) + ((9 x6)/389) ≤ 
            1, ((6 x1)/397) + ((4 x2)/397) + ((6 x5)/397) + ((9 x6)/397) ≤ 
            1, ((6 x1)/655) + ((2 x2)/131) + ((6 x4)/655) + ((6 x5)/655) + ((3 x6)/131) ≤ 1, 
          (x1/79) - ((2 x2)/79) + ((4 x5)/79) ≤ 
            1, ((18 x1)/1207) + ((18 x2)/1207) - ((6 x4)/1207) + ((16 x5)/1207) + ((27 x6)/1207) ≤ 
            1, ((6 x1)/655) + ((6 x2)/655) + ((6 x3)/655) + ((2 x5)/131) + ((3 x6)/131) ≤ 
            1, ((2 x1)/185) + ((2 x2)/185) + ((2 x3)/185) + 
              (x6/37) ≤ 
            1, ((2 x1)/179) + ((2 x3)/179) + ((5 x5)/179) + ((2 x6)/179) ≤ 1, 
          (x1/72) + (x2/180) + (x3/180) + (x4/180) + (x5/45) + (x6/72) ≤ 
            1, ((6 x1)/655) + ((6 x2)/655) + ((6 x3)/655) + ((2 x4)/131) + ((3 x6)/131) ≤ 1, 
          (x1/72) + (x2/180) + (x3/180) + (x4/45) + (x5/180) + (x6/72) ≤ 
            1, ((2 x1)/179) + ((2 x2)/179) + ((5 x4)/179) + ((2 x6)/179) ≤ 
            1, ((3 x3)/100) - (x4/50) + ((3 x6)/100) ≤ 
            1, ((6 x1)/389) + ((6 x3)/389) + ((4 x4)/389) - ((2 x5)/389) + ((9 x6)/389) ≤ 
            1, ((3 x3)/62) - (x4/31) + (x6/62) ≤ 
            1, ((3 x3)/62) - (x4/31) + (x5/62) ≤ 
            1, ((12 x1)/655) + ((6 x2)/655) + ((3 x3)/131) + ((4 x4)/655) + ((6 x6)/655) ≤ 1, 
          (x1/72) + (x2/180) + (x3/45) + (x4/180) + (x5/180) + (x6/72) ≤ 
            1, ((16 x1)/1041) + ((10 x2)/1041) + ((25 x3)/1041) + ((4 x4)/1041) + ((4 x5)/1041) + ((10 x6)/1041) ≤ 1, 
          (x3/34) + (x5/34) - (x6/17) ≤ 
            1, ((2 x1)/175) + ((2 x3)/175) + ((2 x4)/175) + 
              (x5/35) - ((4 x6)/175) ≤ 
            1, ((4 x2)/385) + ((9 x3)/385) + ((6 x4)/385) + ((6 x5)/385) - ((6 x6)/385) ≤ 
            1, ((2 x1)/175) + 
              (x3/35) + ((2 x4)/175) + ((2 x5)/175) - ((2 x6)/35) ≤ 1, ((3 x3)/85) + ((2 x5)/85) - ((6 x6)/85) ≤ 
            1, ((2 x1)/175) + ((2 x2)/175) + 
              (x3/35) + ((2 x5)/175) - ((4 x6)/175) ≤ 
            1, ((3 x1)/100) + ((3 x3)/100) - (x6/50) ≤ 1, 
          (x1/32) + (x3/32) - (x6/16) ≤ 1, 
          (x1/49) + (x3/49) + (x4/49) - ((2 x6)/49) ≤ 
            1, ((2 x1)/135) + ((2 x2)/945) + ((8 x3)/945) + ((23 x4)/945) - ((4 x5)/945) + ((2 x6)/135) ≤ 
            1, ((54 x1)/3335) + ((32 x3)/3335) + ((81 x4)/3335) - ((18 x5)/3335) + ((48 x6)/3335) ≤ 
            1, ((6 x1)/655) + ((6 x2)/655) + ((4 x3)/655) + ((3 x4)/131) + ((12 x6)/655) ≤ 
            1, ((6 x1)/629) + ((6 x2)/629) + ((4 x3)/629) + ((15 x4)/629) + ((10 x6)/629) ≤ 
            1, ((6 x1)/271) + ((9 x4)/271) - ((2 x5)/271) ≤ 
            1, (x1/60) + (x2/60) + (x5/60) + (x6/60) ≤ 
            1, ((3 x1)/167) + ((3 x2)/167) + ((2 x5)/167) + ((3 x6)/167) ≤ 
            1, ((3 x1)/167) + ((3 x2)/167) + ((3 x5)/167) + ((2 x6)/167) ≤ 1, ((2 x1)/93) + (x5/31) ≤ 
            1, ((2 x1)/135) + ((8 x2)/945) + ((2 x3)/945) - ((4 x4)/945) + ((23 x5)/945) + ((2 x6)/135) ≤ 
            1, ((54 x1)/3335) + ((32 x2)/3335) - ((18 x4)/3335) + ((81 x5)/3335) + ((48 x6)/3335) ≤ 
            1, ((6 x1)/655) + ((4 x2)/655) + ((6 x3)/655) + ((3 x5)/131) + ((12 x6)/655) ≤ 
            1, ((6 x1)/629) + ((4 x2)/629) + ((6 x3)/629) + ((15 x5)/629) + ((10 x6)/629) ≤ 
            1, ((6 x1)/271) - ((2 x4)/271) + ((9 x5)/271) ≤ 
            1, (x1/45) + (x2/45) + (x3/45) ≤ 
            1, ((6 x2)/385) + ((6 x3)/385) + ((4 x4)/385) + ((9 x5)/385) - ((6 x6)/385) ≤ 
            1, ((2 x3)/85) + ((3 x5)/85) - ((6 x6)/85) ≤ 
            1, ((2 x1)/175) + ((2 x2)/175) + ((2 x3)/175) + 
              (x5/35) - ((2 x6)/35) ≤ 1, 
          (x1/32) + (x5/32) - (x6/16) ≤ 
            1, ((3 x1)/100) + ((3 x5)/100) - (x6/50) ≤ 
            1, -x6 ≤ 0, 
          (x1/32) + (x4/32) - (x6/16) ≤ 
            1, ((6 x2)/385) + ((6 x3)/385) + ((9 x4)/385) + ((4 x5)/385) - ((6 x6)/385) ≤ 
            1, ((2 x1)/175) + ((2 x2)/175) + ((2 x3)/175) + 
              (x4/35) - ((2 x6)/35) ≤ 
            1, ((3 x1)/100) + ((3 x4)/100) - (x6/50) ≤ 
            1, ((2 x1)/165) + ((2 x2)/165) + (x6/33) ≤ 
            1, ((6 x1)/397) + ((6 x2)/397) + ((4 x5)/397) + ((9 x6)/397) ≤ 1, 
          (x1/51) + (x2/51) + (x5/51) ≤ 
            1, ((6 x1)/389) + ((6 x2)/389) - ((2 x4)/389) + ((4 x5)/389) + ((9 x6)/389) ≤ 
            1, ((3 x2)/100) - (x5/50) + ((3 x6)/100) ≤ 1, 
          (x1/48) + (x2/48) + (x3/120) + (x5/120) + (x6/120) ≤ 1, 
          (x2/62) - (x3/31) + ((3 x4)/62) ≤ 1, 
          (x1/50) + (x2/50) - (x4/225) + (x5/75) + (x6/75) ≤ 
            1, ((3 x2)/62) - (x5/31) + (x6/62) ≤ 
            1, ((3 x2)/62) + (x4/62) - (x5/31) ≤ 
            1, ((12 x1)/655) + ((3 x2)/131) + ((6 x3)/655) + ((4 x5)/655) + ((6 x6)/655) ≤ 
            1, ((3 x1)/122) + ((3 x2)/122) + (x3/61) ≤ 1, 
          (x1/72) + (x2/45) + (x3/180) + (x4/180) + (x5/180) + (x6/72) ≤ 
            1, ((16 x1)/1041) + ((25 x2)/1041) + ((10 x3)/1041) + ((4 x4)/1041) + ((4 x5)/1041) + ((10 x6)/1041) ≤ 1, 
          (x1/49) + (x2/49) + (x5/49) - ((2 x6)/49) ≤ 
            1, ((9 x2)/385) + ((4 x3)/385) + ((6 x4)/385) + ((6 x5)/385) - ((6 x6)/385) ≤ 
            1, ((2 x1)/175) + 
              (x2/35) + ((2 x4)/175) + ((2 x5)/175) - ((2 x6)/35) ≤ 1, 
          (x1/32) + (x2/32) - (x6/16) ≤ 
            1, ((2 x2)/85) + ((3 x4)/85) - ((6 x6)/85) ≤ 
            1, ((3 x2)/85) + ((2 x4)/85) - ((6 x6)/85) ≤ 1, 
          (x2/34) + (x4/34) - (x6/17) ≤ 
            1, ((2 x1)/175) + ((2 x2)/175) + 
              (x4/35) + ((2 x5)/175) - ((4 x6)/175) ≤ 
            1, ((2 x1)/175) + 
              (x2/35) + ((2 x3)/175) + ((2 x4)/175) - ((4 x6)/175) ≤ 
            1, ((2 x1)/135) + ((23 x2)/945) - ((4 x3)/945) + ((2 x4)/945) + ((8 x5)/945) + ((2 x6)/135) ≤ 
            1, ((54 x1)/3335) + ((81 x2)/3335) - ((18 x3)/3335) + ((32 x5)/3335) + ((48 x6)/3335) ≤ 
            1, ((6 x1)/655) + ((3 x2)/131) + ((6 x4)/655) + ((4 x5)/655) + ((12 x6)/655) ≤ 
            1, ((6 x1)/629) + ((15 x2)/629) + ((6 x4)/629) + ((4 x5)/629) + ((10 x6)/629) ≤ 
            1, ((2 x1)/179) + ((5 x2)/179) + ((2 x4)/179) + ((2 x6)/179) ≤ 1, 
          (x1/79) + ((4 x2)/79) - ((2 x5)/79) ≤ 
            1, ((2 x1)/93) + (x2/31) ≤ 
            1, ((6 x1)/271) + ((9 x2)/271) - ((2 x3)/271) ≤ 
            1, ((3 x1)/100) + ((3 x2)/100) - (x6/50) ≤ 1, 
          (x1/94) - (x2/47) + ((2 x5)/47) + (x6/94) ≤ 
            1, -(x2/16) + (x5/32) + (x6/32) ≤ 
            1, ((2 x1)/175) - ((2 x2)/35) + ((2 x4)/175) + ((2 x5)/175) + (x6/35) ≤ 
            1, ((3 x1)/154) + (x3/77) + (x4/77) + ((3 x6)/154) ≤ 
            1, ((6 x1)/385) - ((6 x2)/385) + ((4 x3)/385) + ((6 x4)/385) + ((9 x6)/385) ≤ 1, 
          (x1/94) - (x2/47) + (x3/94) + ((2 x5)/47) ≤ 
            1, ((2 x1)/175) - ((4 x2)/175) + 
              (x3/35) + ((2 x5)/175) + ((2 x6)/175) ≤ 
            1, ((2 x1)/85) - ((6 x2)/85) + ((3 x3)/85) ≤ 1, 
          (x1/51) + (x5/51) + (x6/51) ≤ 1, 
          (x1/38) + (x6/38) ≤ 1, (x1/36) + (x3/36) ≤ 1, 
          (x1/51) + (x3/51) + (x5/51) ≤ 1, 
          (x1/51) + (x4/51) + (x6/51) ≤ 1, 
          (x1/51) + (x3/51) + (x6/51) ≤ 1, 
          (x1/94) + ((2 x3)/47) - (x4/47) + (x6/94) ≤ 
            1, ((7 x1)/419) - ((2 x2)/419) + ((10 x3)/419) + ((4 x4)/419) + ((6 x6)/419) ≤ 1, 
          (x1/94) + ((2 x3)/47) - (x4/47) + (x5/94) ≤ 
            1, ((3 x1)/154) + ((3 x3)/154) + (x4/77) + (x6/77) ≤ 
            1, ((2 x1)/47) + (x3/94) + (x5/94) - (x6/47) ≤ 
            1, ((3 x1)/62) + (x3/62) - (x6/31) ≤ 
            1, ((2 x1)/47) + (x3/94) + (x4/94) - (x6/47) ≤ 1, 
          (x1/36) + (x4/36) ≤ 1, 
          (x1/94) - (x3/47) + ((2 x4)/47) + (x6/94) ≤ 
            1, -(x3/16) + (x4/32) + (x6/32) ≤ 
            1, ((2 x1)/175) - ((2 x3)/35) + ((2 x4)/175) + ((2 x5)/175) + (x6/35) ≤ 
            1, ((3 x1)/154) + (x2/77) + (x5/77) + ((3 x6)/154) ≤ 
            1, (x1/36) + (x5/36) ≤ 1, 
          (x1/54) + (x2/135) + (x3/135) + (x4/135) + (x5/135) + 
              (x6/54) ≤ 1, (x1/15) - ((2 x6)/45) ≤ 1, 
          (x1/63) + ((2 x2)/315) + (x3/63) + ((2 x4)/315) + 
              (x5/63) + ((2 x6)/315) ≤ 1, 
          (x1/45) + (x2/180) + (x3/72) + (x4/72) + (x5/180) + (x6/180) ≤ 
            1, ((6 x1)/385) + ((4 x2)/385) - ((6 x3)/385) + ((6 x5)/385) + ((9 x6)/385) ≤ 1, 
          (x3/32) - (x4/16) + (x6/32) ≤ 
            1, ((6 x1)/385) + ((6 x2)/385) - ((6 x4)/385) + ((4 x5)/385) + ((9 x6)/385) ≤ 
            1, ((2 x1)/175) + ((2 x2)/175) + ((2 x3)/175) - ((2 x4)/35) + (x6/35) ≤ 
            1, ((7 x1)/419) + ((4 x2)/419) - ((2 x4)/419) + ((10 x5)/419) + ((6 x6)/419) ≤ 
            1, ((3 x1)/62) + (x5/62) - (x6/31) ≤ 
            1, ((3 x1)/62) + (x4/62) - (x6/31) ≤ 
            1, ((6 x1)/385) + ((6 x3)/385) + ((4 x4)/385) - ((6 x5)/385) + ((9 x6)/385) ≤ 
            1, ((7 x1)/419) + ((4 x3)/419) + ((10 x4)/419) - ((2 x5)/419) + ((6 x6)/419) ≤ 
            1, ((3 x1)/154) + (x3/77) + ((3 x4)/154) + (x6/77) ≤ 
            1, (x1/51) + (x2/51) + (x6/51) ≤ 1, 
          (x2/32) - (x5/16) + (x6/32) ≤ 
            1, ((2 x1)/175) + ((2 x2)/175) + ((2 x3)/175) - ((2 x5)/35) + (x6/35) ≤ 
            1, ((3 x1)/154) + (x2/77) + ((3 x5)/154) + (x6/77) ≤ 
            1, ((2 x1)/175) + ((2 x3)/175) - ((4 x4)/175) + 
              (x5/35) + ((2 x6)/175) ≤ 
            1, ((2 x1)/85) - ((6 x4)/85) + ((3 x5)/85) ≤ 1, 
          (x1/45) + (x2/72) + (x3/180) + (x4/180) + (x5/72) + (x6/180) ≤ 
            1, (x1/39) + ((2 x2)/195) + ((2 x3)/195) + ((2 x4)/195) + ((2 x5)/195) ≤ 1, 
          (x1/94) + (x2/94) - (x3/47) + ((2 x4)/47) ≤ 1, 
          (x1/51) + (x2/51) + (x4/51) ≤ 
            1, ((2 x1)/47) + (x2/94) + (x5/94) - (x6/47) ≤ 1, 
          (x1/94) + ((2 x2)/47) - (x5/47) + (x6/94) ≤ 1, 
          (x1/94) + ((2 x2)/47) + (x4/94) - (x5/47) ≤ 
            1, ((2 x1)/47) + (x2/94) + (x4/94) - (x6/47) ≤ 1, 
          (x1/63) + (x2/63) + ((2 x3)/315) + 
              (x4/63) + ((2 x5)/315) + ((2 x6)/315) ≤ 
            1, ((2 x1)/85) + ((3 x4)/85) - ((6 x5)/85) ≤ 
            1, ((2 x1)/175) + ((2 x2)/175) + 
              (x4/35) - ((4 x5)/175) + ((2 x6)/175) ≤ 
            1, ((2 x1)/85) + ((3 x2)/85) - ((6 x3)/85) ≤ 
            1, ((2 x1)/175) + 
              (x2/35) - ((4 x3)/175) + ((2 x4)/175) + ((2 x6)/175) ≤ 1, ((3 x1)/62) + (x2/62) - (x6/31) ≤ 1, 
          (x1/36) + (x2/36) ≤ 
            1, ((3 x1)/154) + ((3 x2)/154) + (x5/77) + (x6/77) ≤ 
            1, ((7 x1)/419) + ((10 x2)/419) - ((2 x3)/419) + ((4 x5)/419) + ((6 x6)/419) ≤ 1, 
          (x1/49) - ((2 x2)/49) + (x5/49) + (x6/49) ≤ 1, 
          (x1/62) - (x2/31) + ((3 x5)/62) ≤ 1, 
          (x1/32) - (x2/16) + (x5/32) ≤ 
            1, ((9 x1)/385) - ((6 x2)/385) + ((6 x3)/385) + ((4 x4)/385) + ((6 x6)/385) ≤ 1, 
          (x1/35) - ((2 x2)/35) + ((2 x3)/175) + ((2 x5)/175) + ((2 x6)/175) ≤ 
            1, ((3 x1)/85) - ((6 x2)/85) + ((2 x3)/85) ≤ 1, 
          (x1/34) - (x2/17) + (x3/34) ≤ 1, 
          (x1/35) - ((4 x2)/175) + ((2 x3)/175) + ((2 x4)/175) + ((2 x5)/175) ≤ 
            1, ((5 x1)/179) + ((2 x3)/179) + ((2 x4)/179) + ((2 x5)/179) ≤ 
            1, ((27 x1)/1207) - ((6 x2)/1207) + ((18 x3)/1207) + ((16 x4)/1207) + ((18 x6)/1207) ≤ 
            1, ((3 x1)/131) + ((6 x3)/655) + ((2 x4)/131) + ((6 x5)/655) + ((6 x6)/655) ≤ 
            1, ((81 x1)/3335) - ((18 x2)/3335) + ((54 x3)/3335) + ((48 x4)/3335) + ((32 x6)/3335) ≤ 
            1, ((10 x1)/419) - ((2 x2)/419) + ((7 x3)/419) + ((6 x4)/419) + ((4 x6)/419) ≤ 
            1, ((3 x1)/131) + ((6 x3)/655) + ((12 x4)/655) + ((6 x5)/655) + ((4 x6)/655) ≤ 
            1, ((15 x1)/629) + ((6 x3)/629) + ((10 x4)/629) + ((6 x5)/629) + ((4 x6)/629) ≤ 
            1, ((23 x1)/945) - ((4 x2)/945) + ((2 x3)/135) + ((2 x4)/135) + ((2 x5)/945) + ((8 x6)/945) ≤ 1, 
          (x1/62) + ((3 x3)/62) - (x4/31) ≤ 
            1, ((11 x1)/265) + ((2 x3)/265) + ((2 x4)/265) + ((2 x5)/265) - ((4 x6)/265) ≤ 
            1, ((4 x1)/79) + (x3/79) - ((2 x6)/79) ≤ 1, 
          (x1/49) - ((2 x3)/49) + (x4/49) + (x6/49) ≤ 1, 
          (x1/49) + (x3/49) - ((2 x4)/49) + (x6/49) ≤ 1, 
          (x1/34) - (x4/17) + (x5/34) ≤ 
            1, ((4 x1)/79) + (x5/79) - ((2 x6)/79) ≤ 
            1, ((4 x1)/79) + (x4/79) - ((2 x6)/79) ≤ 
            1, ((3 x1)/113) + ((4 x2)/565) + ((6 x3)/565) + ((6 x4)/565) + ((6 x5)/565) ≤ 
            1, ((25 x1)/1041) + ((4 x2)/1041) + ((10 x3)/1041) + ((16 x4)/1041) + ((10 x5)/1041) + ((4 x6)/1041) ≤ 
            1, ((5 x1)/203) + ((4 x2)/1015) + ((2 x3)/203) + ((2 x4)/145) + ((2 x5)/203) + ((4 x6)/1015) ≤ 1, 
          (x1/62) - (x3/31) + ((3 x4)/62) ≤ 1, 
          (x1/32) - (x3/16) + (x4/32) ≤ 
            1, ((10 x1)/419) + ((6 x3)/419) + ((7 x4)/419) - ((2 x5)/419) + ((4 x6)/419) ≤ 1, 
          (x1/34) + (x4/34) - (x5/17) ≤ 
            
            1, ((9 x1)/385) + ((6 x2)/385) - ((6 x3)/385) + ((4 x5)/385) + ((6 x6)/385) ≤ 1, 
          (x1/35) + ((2 x2)/175) - ((2 x3)/35) + ((2 x4)/175) + ((2 x6)/175) ≤ 
            1, ((27 x1)/1207) + ((18 x2)/1207) - ((6 x3)/1207) + ((16 x5)/1207) + ((18 x6)/1207) ≤ 
            1, ((3 x1)/131) + ((6 x2)/655) + ((6 x4)/655) + ((2 x5)/131) + ((6 x6)/655) ≤ 1, 
          (x1/49) + (x2/49) - ((2 x5)/49) + (x6/49) ≤ 
            1, ((10 x1)/419) + ((6 x2)/419) - ((2 x4)/419) + ((7 x5)/419) + ((4 x6)/419) ≤ 
            1, ((25 x1)/1041) + ((10 x2)/1041) + ((4 x3)/1041) + ((10 x4)/1041) + ((16 x5)/1041) + ((4 x6)/1041) ≤ 1, 
          (x1/35) + ((2 x3)/175) - ((2 x4)/35) + ((2 x5)/175) + ((2 x6)/175) ≤ 
            1, ((27 x1)/1207) + ((16 x2)/1207) - ((6 x4)/1207) + ((18 x5)/1207) + ((18 x6)/1207) ≤ 
            1, ((3 x1)/131) + ((2 x2)/131) + ((6 x3)/655) + ((6 x5)/655) + ((6 x6)/655) ≤ 
            1, ((9 x1)/385) + ((4 x2)/385) - ((6 x4)/385) + ((6 x5)/385) + ((6 x6)/385) ≤ 1, 
          (x1/32) + (x3/32) - (x4/16) ≤ 
            1, ((3 x1)/131) + ((12 x2)/655) + ((6 x3)/655) + ((6 x5)/655) + ((4 x6)/655) ≤ 
            1, ((15 x1)/629) + ((10 x2)/629) + ((6 x3)/629) + ((6 x5)/629) + ((4 x6)/629) ≤ 
            1, ((3 x1)/85) - ((6 x4)/85) + ((2 x5)/85) ≤ 1, 
          (x1/35) + ((2 x2)/175) + ((2 x3)/175) - ((4 x4)/175) + ((2 x5)/175) ≤ 
            1, ((23 x1)/945) + ((2 x2)/135) + ((2 x3)/945) - ((4 x4)/945) + ((2 x5)/135) + ((8 x6)/945) ≤ 
            1, ((81 x1)/3335) + ((48 x2)/3335) - ((18 x4)/3335) + ((54 x5)/3335) + ((32 x6)/3335) ≤ 
            1, ((5 x1)/179) + ((2 x2)/179) + ((2 x3)/179) + ((2 x5)/179) ≤ 
            1, ((11 x1)/265) + ((2 x2)/265) + ((2 x3)/265) + ((2 x5)/265) - ((4 x6)/265) ≤ 
            1, ((3 x1)/113) + ((6 x2)/565) + ((6 x3)/565) + ((4 x4)/565) + ((6 x5)/565) ≤ 
            1, ((5 x1)/203) + ((2 x2)/145) + ((2 x3)/203) + ((4 x4)/1015) + ((2 x5)/203) + ((4 x6)/1015) ≤ 
            1, ((25 x1)/1041) + ((16 x2)/1041) + ((10 x3)/1041) + ((4 x4)/1041) + ((10 x5)/1041) + ((4 x6)/1041) ≤ 1, 
          (x1/35) + ((2 x2)/175) + ((2 x4)/175) - ((2 x5)/35) + ((2 x6)/175) ≤ 
            1, ((9 x1)/385) + ((4 x3)/385) + ((6 x4)/385) - ((6 x5)/385) + ((6 x6)/385) ≤ 
            1, ((27 x1)/1207) + ((16 x3)/1207) + ((18 x4)/1207) - ((6 x5)/1207) + ((18 x6)/1207) ≤ 
            1, ((25 x1)/1041) + ((10 x2)/1041) + ((16 x3)/1041) + ((10 x4)/1041) + ((4 x5)/1041) + ((4 x6)/1041) ≤ 
            1, ((3 x1)/131) + ((6 x2)/655) + ((12 x3)/655) + ((6 x4)/655) + ((4 x6)/655) ≤ 
            1, ((81 x1)/3335) + ((48 x3)/3335) + ((54 x4)/3335) - ((18 x5)/3335) + ((32 x6)/3335) ≤ 
            1, ((23 x1)/945) + ((2 x2)/945) + ((2 x3)/135) + ((2 x4)/135) - ((4 x5)/945) + ((8 x6)/945) ≤ 
            1, ((3 x1)/85) + ((2 x4)/85) - ((6 x5)/85) ≤ 1, 
          (x1/35) + ((2 x2)/175) + ((2 x3)/175) + ((2 x4)/175) - ((4 x5)/175) ≤ 
            1, ((11 x1)/265) + ((2 x2)/265) + ((2 x3)/265) + ((2 x4)/265) - ((4 x6)/265) ≤ 
            1, ((3 x1)/113) + ((6 x2)/565) + ((6 x3)/565) + ((6 x4)/565) + ((4 x5)/565) ≤ 
            1, ((5 x1)/179) + ((2 x2)/179) + ((2 x3)/179) + ((2 x4)/179) ≤ 
            1, ((3 x1)/131) + ((6 x2)/655) + ((6 x4)/655) + ((12 x5)/655) + ((4 x6)/655) ≤ 
            1, ((11 x1)/265) + ((2 x2)/265) + ((2 x4)/265) + ((2 x5)/265) - ((4 x6)/265) ≤ 
            1, ((4 x1)/79) + (x2/79) - ((2 x6)/79) ≤ 1, 
          (x1/62) + ((3 x2)/62) - (x5/31) ≤ 1, 
          (x1/32) + (x2/32) - (x5/16) ≤ 
            1, ((3 x1)/113) + ((6 x2)/565) + ((4 x3)/565) + ((6 x4)/565) + ((6 x5)/565) ≤ 
            1, ((3 x1)/131) + ((6 x2)/655) + ((2 x3)/131) + ((6 x4)/655) + ((6 x6)/655) ≤ 
            1, ((5 x1)/203) + ((2 x2)/203) + ((4 x3)/1015) + ((2 x4)/203) + ((2 x5)/145) + ((4 x6)/1015) ≤ 
            1, ((5 x1)/203) + ((2 x2)/203) + ((2 x3)/145) + ((2 x4)/203) + ((4 x5)/1015) + ((4 x6)/1015) ≤ 
            1, ((15 x1)/629) + ((6 x2)/629) + ((10 x3)/629) + ((6 x4)/629) + ((4 x6)/629) ≤ 
            1, ((3 x1)/85) + ((2 x2)/85) - ((6 x3)/85) ≤ 
            1, ((81 x1)/3335) + ((54 x2)/3335) - ((18 x3)/3335) + ((48 x5)/3335) + ((32 x6)/3335) ≤ 
            1, ((10 x1)/419) + ((7 x2)/419) - ((2 x3)/419) + ((6 x5)/419) + ((4 x6)/419) ≤ 1, 
          (x1/34) + (x2/34) - (x3/17) ≤ 1, 
          (x1/35) + ((2 x2)/175) - ((4 x3)/175) + ((2 x4)/175) + ((2 x5)/175) ≤ 
            1, ((5 x1)/179) + ((2 x2)/179) + ((2 x4)/179) + ((2 x5)/179) ≤ 
            1, ((23 x1)/945) + ((2 x2)/135) - ((4 x3)/945) + ((2 x4)/945) + ((2 x5)/135) + ((8 x6)/945) ≤ 
            1, ((15 x1)/629) + ((6 x2)/629) + ((6 x4)/629) + ((10 x5)/629) + ((4 x6)/629) ≤ 1, 
          (x1/37) + ((2 x3)/185) + ((2 x5)/185) + ((2 x6)/185) ≤ 1, ((3 x1)/100) - (x2/50) + ((3 x5)/100) ≤ 
            1, ((5 x1)/159) + ((2 x3)/159) + ((2 x5)/159) ≤ 
            1, ((3 x1)/109) + ((2 x4)/109) + ((2 x5)/109) ≤ 
            1, ((3 x1)/139) + ((2 x3)/139) + ((2 x4)/139) + ((2 x6)/139) ≤ 
            1, ((9 x1)/391) + ((6 x3)/391) + ((6 x4)/391) + ((4 x6)/391) ≤ 
            1, ((9 x1)/389) - ((2 x2)/389) + ((6 x3)/389) + ((4 x4)/389) + ((6 x6)/389) ≤ 
            1, ((11 x1)/245) + ((2 x3)/245) + ((2 x5)/245) - ((4 x6)/245) ≤ 
            1, ((11 x1)/245) + ((2 x3)/245) + ((2 x4)/245) - ((4 x6)/245) ≤ 
            1, ((9 x1)/271) - ((2 x2)/271) + ((6 x3)/271) ≤ 
            1, ((19 x1)/777) + ((4 x2)/777) + ((10 x3)/777) + ((10 x4)/777) + ((4 x5)/777) + ((4 x6)/777) ≤ 
            1, ((3 x1)/100) + ((3 x3)/100) - (x4/50) ≤ 
            1, ((3 x1)/109) + ((4 x2)/545) + ((6 x3)/545) + ((4 x4)/545) + ((6 x5)/545) ≤ 
            1, ((3 x1)/109) + ((4 x2)/545) + ((6 x3)/545) + ((6 x4)/545) + ((4 x5)/545) ≤ 1, 
          (x1/37) + ((2 x2)/185) + ((2 x4)/185) + ((2 x6)/185) ≤ 1, ((3 x1)/100) - (x3/50) + ((3 x4)/100) ≤ 
            1, ((3 x1)/139) + ((2 x2)/139) + ((2 x5)/139) + ((2 x6)/139) ≤ 
            1, ((9 x1)/391) + ((6 x2)/391) + ((6 x5)/391) + ((4 x6)/391) ≤ 
            1, ((19 x1)/777) + ((10 x2)/777) + ((4 x3)/777) + ((4 x4)/777) + ((10 x5)/777) + ((4 x6)/777) ≤ 
            1, ((9 x1)/389) + ((4 x2)/389) - ((2 x4)/389) + ((6 x5)/389) + ((6 x6)/389) ≤ 
            1, ((9 x1)/271) - ((2 x4)/271) + ((6 x5)/271) ≤ 
            1, ((5 x1)/159) + ((2 x2)/159) + ((2 x4)/159) ≤ 
            1, ((11 x1)/245) + ((2 x2)/245) + ((2 x5)/245) - ((4 x6)/245) ≤ 
            1, ((11 x1)/245) + ((2 x2)/245) + ((2 x4)/245) - ((4 x6)/245) ≤ 
            1, ((9 x1)/389) + ((6 x2)/389) - ((2 x3)/389) + ((4 x5)/389) + ((6 x6)/389) ≤ 
            1, ((3 x1)/109) + ((2 x2)/109) + ((2 x3)/109) ≤ 
            1, ((3 x1)/109) + ((6 x2)/545) + ((4 x3)/545) + ((4 x4)/545) + ((6 x5)/545) ≤ 
            1, ((9 x1)/389) + ((4 x3)/389) + ((6 x4)/389) - ((2 x5)/389) + ((6 x6)/389) ≤ 
            1, ((3 x1)/100) + ((3 x2)/100) - (x5/50) ≤ 
            1, ((3 x1)/109) + ((6 x2)/545) + ((4 x3)/545) + ((6 x4)/545) + ((4 x5)/545) ≤ 
            1, ((9 x1)/271) + ((6 x4)/271) - ((2 x5)/271) ≤ 
            1, ((9 x1)/271) + ((6 x2)/271) - ((2 x3)/271) ≤ 
            1, ((9 x1)/307) + ((6 x4)/307) + ((4 x5)/307) ≤ 
            1, ((9 x1)/397) + ((4 x3)/397) + ((6 x4)/397) + ((6 x6)/397) ≤ 
            1, ((9 x1)/307) + ((4 x4)/307) + ((6 x5)/307) ≤ 
            1, ((9 x1)/397) + ((6 x3)/397) + ((4 x4)/397) + ((6 x6)/397) ≤ 1, 
          (x1/33) + ((2 x5)/165) + ((2 x6)/165) ≤ 1, 
          (x1/33) + ((2 x4)/165) + ((2 x6)/165) ≤ 1, 
          (x1/33) + ((2 x3)/165) + ((2 x6)/165) ≤ 1, 
          (x1/31) + ((2 x3)/93) ≤ 
            1, ((9 x1)/179) + ((2 x3)/179) - ((4 x6)/179) ≤ 
            1, (x1/31) + ((2 x5)/93) ≤ 
            1, ((9 x1)/179) + ((2 x5)/179) - ((4 x6)/179) ≤ 
            1, ((9 x1)/179) + ((2 x4)/179) - ((4 x6)/179) ≤ 
            1, (x1/23) ≤ 1, 
          (x1/31) + ((2 x4)/93) ≤ 
            1, ((9 x1)/307) + ((4 x2)/307) + ((6 x3)/307) ≤ 
            1, ((9 x1)/397) + ((4 x2)/397) + ((6 x5)/397) + ((6 x6)/397) ≤ 
            1, ((9 x1)/397) + ((6 x2)/397) + ((4 x5)/397) + ((6 x6)/397) ≤ 1, 
          (x1/33) + ((2 x2)/165) + ((2 x6)/165) ≤ 
            1, ((9 x1)/179) + ((2 x2)/179) - ((4 x6)/179) ≤ 
            1, ((9 x1)/307) + ((6 x2)/307) + ((4 x3)/307) ≤ 
            1, (x1/31) + ((2 x2)/93) ≤ 1};

This is the polytope P1 of section 4.1 and it has 2881 vertices and 964 facets.

Length[acconv]
Length[acineq]

The Big Minkowski

In this subsection we find the Minkowski sum P = P1 + P2.   Many of the computations in this section may take up to 30 minutes or so depending on the hardware used.  Some are also quite memory intensive. However, the final results are contained in the last two cells of the subsection which can be executed independently.

As described in section 4.1, we will exploit the fact that each facet Fi of P can be written as a sum of faces from P1 and P2, i.e. Fi  = gi + hi.  For our purposes it suffices to consider sums where dim(gi) + dim(hi) = 5.  We will also exploit the S4 symmetry of P1 and P2 by only considering a representative gi from each orbit of the S4 action.  We will need some functions which can compute face lattices of polytopes.  The first step is computing the facet-vertex relations:

VerticesOfFaces[normals_, mins_, vertices_] := 
        Module[{i = 1, j = 1, 
            inclist = 
              Table[{}, {k, 1, Length[normals]}]}, 
While[
            i < Length[normals] + 1, 
j = 
              1; 
While[
              j < Length[vertices] + 1, 
If[
                Dot[vertices[[j]], normals[[i]]] == 
                  mins[[i]], 
                inclist[[i]] = Append[inclist[[i]], j], 
                Null]; 
j = j + 1]; 
i = 
              i + 1;
]; 
inclist]; 
FacesOfVertices[inclist_] := 
        Module[{NormalIndices = Table[j, {j, 1, Length[inclist]}]}, 
          Table[Select[NormalIndices, 
              Intersection[inclist[[#]], {i}] ≠ {} &], {i, 1, 
              Max[Flatten[inclist]]}]];
P1normals = -Table[{Coefficient[acineq[[i, 1]], x1], 
              Coefficient[acineq[[i, 1]], x2], 
              Coefficient[acineq[[i, 1]], x3], 
              Coefficient[acineq[[i, 1]], x4], 
              Coefficient[acineq[[i, 1]], x5], 
              Coefficient[acineq[[i, 1]], x6]}, {i, 1, 
              Length[acineq]}];
P1mins = -acineq[[All, 2]];
P2normals = -Table[{Coefficient[dzineq[[i, 1]], x1], 
              Coefficient[dzineq[[i, 1]], x2], 
              Coefficient[dzineq[[i, 1]], x3], 
              Coefficient[dzineq[[i, 1]], x4], 
              Coefficient[dzineq[[i, 1]], x5], 
              Coefficient[dzineq[[i, 1]], x6]}, {i, 1, 
              Length[dzineq]}];
P2mins = -dzineq[[All, 2]];

P1voff = 
        VerticesOfFaces[P1normals, P1mins, 
          acconv];
P1fofv = FacesOfVertices[P1voff];
P2voff = 
        VerticesOfFaces[P2normals, P2mins, 
          dzconv];
P2fofv = FacesOfVertices[P2voff];

P1VIndex = 
        Table[i, {i, 1, Length[P1fofv]}];
P1FIndex = 
        Table[i, {i, 1, Length[P1voff]}];
P1vlist = 
        Table[{i}, {i, 1, Length[P1fofv]}];
P2VIndex = 
        Table[i, {i, 1, Length[P2fofv]}];
P2FIndex = 
        Table[i, {i, 1, Length[P2voff]}];
P2vlist = Table[{i}, {i, 1, Length[P2fofv]}];

We now find the orbit representatives for the vertices of P1

s4orbits = {{1, 2, 3, 4, 5, 6}, {1, 3, 2, 5, 4, 6}, {2, 1, 3, 4, 6, 
            5}, {2, 3, 1, 6, 4, 5}, {3, 1, 2, 5, 6, 4}, {3, 2, 1, 6, 5, 
            4}, {1, 4, 5, 2, 3, 6}, {1, 5, 4, 3, 2, 6}, {4, 1, 5, 2, 6, 
            3}, {4, 5, 1, 6, 2, 3}, {5, 1, 4, 3, 6, 2}, {5, 4, 1, 6, 3, 
            2}, {2, 4, 6, 1, 3, 5}, {2, 6, 4, 3, 1, 5}, {4, 2, 6, 1, 5, 
            3}, {4, 6, 2, 5, 1, 3}, {6, 2, 4, 3, 5, 1}, {6, 4, 2, 5, 3, 
            1}, {3, 5, 6, 1, 2, 4}, {3, 6, 5, 2, 1, 4}, {5, 3, 6, 1, 4, 
            2}, {5, 6, 3, 4, 1, 2}, {6, 3, 5, 2, 4, 1}, {6, 5, 3, 4, 2, 
            1}};
PermuteAList[alist_, perm_] := 
      Table[alist[[perm[[i]]]], {i, 1, Length[alist]}]; 
    MakePermIndex[alist_] := 
      Table[Position[alist, 
            PermuteAList[alist[[i]], s4orbits[[j]]]][[1, 
            1]], {i, 1, Length[alist]}, {j, 1, 
          Length[s4orbits]}];

The following evaluation may take a considerable amount of time.

P1perms = MakePermIndex[acconv];
P1vreps = GetIndexReps[P1vlist, P1perms];

PermuteAnIndex[indexlist_, permindex_, permnumber_] := 
        Map[permindex[[#, permnumber]] &, 
          indexlist];
IndexOrbit[alist_, pindex_] := 
        Union[Sort[
            Map[Sort, 
              Map[PermuteAnIndex[alist, pindex, #] &, 
                Table[i, {i, 1, 
                    Length[s4orbits]}]]]]];
GetIndexReps[alist_, pindex_] := 
        Module[{replist = {}, 
            remainder = Sort[alist]}, 
While[
            remainder ≠ {}, 
replist = 
              Join[replist, {remainder[[1]]}]; 
remainder = 
              Complement[remainder, 
                IndexOrbit[remainder[[1]], 
                  pindex]];
]; 
replist
];

P1VertexReps = GetIndexReps[P1vlist, P1perms];

With the vertex representatives in hand, we will use the functions below to find representatives of the edges, and so on.  To do this we consider every pair consisting of a representative face and any other face.  The set of all facets which contain both faces is computed, and then the common vertices of those facets are found.  The minimal sets under inclusion are the vertex sets of faces of the next higher dimension.

\(\(Closure[vertices_, voff_, fofv_] := 
        Module[{vs, fs}, 
fs = 
            Fold[Intersection, fofv[\([vertices[\([1]\)]]\)], 
              Map[fofv[\([#]\)] &, vertices]]; 
If[
            fs ≠ {}, 
            vs = Fold[Intersection, voff[\([fs[\([1]\)]]\)], 
                Map[voff[\([#]\)] &, fs]], 
            vs = {}]; 
vs
];\)\ \ 
\ 
\)
AddOn[subfacevertices_, vertlist_] := 
      Map[Union[subfacevertices, {#}] &, 
        Complement[vertlist, subfacevertices]]; 
    MinInclusiveSort[alist_, vertlist_] := 
      Module[{mins = {},  remainder = alist}, 
remainder = 
          Sort[Complement[alist, {{}}]]; 
While[
          remainder ≠ {}, 
mins = 
            Join[mins, {remainder[[1]]}]; 
remainder = 
            Sort[Select[remainder, 
                Length[Intersection[#, remainder[[1]]]] != 
                    Length[remainder[[1]]] &]];
]; 
mins
];
LatticeStep[subfaces_, vertices_, voff_, fofv_] := 
        Module[{candids, closedcandids}, 
candids = 
            Union[Flatten[Map[AddOn[#, vertices] &, subfaces], 
                1]]; 
closedcandids = 
            Union[Map[Closure[#, voff, fofv] &, 
                candids]]; 
MinInclusiveSort[closedcandids, 
            verticesvertices]
];

P1EdgeRepsWithExtras = 
        LatticeStep[P1VertexReps, P1VIndex, P1voff, 
          P1fofv];
P1EdgeReps = 
        GetIndexReps[P1EdgeRepsWithExtras, 
          P1perms];
Dimensions[P1EdgeReps]

For the higher dimenionsal faces of P1, we split the computation into pieces to avoid excessive memory usage.

P1EdgeRepsTablePartA = 
        Partition[P1EdgeReps, 100];
P1EdgeRepsTable = 
        Join[P1EdgeRepsTablePartA, {Complement[P1EdgeReps, 
              Flatten[P1EdgeRepsTablePartA, 
                1]]}];
P1dim2RepsWithExtrasTable = 
        Map[LatticeStep[#, P1VIndex, P1voff, P1fofv] &, 
          P1EdgeRepsTable];
P1dim2RepsWithExtras = 
        Union[Flatten[P1dim2RepsWithExtrasTable, 
            1]];
P1dim2Reps = 
        GetIndexReps[P1dim2RepsWithExtras, 
          P1perms];
Dimensions[P1dim2Reps]

P1dim2RepsTablePartA = 
        Partition[P1dim2Reps, 100];
P1dim2RepsTable = 
        Join[P1dim2RepsTablePartA, {Complement[P1dim2Reps, 
              Flatten[P1dim2RepsTablePartA, 
                1]]}];
P1dim3RepsWithExtrasTable = 
        Map[LatticeStep[#, P1VIndex, P1voff, P1fofv] &, 
          P1dim2RepsTable];
P1dim3RepsWithExtras = 
        Union[Flatten[P1dim3RepsWithExtrasTable, 
            1]];
P1dim3Reps = 
        GetIndexReps[P1dim3RepsWithExtras, 
          P1perms];
Dimensions[P1dim3Reps]

P1dim3RepsTablePartA = 
        Partition[P1dim3Reps, 100];
P1dim3RepsTable = 
        Join[P1dim3RepsTablePartA, {Complement[P1dim3Reps, 
              Flatten[P1dim3RepsTablePartA, 
                1]]}];
P1dim4RepsWithExtrasTable = 
        Map[LatticeStep[#, P1VIndex, P1voff, P1fofv] &, 
          P1dim3RepsTable];
P1dim4RepsWithExtras = 
        Union[Flatten[P1dim4RepsWithExtrasTable, 
            1]];
P1dim4Reps = 
        GetIndexReps[P1dim4RepsWithExtras, 
          P1perms];
Dimensions[P1dim4Reps]

Although unnecessary, its a nice check of our calculations to compute the facets of P1 from "below" and compare to the Porta output:

P1dim4RepsTablePartA = 
        Partition[P1dim4Reps, 100];
P1dim4RepsTable = 
        Join[P1dim4RepsTablePartA, {Complement[P1dim4Reps, 
              Flatten[P1dim4RepsTablePartA, 
                1]]}];
P1dim5RepsWithExtrasTable = 
        Map[LatticeStep[#, P1VIndex, P1voff, P1fofv] &, 
          P1dim4RepsTable];
P1dim5RepsWithExtras = 
        Union[Flatten[P1dim5RepsWithExtrasTable, 
            1]];
P1dim5Reps = 
        GetIndexReps[P1dim5RepsWithExtras, 
          P1perms];
Dimensions[P1dim5Reps]

P1dim5Faces = 
        Union[Flatten[Map[IndexOrbit[#, P1perms] &, P1dim5Reps], 
            1]];
Dimensions[P1dim5Faces]

Next we find all the faces of P2.

dzEdges = 
        LatticeStep[P2vlist, P2VIndex, P2voff, 
          P2fofv];
dzEdges = Union[dzEdges];
Dimensions[dzEdges]

dz2dims = 
        LatticeStep[dzEdges, P2VIndex, P2voff, 
          P2fofv];
dz2dims = Union[dz2dims];
Dimensions[dz2dims]

dz3dims = 
        LatticeStep[dz2dims, P2VIndex, P2voff, 
          P2fofv];
dz3dims = Union[dz3dims];
Dimensions[dz3dims]

dz4dims = 
        LatticeStep[dz3dims, P2VIndex, P2voff, 
          P2fofv];
dz4dims = Union[dz4dims];
Dimensions[dz4dims]

dz5dims = 
        LatticeStep[dz4dims, P2VIndex, P2voff, 
          P2fofv];
dz5dims = Union[dz5dims];
Dimensions[dz5dims]

Now we compute the normals to combinations of faces from polytopes P1 and P2.

GetVectors[indexlist_, vertices_] := 
      Map[vertices[[#]] - vertices[[indexlist[[1]]]] &, 
        Rest[indexlist]]; 
    Normals[vect1_, vect2_] := NullSpace[Union[vect1, vect2]]; 
    NewNormals[list1_, vertices1_, list2_, vertices2_, 
        fofv1_] := 
Module[{vectlist1, vectlist2, 
          newnormlist = {}, tempnorm}, 
For[i = 1, 
          i < Length[list1] + 1, 
          i = i + 1, 
vectlist1 = 
            GetVectors[list1[[i]], vertices1]; 
For[
            j = 1, j < Length[list2] + 1, 
            j = j + 1, 
vectlist2 = 
              GetVectors[list2[[j]], 
                vertices2]; 
tempnorm = 
              Normals[vectlist1, vectlist2]; 
If[
              Length[tempnorm] == 
                1, 
newnormlist = 
                  Join[newnormlist, 
                    tempnorm];
];
];
]; 
newnormlist
];

Pdim3Anddim2 = 
        Union[NewNormals[P1dim3Reps, acconv, dz2dims, dzconv, 
            P1fofv]];
Dimensions[Pdim3Anddim2]

Pdim2Anddim3 = 
        Union[NewNormals[P1dim2Reps, acconv, dz3dims, dzconv, 
            P1fofv]];
Dimensions[Pdim2Anddim3]

Pdim1Anddim4 = 
        Union[NewNormals[P1EdgeReps, acconv, dz4dims, dzconv, 
            P1fofv]];
Dimensions[Pdim1Anddim4]

Pdim4Anddim1 = 
        Union[NewNormals[P1dim4Reps, acconv, dzEdges, dzconv, 
            P1fofv]];
Dimensions[Pdim4Anddim1]

Now we have a large list of candidate normals.  Again we exploit the symmetry of P by doing most of our calculations on representatives from each orbit.

GetReps[alist_] := 
        Module[{newlist = {}, complist = alist, temp, 
            temporbit}, 
While[
            complist ≠ {}, 
temporbit = 
              Sort[Flatten[
                  Table[Map[
                      PermuteAList[#, 
                          s4orbits[[i]]] &, {complist[[1]]}], {i, 1, 
                      Length[s4orbits]}], 1]]; 
temp = 
              temporbit[[1]]; 
complist = 
              Complement[complist, temporbit]; 
newlist = 
              Join[newlist, {temp}];
]; 
newlist];

Our construction does not detect whether the computed normal is outward or inward pointing so we add in the negatives of each candidate.

NewNormalCandidates = 
        Union[Pdim3Anddim2, Pdim2Anddim3, Pdim1Anddim4, 
          Pdim4Anddim1];
NewNormalCandidateReps = 
        GetReps[NewNormalCandidates];
NewNormalCandidateReps = 
        Union[NewNormalCandidateReps, -NewNormalCandidateReps]; 
Dimensions[NewNormalCandidateReps]

Now we need to determine the true normals of facets from our candidate list.  To do this we need the vertices of P.

PVertexCandidates = 
        MinkSum[acconv, dzconv];
Dimensions[PVertexCandidates]

To cut down on the size of the vertices under consideration, we computed the convex hulls of other partial Minkowski sums.  For example, we could compute P = P1' + P2' where P1' is the convex hull of the Minkowski sum of the first 
5 Albouy-Chenciner equations and P2' is the convex hull of the Minkowski sum of the 3 Dziobek equations plus the remaining Albouy-Chenciner equation.  Any candidate vertices of P computed in this way which are lacking a full orbit under the S4 action must be spurious and can be deleted.  Intersecting various such candidate lists whittles down the list considerably.  After a few such iterations we arrive at the list in the cell below, which is not open due to its size.

PVertexCandidates2 = {{0, 13, 19, 23, 20, 15}, {0, 13, 19, 23, 20, 
            21}, {0, 13, 19, 23, 23, 15}, {0, 13, 19, 23, 23, 21}, {0, 13, 
            21, 23, 20, 13}, {0, 13, 21, 23, 20, 19}, {0, 13, 21, 23, 23, 
            13}, {0, 13, 21, 23, 23, 19}, {0, 13, 23, 23, 16, 15}, {0, 13, 
            23, 23, 16, 21}, {0, 13, 23, 23, 19, 15}, {0, 13, 23, 23, 19, 
            21}, {0, 13, 25, 23, 16, 13}, {0, 13, 25, 23, 16, 19}, {0, 13, 
            25, 23, 19, 13}, {0, 13, 25, 23, 19, 19}, {0, 16, 16, 20, 23, 
            15}, {0, 16, 16, 20, 23, 21}, {0, 16, 16, 23, 20, 15}, {0, 16, 
            16, 23, 20, 21}, {0, 16, 18, 20, 23, 13}, {0, 16, 18, 20, 23, 
            19}, {0, 16, 19, 20, 25, 13}, {0, 16, 19, 20, 25, 19}, {0, 16, 
            19, 23, 20, 12}, {0, 16, 19, 23, 20, 15}, {0, 16, 19, 23, 20, 
            18}, {0, 16, 19, 23, 23, 12}, {0, 16, 19, 23, 23, 15}, {0, 16, 
            19, 23, 23, 18}, {0, 16, 19, 23, 23, 21}, {0, 16, 19, 25, 17, 
            13}, {0, 16, 19, 25, 17, 19}, {0, 16, 19, 25, 20, 13}, {0, 16, 
            19, 25, 20, 19}, {0, 16, 23, 23, 13, 15}, {0, 16, 23, 23, 13, 
            21}, {0, 16, 23, 23, 16, 12}, {0, 16, 23, 23, 16, 15}, {0, 16, 
            23, 23, 16, 18}, {0, 16, 23, 23, 19, 12}, {0, 16, 23, 23, 19, 
            15}, {0, 16, 23, 23, 19, 18}, {0, 16, 23, 23, 19, 21}, {0, 16, 
            23, 25, 13, 13}, {0, 16, 23, 25, 13, 19}, {0, 16, 23, 25, 16, 
            13}, {0, 16, 23, 25, 16, 19}, {0, 16, 25, 23, 16, 13}, {0, 16, 
            25, 23, 16, 19}, {0, 17, 25, 19, 16, 13}, {0, 17, 25, 19, 16, 
            19}, {0, 18, 16, 23, 20, 13}, {0, 18, 16, 23, 20, 19}, {0, 19, 
            13, 20, 23, 15}, {0, 19, 13, 20, 23, 21}, {0, 19, 13, 23, 23, 
            15}, {0, 19, 13, 23, 23, 21}, {0, 19, 16, 17, 25, 13}, {0, 19, 
            16, 17, 25, 19}, {0, 19, 16, 20, 23, 12}, {0, 19, 16, 20, 23, 
            15}, {0, 19, 16, 20, 23, 18}, {0, 19, 16, 20, 25, 13}, {0, 19, 
            16, 20, 25, 19}, {0, 19, 16, 23, 23, 12}, {0, 19, 16, 23, 23, 
            15}, {0, 19, 16, 23, 23, 18}, {0, 19, 16, 23, 23, 21}, {0, 19, 
            16, 25, 20, 13}, {0, 19, 16, 25, 20, 19}, {0, 19, 23, 23, 13, 
            15}, {0, 19, 23, 23, 13, 21}, {0, 19, 23, 23, 16, 12}, {0, 19, 
            23, 23, 16, 15}, {0, 19, 23, 23, 16, 18}, {0, 19, 23, 23, 16, 
            21}, {0, 19, 23, 25, 13, 13}, {0, 19, 23, 25, 13, 19}, {0, 20, 
            23, 16, 16, 15}, {0, 20, 23, 16, 16, 21}, {0, 20, 23, 16, 18, 
            13}, {0, 20, 23, 16, 18, 19}, {0, 20, 23, 19, 13, 15}, {0, 20, 
            23, 19, 13, 21}, {0, 20, 23, 19, 16, 12}, {0, 20, 23, 19, 16, 
            15}, {0, 20, 23, 19, 16, 18}, {0, 20, 23, 21, 13, 13}, {0, 20, 
            23, 21, 13, 19}, {0, 20, 25, 16, 19, 13}, {0, 20, 25, 16, 19, 
            19}, {0, 20, 25, 19, 16, 13}, {0, 20, 25, 19, 16, 19}, {0, 21, 
            13, 20, 23, 13}, {0, 21, 13, 20, 23, 19}, {0, 21, 13, 23, 23, 
            13}, {0, 21, 13, 23, 23, 19}, {0, 23, 13, 16, 23, 15}, {0, 23, 
            13, 16, 23, 21}, {0, 23, 13, 19, 23, 15}, {0, 23, 13, 19, 23, 
            21}, {0, 23, 16, 13, 23, 15}, {0, 23, 16, 13, 23, 21}, {0, 23, 
            16, 13, 25, 13}, {0, 23, 16, 13, 25, 19}, {0, 23, 16, 16, 23, 
            12}, {0, 23, 16, 16, 23, 15}, {0, 23, 16, 16, 23, 18}, {0, 23, 
            16, 16, 25, 13}, {0, 23, 16, 16, 25, 19}, {0, 23, 16, 19, 23, 
            12}, {0, 23, 16, 19, 23, 15}, {0, 23, 16, 19, 23, 18}, {0, 23, 
            16, 19, 23, 21}, {0, 23, 19, 13, 23, 15}, {0, 23, 19, 13, 23, 
            21}, {0, 23, 19, 13, 25, 13}, {0, 23, 19, 13, 25, 19}, {0, 23, 
            19, 16, 23, 12}, {0, 23, 19, 16, 23, 15}, {0, 23, 19, 16, 23, 
            18}, {0, 23, 19, 16, 23, 21}, {0, 23, 20, 13, 19, 15}, {0, 23, 
            20, 13, 19, 21}, {0, 23, 20, 13, 21, 13}, {0, 23, 20, 13, 21, 
            19}, {0, 23, 20, 16, 16, 15}, {0, 23, 20, 16, 16, 21}, {0, 23, 
            20, 16, 19, 12}, {0, 23, 20, 16, 19, 15}, {0, 23, 20, 16, 19, 
            18}, {0, 23, 20, 18, 16, 13}, {0, 23, 20, 18, 16, 19}, {0, 23, 
            23, 13, 19, 15}, {0, 23, 23, 13, 19, 21}, {0, 23, 23, 13, 21, 
            13}, {0, 23, 23, 13, 21, 19}, {0, 23, 23, 16, 19, 12}, {0, 23, 
            23, 16, 19, 15}, {0, 23, 23, 16, 19, 18}, {0, 23, 23, 16, 19, 
            21}, {0, 23, 23, 19, 13, 15}, {0, 23, 23, 19, 13, 21}, {0, 23, 
            23, 19, 16, 12}, {0, 23, 23, 19, 16, 15}, {0, 23, 23, 19, 16, 
            18}, {0, 23, 23, 19, 16, 21}, {0, 23, 23, 21, 13, 13}, {0, 23, 
            23, 21, 13, 19}, {0, 25, 13, 16, 23, 13}, {0, 25, 13, 16, 23, 
            19}, {0, 25, 13, 19, 23, 13}, {0, 25, 13, 19, 23, 19}, {0, 25, 
            16, 16, 23, 13}, {0, 25, 16, 16, 23, 19}, {0, 25, 17, 16, 19, 
            13}, {0, 25, 17, 16, 19, 19}, {0, 25, 20, 16, 19, 13}, {0, 25, 
            20, 16, 19, 19}, {0, 25, 20, 19, 16, 13}, {0, 25, 20, 19, 16, 
            19}, {1, 10, 19, 25, 20, 15}, {1, 10, 19, 25, 20, 21}, {1, 10, 
            19, 25, 23, 15}, {1, 10, 19, 25, 23, 21}, {1, 10, 21, 25, 20, 
            13}, {1, 10, 21, 25, 20, 19}, {1, 10, 21, 25, 23, 13}, {1, 10, 
            21, 25, 23, 19}, {1, 10, 23, 25, 16, 15}, {1, 10, 23, 25, 16, 
            21}, {1, 10, 23, 25, 19, 15}, {1, 10, 23, 25, 19, 21}, {1, 10, 
            25, 25, 16, 13}, {1, 10, 25, 25, 16, 19}, {1, 10, 25, 25, 19, 
            13}, {1, 10, 25, 25, 19, 19}, {1, 13, 16, 22, 23, 15}, {1, 13, 
            16, 22, 23, 21}, {1, 13, 16, 23, 25, 15}, {1, 13, 16, 23, 25, 
            21}, {1, 13, 16, 25, 20, 15}, {1, 13, 16, 25, 20, 21}, {1, 13, 
            18, 22, 23, 13}, {1, 13, 18, 22, 23, 19}, {1, 13, 18, 23, 25, 
            13}, {1, 13, 18, 23, 25, 19}, {1, 13, 19, 22, 25, 13}, {1, 13, 
            19, 22, 25, 19}, {1, 13, 19, 25, 20, 12}, {1, 13, 19, 25, 20, 
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            18}, {29, 16, 16, 10, 18, 13}, {29, 16, 16, 13, 4, 21}, {29, 16, 
            16, 13, 7, 18}, {29, 16, 16, 13, 10, 15}, {29, 16, 16, 13, 10, 
            21}, {29, 16, 16, 13, 16, 12}, {29, 16, 16, 13, 16, 15}, {29, 16, 
            16, 16, 10, 12}, {29, 16, 16, 16, 10, 18}, {29, 16, 16, 16, 13, 
            12}, {29, 16, 16, 16, 13, 15}, {29, 16, 16, 18, 4, 16}, {29, 16, 
            16, 18, 7, 13}, {29, 16, 16, 18, 7, 16}, {29, 16, 16, 18, 10, 
            13}, {29, 18, 4, 10, 13, 19}, {29, 18, 4, 10, 16, 16}, {29, 18, 
            4, 16, 13, 19}, {29, 18, 4, 16, 16, 16}, {29, 18, 7, 7, 13, 
            19}, {29, 18, 7, 7, 16, 16}, {29, 18, 7, 10, 10, 19}, {29, 18, 7, 
            10, 13, 16}, {29, 18, 7, 10, 13, 19}, {29, 18, 7, 10, 16, 
            16}, {29, 18, 7, 13, 10, 19}, {29, 18, 7, 13, 13, 19}, {29, 18, 
            7, 13, 16, 13}, {29, 18, 7, 13, 16, 16}, {29, 18, 7, 16, 13, 
            16}, {29, 18, 7, 16, 13, 19}, {29, 18, 7, 16, 16, 13}, {29, 18, 
            7, 16, 16, 16}, {29, 18, 10, 10, 10, 19}, {29, 18, 10, 10, 13, 
            19}, {29, 18, 10, 10, 16, 13}, {29, 18, 10, 10, 16, 16}, {29, 18, 
            10, 13, 7, 19}, {29, 18, 10, 13, 10, 19}, {29, 18, 10, 13, 13, 
            13}, {29, 18, 10, 16, 7, 19}, {29, 18, 10, 16, 10, 16}, {29, 18, 
            10, 16, 10, 19}, {29, 18, 10, 16, 16, 13}, {29, 18, 13, 7, 13, 
            19}, {29, 18, 13, 7, 16, 16}, {29, 18, 13, 10, 13, 16}, {29, 18, 
            13, 10, 13, 19}, {29, 18, 13, 10, 16, 13}, {29, 18, 13, 10, 16, 
            16}, {29, 18, 13, 13, 7, 19}, {29, 18, 13, 13, 10, 16}, {29, 18, 
            13, 13, 10, 19}, {29, 18, 13, 13, 16, 13}, {29, 18, 13, 16, 7, 
            16}, {29, 18, 13, 16, 10, 13}, {29, 18, 13, 16, 10, 16}, {29, 18, 
            13, 16, 13, 13}};

Dimensions[PVertexCandidates2]

Now we find the minimal values of the candidate normals on P, thinking of the normal as a linear function.

FindMinForNormal[normal_, vertexlist_] := 
      Module[{vals}, vals = Map[Dot[normal, #] &, vertexlist]; Min[vals]]; 
    MinsForNormals[normallist_, vertexlist_] := 
      Module[{minlist = {}, i}, 
For[i = 1, 
          i < Length[normallist] + 1, 
          i = i + 1, 
minlist = 
              Join[minlist, {FindMinForNormal[normallist[[i]], 
                    vertexlist]}];
]; 
minlist
];

MinList = 
        MinsForNormals[NewNormalCandidateReps, 
          PVertexCandidates2];

The vertices for each candidate facet are computed:

FaceCandidates = 
        Table[Select[PVertexCandidates2, 
            Dot[#, NewNormalCandidateReps[[i]]] == 
                MinList[[i]] &], {i, 1, 
            Length[NewNormalCandidateReps]}];

We can throw out any facet candidates which have fewer than 6 vertices, since then they could not be 5-dimensional.

NormalIndex = 
        Table[i, {i, 1, 
            Length[NewNormalCandidateReps]}];
NewNormalCandidateReps2 = 
        Select[NormalIndex, 
          Length[FaceCandidates[[#]]] > 
              5 &];
Dimensions[NewNormalCandidateReps2]

Now we weed out the remainder by requiring the vertex sets of each candidate facet to be strictly 5-dimensional.

GetVectors2[vertlist_] := 
        Map[vertlist[[1]] - # &, 
          Rest[vertlist]];
TrueFaces[verts_] := 
        Module[{vertlist = {}, i}, 
For[i = 1, 
            i < Length[verts] + 1, 
            i = i + 1, 
If[
                Length[NullSpace[GetVectors2[verts[[i]]]]] == 1, 
                vertlist = 
                  Join[vertlist, {verts[[i]]}]];
]; 
vertlist
];

FaceCandidates2 = 
        Map[FaceCandidates[[#]] &, 
          NewNormalCandidateReps2];
TrueFaceVertices = 
        TrueFaces[FaceCandidates2];
Dimensions[TrueFaceVertices]

FaceIndex = 
        Map[Position[FaceCandidates, #] &, 
          TrueFaceVertices];
FaceIndex = FaceIndex[[All, 1, 1]];
TrueNormalReps = 
        Map[NewNormalCandidateReps[[#]] &, 
          FaceIndex];
Dimensions[TrueNormalReps]

For completeness and to verify our results with Porta, we recover the full set of new normals by computing the orbits of the representatives that we have found.

Orbit[alist_] := 
        Map[PermuteAList[alist, #] &, s4orbits];

AllNewNormals = 
        Union[Flatten[Map[Union[Orbit[#]] &, TrueNormalReps], 
            1]];
Dimensions[AllNewNormals]

So far we have not added in the facet normals from polytopes P1 and P2.  In order to eliminate redundancies from the combination, we convert all our rational normals to integer normals.

It turns out that the new normals contained the facet normals of P1 and P2.

lcmlist[list_] := Fold[LCM, 1, list];
CleanNormal[list_] := 
        Module[{denom = lcmlist[Denominator[list]]}, 
          denom*list];
AllNormals = 
        Union[Map[CleanNormal[#] &, 
            Union[AllNewNormals, P1normals, 
              P2normals]]];
Dimensions[AllNormals]

Now we compute the true vertices of the convex hull of P1 + P2, which are useful for verification.  First we weed out any vertices which do not lie on at least 6 supporting hyperplanes.

TrueFaceMinList = 
        MinsForNormals[AllNormals, PVertexCandidates2];

Pvoff = 
        VerticesOfFaces[AllNormals, TrueFaceMinList, 
          PVertexCandidates2];

Pfofv = FacesOfVertices[Pvoff];
PVIndex = Range[Length[Pfofv]];
VertexIndex2 = 
        Select[PVIndex, Length[Pfofv[[#]]] > 5 &];

Pvertices = 
        Map[PVertexCandidates2[[#]] &, 
          VertexIndex2];
Dimensions[Pvertices]

Finally we weed out vertices which are not extreme points by checking the dimension of the span of the facet normals.

KernelDimensions = 
        Table[Length[
            NullSpace[
              Map[AllNormals[[#]] &, 
                Pfofv[[VertexIndex2[[i]]]]]]], {i, 1, 
            Length[VertexIndex2]}];

KernelDimIndex = 
        Select[Range[Length[KernelDimensions]], 
          KernelDimensions[[#]] == 0 &];

Pvertices2 = 
        Map[Pvertices[[#]] &, 
          KernelDimIndex];
Dimensions[Pvertices2]

The final results for the big Minkowski sum are contained in the following closed cell, which should be executed before continuing.  The vertices are stored in the variable acdzconv and the facet inequalities are in acdzineq.

acdzconv  = {{6, 13, 13, 17, 20, 21}, {3, 16, 13, 17, 23, 18}, {0, 
            16, 16, 20, 23, 15}, {0, 13, 19, 23, 20, 15}, {0, 13, 23, 23, 16, 
            15}, {0, 16, 19, 25, 20, 13}, {0, 16, 18, 20, 23, 13}, {0, 13, 
            21, 23, 20, 13}, {9, 13, 27, 21, 16, 4}, {12, 13, 25, 23, 16, 
            1}, {3, 13, 21, 21, 22, 10}, {1, 13, 18, 22, 23, 13}, {1, 10, 21, 
            25, 20, 13}, {4, 7, 21, 25, 20, 13}, {7, 4, 23, 25, 18, 13}, {10, 
            4, 25, 23, 18, 10}, {4, 10, 21, 23, 22, 10}, {4, 10, 21, 27, 18, 
            10}, {1, 13, 19, 25, 20, 12}, {4, 13, 19, 27, 18, 9}, {4, 13, 19, 
            23, 22, 9}, {4, 10, 18, 22, 23, 13}, {7, 9, 18, 20, 23, 13}, {10, 
            6, 20, 20, 21, 13}, {17, 6, 20, 13, 21, 13}, {17, 3, 23, 16, 18, 
            13}, {15, 9, 20, 13, 23, 10}, {10, 3, 23, 23, 18, 13}, {7, 12, 
            18, 18, 25, 10}, {10, 9, 20, 18, 23, 10}, {4, 13, 18, 20, 25, 
            10}, {3, 16, 18, 18, 25, 10}, {6, 16, 20, 16, 25, 7}, {6, 13, 23, 
            19, 22, 7}, {6, 13, 27, 19, 18, 7}, {7, 10, 27, 21, 18, 7}, {7, 
            15, 27, 16, 18, 7}, {10, 15, 27, 16, 18, 4}, {9, 13, 27, 19, 18, 
            4}, {7, 10, 23, 21, 22, 7}, {10, 7, 25, 21, 20, 7}, {9, 13, 23, 
            19, 22, 4}, {12, 13, 25, 19, 20, 1}, {13, 15, 25, 16, 20, 1}, {7, 
            13, 20, 18, 25, 7}, {10, 10, 22, 18, 23, 7}, {9, 16, 20, 16, 25, 
            4}, {12, 16, 22, 16, 23, 1}, {0, 13, 21, 23, 23, 13}, {0, 13, 25, 
            23, 19, 13}, {0, 20, 25, 16, 19, 13}, {1, 22, 25, 13, 19, 
            13}, {4, 22, 25, 10, 19, 13}, {7, 20, 25, 9, 19, 13}, {14, 13, 
            25, 9, 19, 13}, {17, 13, 23, 6, 21, 13}, {7, 18, 27, 12, 19, 
            10}, {12, 13, 27, 12, 19, 10}, {15, 13, 25, 9, 21, 10}, {7, 22, 
            25, 7, 19, 16}, {10, 20, 25, 6, 19, 16}, {17, 13, 25, 6, 19, 
            16}, {20, 13, 23, 3, 21, 16}, {10, 18, 27, 9, 19, 13}, {15, 13, 
            27, 9, 19, 13}, {18, 13, 25, 6, 21, 13}, {18, 16, 25, 6, 21, 
            10}, {15, 16, 27, 9, 19, 10}, {13, 18, 27, 9, 19, 10}, {16, 18, 
            27, 9, 19, 10}, {3, 13, 27, 21, 19, 10}, {3, 18, 27, 16, 19, 
            10}, {4, 20, 27, 13, 19, 10}, {7, 20, 27, 10, 19, 13}, {9, 13, 
            27, 21, 19, 4}, {18, 13, 27, 21, 19, 4}, {12, 13, 25, 23, 19, 
            1}, {10, 16, 27, 19, 18, 3}, {16, 16, 27, 19, 18, 3}, {10, 16, 
            27, 21, 16, 3}, {16, 16, 27, 21, 16, 3}, {0, 16, 25, 23, 16, 
            13}, {3, 16, 27, 21, 16, 10}, {4, 19, 27, 21, 13, 9}, {3, 18, 27, 
            19, 16, 10}, {0, 20, 25, 19, 16, 13}, {3, 13, 21, 21, 25, 
            10}, {6, 13, 23, 19, 25, 7}, {6, 13, 27, 19, 21, 7}, {6, 16, 27, 
            16, 21, 7}, {7, 18, 27, 13, 21, 7}, {10, 18, 27, 10, 21, 
            10}, {13, 18, 27, 10, 21, 7}, {16, 18, 27, 10, 21, 7}, {7, 10, 
            27, 21, 21, 7}, {10, 7, 27, 21, 21, 7}, {12, 7, 27, 19, 21, 
            7}, {12, 13, 27, 13, 21, 7}, {15, 13, 27, 10, 21, 10}, {15, 16, 
            27, 10, 21, 7}, {15, 7, 25, 16, 23, 7}, {15, 13, 25, 10, 23, 
            7}, {18, 13, 25, 7, 23, 10}, {18, 16, 25, 7, 23, 7}, {18, 4, 25, 
            16, 23, 10}, {15, 4, 27, 19, 21, 10}, {13, 4, 27, 21, 21, 
            10}, {16, 4, 27, 21, 21, 10}, {12, 16, 27, 13, 21, 4}, {15, 16, 
            25, 10, 23, 4}, {15, 16, 25, 13, 23, 1}, {12, 10, 27, 19, 21, 
            4}, {10, 10, 27, 21, 21, 4}, {16, 10, 27, 21, 21, 4}, {10, 18, 
            27, 13, 21, 4}, {16, 18, 27, 13, 21, 4}, {19, 18, 25, 13, 23, 
            1}, {9, 16, 27, 16, 21, 4}, {9, 13, 27, 19, 21, 4}, {18, 13, 27, 
            19, 21, 4}, {18, 16, 27, 16, 21, 4}, {7, 10, 23, 21, 25, 7}, {10, 
            7, 25, 21, 23, 7}, {10, 7, 23, 21, 25, 10}, {13, 4, 25, 21, 23, 
            10}, {10, 10, 23, 21, 25, 4}, {13, 7, 23, 21, 25, 7}, {9, 13, 23, 
            19, 25, 4}, {12, 13, 25, 19, 23, 1}, {12, 16, 25, 16, 23, 
            1}, {13, 18, 25, 13, 23, 1}, {18, 13, 23, 19, 25, 4}, {0, 16, 19, 
            23, 23, 12}, {0, 16, 23, 23, 19, 12}, {3, 16, 25, 21, 19, 9}, {9, 
            16, 25, 21, 19, 3}, {18, 16, 25, 21, 19, 3}, {6, 16, 25, 19, 21, 
            6}, {9, 16, 25, 19, 21, 3}, {18, 16, 25, 19, 21, 3}, {3, 19, 25, 
            21, 16, 9}, {9, 19, 25, 21, 16, 3}, {18, 19, 25, 21, 16, 3}, {3, 
            21, 25, 19, 16, 9}, {6, 21, 25, 19, 16, 6}, {15, 21, 25, 19, 16, 
            6}, {3, 21, 25, 16, 19, 9}, {6, 21, 25, 16, 19, 6}, {15, 21, 25, 
            16, 19, 6}, {6, 19, 25, 16, 21, 6}, {9, 19, 25, 16, 21, 3}, {18, 
            19, 25, 16, 21, 3}, {3, 16, 21, 25, 19, 9}, {9, 16, 21, 25, 19, 
            3}, {18, 16, 21, 25, 19, 3}, {12, 16, 23, 23, 19, 0}, {3, 19, 21, 
            25, 16, 9}, {9, 19, 21, 25, 16, 3}, {18, 19, 21, 25, 16, 3}, {12, 
            19, 23, 23, 16, 0}, {12, 23, 19, 23, 16, 0}, {6, 21, 19, 25, 16, 
            6}, {9, 21, 19, 25, 16, 3}, {18, 21, 19, 25, 16, 3}, {0, 19, 23, 
            23, 16, 12}, {0, 23, 23, 19, 16, 12}, {3, 16, 19, 25, 21, 9}, {6, 
            16, 19, 25, 21, 6}, {15, 16, 19, 25, 21, 6}, {3, 19, 16, 25, 21, 
            9}, {6, 19, 16, 25, 21, 6}, {15, 19, 16, 25, 21, 6}, {6, 21, 16, 
            25, 19, 6}, {9, 21, 16, 25, 19, 3}, {18, 21, 16, 25, 19, 3}, {0, 
            19, 16, 23, 23, 12}, {0, 23, 16, 19, 23, 12}, {3, 25, 16, 19, 21, 
            9}, {9, 25, 16, 19, 21, 3}, {18, 25, 16, 19, 21, 3}, {6, 25, 16, 
            21, 19, 6}, {9, 25, 16, 21, 19, 3}, {18, 25, 16, 21, 19, 3}, {3, 
            25, 19, 16, 21, 9}, {9, 25, 19, 16, 21, 3}, {18, 25, 19, 16, 21, 
            3}, {3, 25, 21, 16, 19, 9}, {6, 25, 21, 16, 19, 6}, {15, 25, 21, 
            16, 19, 6}, {3, 25, 21, 19, 16, 9}, {6, 25, 21, 19, 16, 6}, {15, 
            25, 21, 19, 16, 6}, {6, 25, 19, 21, 16, 6}, {9, 25, 19, 21, 16, 
            3}, {18, 25, 19, 21, 16, 3}, {3, 21, 16, 19, 25, 9}, {9, 21, 16, 
            19, 25, 3}, {18, 21, 16, 19, 25, 3}, {12, 23, 16, 19, 23, 
            0}, {12, 23, 16, 23, 19, 0}, {3, 21, 19, 16, 25, 9}, {9, 21, 19, 
            16, 25, 3}, {18, 21, 19, 16, 25, 3}, {12, 23, 19, 16, 23, 0}, {6, 
            19, 21, 16, 25, 6}, {9, 19, 21, 16, 25, 3}, {18, 19, 21, 16, 25, 
            3}, {12, 19, 23, 16, 23, 0}, {0, 23, 19, 16, 23, 12}, {0, 23, 23, 
            16, 19, 12}, {3, 16, 19, 21, 25, 9}, {6, 16, 19, 21, 25, 6}, {15, 
            16, 19, 21, 25, 6}, {6, 16, 21, 19, 25, 6}, {9, 16, 21, 19, 25, 
            3}, {18, 16, 21, 19, 25, 3}, {12, 16, 23, 19, 23, 0}, {3, 19, 16, 
            21, 25, 9}, {6, 19, 16, 21, 25, 6}, {15, 19, 16, 21, 25, 6}, {0, 
            13, 19, 23, 23, 15}, {0, 23, 16, 13, 23, 15}, {0, 23, 20, 13, 19, 
            15}, {0, 20, 23, 16, 16, 15}, {0, 23, 23, 13, 19, 15}, {1, 25, 
            16, 13, 23, 12}, {3, 19, 13, 14, 25, 16}, {3, 23, 13, 10, 25, 
            16}, {4, 25, 13, 7, 25, 16}, {10, 25, 13, 1, 25, 16}, {13, 23, 
            13, 0, 25, 16}, {17, 19, 13, 0, 25, 16}, {1, 25, 16, 10, 25, 
            13}, {7, 25, 16, 4, 25, 13}, {10, 23, 16, 3, 25, 13}, {14, 19, 
            16, 3, 25, 13}, {4, 27, 16, 10, 23, 10}, {4, 23, 16, 10, 27, 
            10}, {10, 23, 16, 4, 27, 10}, {10, 21, 18, 10, 27, 4}, {10, 21, 
            18, 7, 27, 7}, {4, 27, 19, 10, 23, 10}, {1, 27, 16, 13, 23, 
            13}, {13, 27, 13, 1, 23, 13}, {10, 27, 16, 4, 23, 10}, {10, 27, 
            16, 10, 23, 4}, {10, 27, 16, 13, 21, 3}, {10, 27, 16, 15, 19, 
            3}, {16, 27, 13, 1, 23, 13}, {4, 16, 13, 16, 25, 16}, {7, 13, 13, 
            16, 25, 16}, {10, 12, 13, 14, 25, 16}, {17, 12, 13, 7, 25, 
            16}, {19, 13, 13, 4, 25, 16}, {19, 16, 13, 1, 25, 16}, {1, 25, 
            19, 13, 23, 12}, {0, 23, 16, 16, 25, 13}, {3, 21, 16, 16, 27, 
            10}, {13, 25, 16, 16, 23, 0}, {19, 25, 16, 16, 23, 0}, {19, 25, 
            16, 20, 19, 0}, {4, 21, 13, 19, 27, 9}, {0, 19, 16, 17, 25, 
            13}, {0, 23, 16, 13, 25, 13}, {0, 23, 20, 13, 21, 13}, {0, 20, 
            23, 16, 18, 13}, {1, 22, 23, 13, 18, 13}, {7, 20, 23, 9, 18, 
            13}, {10, 20, 21, 6, 20, 13}, {17, 13, 21, 6, 20, 13}, {15, 13, 
            23, 9, 20, 10}, {7, 18, 25, 12, 18, 10}, {10, 18, 23, 9, 20, 
            10}, {7, 16, 27, 15, 15, 10}, {7, 19, 27, 12, 18, 10}, {4, 20, 
            25, 13, 18, 10}, {4, 18, 27, 16, 15, 10}, {4, 20, 25, 16, 16, 
            9}, {1, 25, 20, 13, 19, 12}, {4, 27, 18, 13, 19, 9}, {1, 23, 22, 
            16, 16, 12}, {4, 23, 22, 13, 19, 9}, {1, 22, 23, 16, 16, 12}, {1, 
            25, 20, 10, 21, 13}, {4, 25, 20, 7, 21, 13}, {7, 25, 18, 4, 23, 
            13}, {10, 23, 18, 3, 23, 13}, {17, 16, 18, 3, 23, 13}, {4, 22, 
            23, 10, 18, 13}, {10, 23, 18, 4, 25, 10}, {4, 23, 22, 10, 21, 
            10}, {4, 27, 18, 10, 21, 10}, {3, 18, 25, 16, 18, 10}, {3, 21, 
            22, 13, 21, 10}, {9, 21, 16, 13, 27, 4}, {12, 23, 16, 13, 25, 
            1}, {3, 21, 16, 13, 27, 10}, {1, 16, 16, 19, 25, 13}, {4, 13, 16, 
            19, 25, 13}, {7, 12, 16, 17, 25, 13}, {14, 12, 16, 10, 25, 
            13}, {16, 13, 16, 7, 25, 13}, {16, 16, 16, 4, 25, 13}, {17, 9, 
            18, 10, 23, 13}, {7, 15, 16, 15, 27, 10}, {12, 15, 16, 10, 27, 
            10}, {15, 12, 18, 10, 25, 10}, {15, 12, 18, 13, 25, 7}, {15, 9, 
            21, 16, 25, 7}, {10, 15, 16, 15, 27, 7}, {10, 12, 19, 18, 27, 
            7}, {3, 19, 16, 15, 27, 10}, {4, 16, 16, 17, 27, 10}, {6, 19, 18, 
            13, 27, 7}, {6, 19, 22, 13, 23, 7}, {7, 21, 22, 10, 23, 7}, {10, 
            21, 20, 7, 25, 7}, {6, 16, 25, 16, 20, 7}, {7, 18, 25, 13, 20, 
            7}, {10, 18, 23, 10, 22, 7}, {9, 16, 25, 16, 20, 4}, {7, 21, 18, 
            10, 27, 7}, {9, 19, 22, 13, 23, 4}, {12, 19, 20, 13, 25, 1}, {12, 
            16, 23, 16, 22, 1}, {13, 16, 20, 15, 25, 1}, {9, 19, 18, 13, 27, 
            4}, {7, 16, 18, 15, 27, 7}, {10, 16, 18, 15, 27, 4}, {0, 19, 16, 
            20, 25, 13}, {0, 16, 19, 20, 25, 13}, {0, 23, 19, 13, 25, 
            13}, {1, 25, 19, 10, 25, 13}, {7, 25, 19, 4, 25, 13}, {10, 25, 
            19, 1, 25, 16}, {13, 23, 19, 0, 25, 16}, {17, 19, 19, 0, 25, 
            16}, {10, 23, 19, 3, 25, 13}, {14, 19, 19, 3, 25, 13}, {10, 23, 
            19, 10, 27, 4}, {16, 23, 19, 10, 27, 4}, {4, 23, 19, 10, 27, 
            10}, {10, 23, 19, 4, 27, 10}, {13, 23, 19, 1, 27, 13}, {0, 23, 
            23, 13, 21, 13}, {3, 21, 25, 13, 21, 10}, {3, 21, 19, 13, 27, 
            10}, {9, 21, 19, 13, 27, 4}, {18, 21, 19, 13, 27, 4}, {12, 23, 
            19, 13, 25, 1}, {1, 13, 19, 22, 25, 13}, {4, 10, 19, 22, 25, 
            13}, {7, 9, 19, 20, 25, 13}, {14, 9, 19, 13, 25, 13}, {16, 10, 
            19, 10, 25, 13}, {16, 16, 19, 4, 25, 13}, {19, 16, 19, 1, 25, 
            16}, {19, 7, 19, 10, 25, 16}, {17, 6, 21, 13, 23, 13}, {19, 7, 
            21, 10, 23, 13}, {19, 13, 21, 4, 23, 13}, {22, 13, 21, 1, 23, 
            16}, {22, 4, 21, 10, 23, 16}, {17, 10, 21, 10, 25, 10}, {17, 16, 
            21, 4, 25, 10}, {20, 16, 21, 1, 25, 13}, {20, 7, 21, 10, 25, 
            13}, {7, 12, 19, 18, 27, 10}, {12, 12, 19, 13, 27, 10}, {15, 9, 
            21, 13, 25, 10}, {14, 13, 19, 10, 27, 10}, {14, 19, 19, 4, 27, 
            10}, {17, 19, 19, 1, 27, 13}, {17, 10, 19, 10, 27, 13}, {7, 7, 
            19, 22, 25, 16}, {10, 6, 19, 20, 25, 16}, {17, 6, 19, 13, 25, 
            16}, {20, 3, 21, 13, 23, 16}, {10, 9, 19, 18, 27, 13}, {15, 9, 
            19, 13, 27, 13}, {18, 6, 21, 13, 25, 13}, {18, 6, 21, 16, 25, 
            10}, {15, 9, 19, 16, 27, 10}, {13, 9, 19, 18, 27, 10}, {16, 9, 
            19, 18, 27, 10}, {3, 16, 19, 18, 27, 10}, {4, 13, 19, 20, 27, 
            10}, {7, 10, 19, 20, 27, 13}, {6, 19, 21, 13, 27, 7}, {7, 21, 21, 
            10, 27, 7}, {7, 21, 25, 10, 23, 7}, {10, 21, 23, 7, 25, 7}, {10, 
            21, 25, 7, 23, 10}, {13, 21, 23, 4, 25, 10}, {10, 21, 25, 10, 23, 
            4}, {13, 21, 25, 7, 23, 7}, {10, 21, 21, 7, 27, 7}, {13, 21, 21, 
            4, 27, 10}, {16, 21, 21, 4, 27, 10}, {10, 21, 21, 10, 27, 
            4}, {16, 21, 21, 10, 27, 4}, {9, 19, 21, 13, 27, 4}, {18, 19, 21, 
            13, 27, 4}, {6, 19, 25, 13, 23, 7}, {9, 19, 25, 13, 23, 4}, {18, 
            19, 25, 13, 23, 4}, {12, 19, 23, 13, 25, 1}, {6, 16, 21, 16, 27, 
            7}, {7, 13, 21, 18, 27, 7}, {12, 13, 21, 13, 27, 7}, {12, 19, 21, 
            7, 27, 7}, {15, 19, 21, 4, 27, 10}, {15, 10, 21, 13, 27, 
            10}, {15, 10, 21, 16, 27, 7}, {15, 10, 23, 13, 25, 7}, {15, 16, 
            23, 7, 25, 7}, {18, 16, 23, 4, 25, 10}, {18, 7, 23, 13, 25, 
            10}, {18, 7, 23, 16, 25, 7}, {10, 10, 21, 18, 27, 10}, {13, 10, 
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            21}, {7, 4, 19, 25, 23, 21}, {10, 3, 19, 23, 23, 21}, {13, 0, 19, 
            23, 21, 23}, {23, 0, 19, 13, 21, 23}, {23, 3, 19, 10, 23, 
            21}, {13, 3, 19, 23, 23, 21}, {4, 7, 19, 25, 21, 23}, {10, 1, 19, 
            25, 21, 23}, {13, 1, 19, 25, 21, 23}, {13, 7, 19, 25, 21, 
            23}, {16, 0, 19, 23, 21, 23}, {16, 9, 19, 23, 21, 23}, {18, 12, 
            19, 21, 21, 23}, {23, 0, 19, 16, 21, 23}, {23, 3, 19, 13, 23, 
            21}, {23, 9, 19, 13, 23, 21}, {21, 12, 19, 15, 23, 21}, {23, 9, 
            19, 16, 21, 23}, {21, 12, 19, 18, 21, 23}, {21, 15, 19, 15, 21, 
            23}, {21, 15, 21, 18, 21, 21}, {23, 12, 21, 16, 21, 21}, {23, 18, 
            21, 16, 15, 21}, {16, 12, 25, 21, 18, 19}, {16, 18, 25, 21, 12, 
            19}, {19, 12, 25, 21, 18, 16}, {19, 18, 25, 21, 12, 16}, {16, 15, 
            23, 21, 18, 21}, {16, 12, 21, 23, 21, 21}, {16, 18, 21, 23, 15, 
            21}, {18, 15, 21, 21, 21, 21}, {4, 10, 19, 25, 21, 23}, {10, 10, 
            19, 25, 21, 23}, {13, 1, 19, 27, 19, 20}, {4, 10, 19, 27, 18, 
            21}, {10, 4, 19, 27, 18, 21}, {16, 4, 13, 27, 18, 21}, {10, 10, 
            19, 27, 18, 21}, {10, 10, 19, 27, 21, 18}, {4, 13, 19, 27, 21, 
            18}, {7, 13, 19, 27, 21, 18}, {4, 16, 16, 27, 21, 18}, {7, 16, 
            16, 27, 21, 18}, {4, 10, 21, 27, 21, 16}, {7, 10, 21, 27, 21, 
            16}, {10, 4, 21, 27, 21, 16}, {10, 7, 21, 27, 21, 16}, {10, 4, 
            19, 25, 23, 21}, {13, 12, 19, 23, 23, 21}, {7, 13, 19, 27, 20, 
            19}, {4, 10, 19, 27, 21, 18}, {10, 4, 19, 27, 21, 18}, {4, 16, 
            13, 27, 21, 18}, {7, 16, 10, 27, 21, 18}, {10, 16, 10, 27, 21, 
            18}, {7, 18, 10, 27, 21, 16}, {10, 18, 10, 27, 21, 16}, {4, 18, 
            13, 27, 21, 16}, {7, 18, 13, 27, 21, 16}, {10, 16, 13, 27, 21, 
            18}, {1, 13, 19, 27, 20, 19}, {7, 7, 16, 23, 21, 25}, {13, 1, 16, 
            23, 21, 25}, {16, 1, 16, 23, 21, 25}, {16, 7, 16, 23, 21, 
            25}, {10, 7, 16, 21, 18, 27}, {13, 4, 16, 21, 18, 27}, {19, 4, 
            10, 21, 18, 27}, {19, 10, 4, 21, 18, 27}, {10, 10, 16, 21, 18, 
            27}, {13, 10, 16, 21, 18, 27}, {13, 1, 18, 23, 19, 25}, {7, 10, 
            16, 23, 21, 25}, {13, 10, 16, 23, 21, 25}, {1, 13, 19, 25, 23, 
            21}, {7, 13, 19, 25, 23, 21}, {10, 10, 19, 25, 23, 21}, {13, 10, 
            21, 25, 21, 21}, {13, 10, 21, 27, 19, 18}, {10, 13, 21, 25, 21, 
            21}, {3, 13, 19, 23, 21, 23}, {12, 13, 19, 23, 21, 23}, {1, 23, 
            16, 13, 27, 19}, {10, 23, 16, 4, 27, 19}, {13, 21, 16, 3, 27, 
            19}, {18, 16, 16, 3, 27, 19}, {20, 13, 16, 4, 27, 19}, {20, 13, 
            16, 7, 27, 19}, {18, 16, 16, 9, 27, 19}, {7, 23, 16, 13, 27, 
            19}, {10, 21, 16, 15, 27, 19}, {10, 23, 16, 10, 27, 19}, {13, 21, 
            16, 12, 27, 19}, {16, 18, 16, 12, 27, 19}, {10, 23, 16, 13, 25, 
            21}, {13, 21, 16, 15, 25, 21}, {7, 23, 16, 16, 25, 21}, {10, 21, 
            16, 18, 25, 21}, {1, 23, 16, 16, 25, 21}, {12, 16, 16, 21, 23, 
            23}, {1, 13, 16, 23, 25, 21}, {7, 7, 16, 23, 25, 21}, {1, 23, 16, 
            13, 25, 21}, {16, 16, 3, 23, 23, 21}, {16, 21, 3, 23, 23, 
            16}, {16, 21, 6, 25, 21, 13}, {16, 13, 6, 25, 21, 21}, {13, 13, 
            7, 25, 23, 21}, {13, 13, 10, 27, 21, 18}, {13, 18, 10, 27, 21, 
            13}, {13, 18, 13, 27, 21, 10}, {13, 16, 13, 27, 21, 15}, {13, 10, 
            16, 27, 21, 18}, {13, 13, 13, 27, 21, 18}, {13, 10, 19, 27, 21, 
            15}, {13, 7, 21, 27, 21, 13}, {13, 4, 21, 25, 23, 16}, {13, 7, 
            21, 23, 25, 13}, {13, 10, 21, 23, 25, 10}, {13, 10, 21, 25, 23, 
            13}, {13, 10, 21, 27, 21, 10}, {13, 13, 19, 27, 21, 12}, {13, 16, 
            16, 27, 21, 12}, {13, 13, 19, 23, 25, 12}, {13, 13, 19, 25, 23, 
            15}, {16, 13, 21, 21, 25, 9}, {16, 7, 23, 21, 25, 10}, {16, 10, 
            23, 21, 25, 7}, {18, 10, 23, 19, 25, 10}, {13, 7, 21, 25, 23, 
            16}, {13, 10, 19, 25, 23, 18}, {16, 7, 23, 25, 21, 16}, {16, 10, 
            23, 25, 21, 13}, {16, 13, 21, 25, 21, 15}, {16, 16, 18, 25, 21, 
            15}, {16, 10, 21, 25, 21, 18}, {13, 10, 19, 23, 25, 15}, {16, 1, 
            23, 25, 21, 16}, {13, 4, 16, 25, 23, 21}, {13, 10, 16, 25, 23, 
            21}, {13, 13, 13, 25, 23, 21}, {16, 10, 18, 25, 21, 21}, {16, 1, 
            13, 25, 21, 23}, {16, 7, 7, 25, 21, 23}, {16, 10, 9, 27, 19, 
            18}, {16, 18, 9, 27, 19, 10}, {16, 20, 10, 27, 19, 7}, {16, 20, 
            13, 27, 19, 4}, {16, 13, 9, 27, 19, 18}, {16, 18, 9, 27, 19, 
            13}, {16, 18, 12, 27, 19, 13}, {16, 20, 10, 27, 19, 10}, {16, 20, 
            13, 27, 19, 7}, {16, 1, 16, 27, 19, 20}, {16, 7, 10, 27, 19, 
            20}, {16, 1, 23, 27, 19, 13}, {16, 10, 23, 27, 19, 4}, {16, 13, 
            21, 27, 19, 3}, {16, 18, 16, 27, 19, 3}, {16, 7, 23, 27, 19, 
            13}, {16, 10, 21, 27, 19, 15}, {16, 10, 23, 27, 19, 10}, {16, 13, 
            21, 27, 19, 12}, {16, 16, 18, 27, 19, 12}, {16, 18, 16, 27, 19, 
            9}, {16, 10, 7, 25, 21, 23}, {16, 13, 15, 27, 19, 18}, {16, 16, 
            15, 27, 19, 15}, {16, 10, 10, 27, 19, 20}, {16, 7, 16, 27, 19, 
            20}, {16, 10, 13, 27, 19, 20}, {16, 10, 18, 27, 19, 18}, {18, 1, 
            13, 25, 19, 23}, {16, 1, 16, 25, 21, 23}, {16, 7, 16, 25, 21, 
            23}, {16, 10, 13, 25, 21, 23}, {13, 16, 4, 23, 25, 21}, {16, 21, 
            9, 23, 23, 16}, {16, 19, 12, 23, 23, 18}, {16, 21, 9, 25, 21, 
            13}, {16, 19, 12, 25, 21, 15}, {16, 16, 12, 23, 23, 21}, {16, 13, 
            15, 25, 21, 21}, {19, 18, 15, 23, 18, 21}, {16, 16, 15, 25, 21, 
            18}, {13, 21, 7, 21, 27, 13}, {13, 21, 10, 21, 27, 10}, {13, 21, 
            10, 23, 25, 13}, {13, 21, 10, 25, 23, 10}, {13, 21, 4, 23, 25, 
            16}, {13, 21, 7, 23, 25, 16}, {13, 21, 7, 25, 23, 13}, {16, 23, 
            7, 25, 21, 10}, {16, 23, 10, 25, 21, 7}, {18, 23, 10, 25, 19, 
            10}, {13, 19, 10, 25, 23, 15}, {13, 19, 10, 23, 25, 18}, {13, 16, 
            13, 25, 23, 18}, {16, 23, 7, 21, 25, 16}, {16, 21, 10, 19, 27, 
            15}, {16, 23, 10, 21, 25, 13}, {16, 21, 13, 21, 25, 15}, {16, 21, 
            10, 21, 25, 18}, {13, 10, 13, 21, 27, 18}, {13, 13, 13, 21, 27, 
            18}, {13, 16, 10, 21, 27, 18}, {13, 19, 10, 21, 27, 15}, {13, 10, 
            18, 21, 27, 13}, {13, 13, 18, 21, 27, 10}, {13, 16, 16, 21, 27, 
            12}, {13, 19, 13, 21, 27, 12}, {13, 19, 13, 23, 25, 15}, {13, 19, 
            13, 25, 23, 12}, {16, 21, 13, 25, 21, 9}, {13, 16, 16, 25, 23, 
            15}, {16, 19, 15, 25, 21, 12}, {16, 19, 15, 23, 23, 15}, {13, 16, 
            16, 23, 25, 15}, {16, 15, 19, 23, 23, 15}, {16, 15, 19, 21, 25, 
            12}, {13, 13, 16, 21, 27, 15}, {16, 18, 16, 21, 25, 15}, {13, 7, 
            13, 23, 25, 21}, {13, 13, 13, 23, 25, 21}, {13, 16, 10, 23, 25, 
            21}, {13, 13, 16, 23, 25, 18}, {16, 10, 10, 19, 27, 20}, {16, 13, 
            10, 19, 27, 20}, {16, 16, 7, 19, 27, 20}, {16, 15, 13, 19, 27, 
            18}, {16, 15, 16, 19, 27, 15}, {19, 15, 18, 18, 23, 21}, {16, 18, 
            10, 19, 27, 18}, {16, 7, 7, 21, 25, 23}, {16, 13, 1, 21, 25, 
            23}, {18, 13, 1, 19, 25, 23}, {16, 16, 1, 21, 25, 23}, {16, 16, 
            7, 21, 25, 23}, {16, 7, 10, 21, 25, 23}, {16, 13, 10, 21, 25, 
            23}, {16, 9, 21, 21, 25, 13}, {16, 12, 19, 21, 25, 15}, {16, 9, 
            21, 23, 23, 16}, {16, 12, 19, 23, 23, 18}, {16, 15, 13, 21, 25, 
            21}, {16, 18, 10, 21, 25, 21}, {16, 15, 16, 21, 25, 18}, {16, 12, 
            16, 23, 23, 21}, {10, 7, 16, 23, 25, 21}, {10, 18, 16, 21, 25, 
            21}, {4, 13, 16, 21, 27, 18}, {7, 10, 16, 21, 27, 18}, {10, 10, 
            16, 21, 27, 18}, {4, 19, 10, 21, 27, 18}, {10, 19, 4, 21, 27, 
            18}, {10, 13, 16, 21, 27, 18}, {4, 19, 13, 21, 27, 18}, {7, 19, 
            13, 21, 27, 18}, {4, 16, 16, 21, 27, 18}, {7, 16, 16, 21, 27, 
            18}, {1, 16, 16, 23, 25, 21}, {7, 16, 16, 23, 25, 21}, {10, 13, 
            16, 23, 25, 21}, {4, 13, 13, 21, 25, 23}, {10, 7, 13, 21, 25, 
            23}, {10, 6, 16, 21, 25, 21}, {10, 9, 16, 19, 27, 18}, {10, 9, 
            18, 19, 27, 16}, {13, 3, 16, 21, 23, 23}, {21, 3, 16, 13, 23, 
            23}, {21, 6, 16, 10, 25, 21}, {13, 6, 16, 21, 25, 21}, {13, 9, 
            16, 19, 27, 18}, {13, 9, 18, 19, 27, 16}, {16, 3, 16, 21, 23, 
            23}, {21, 3, 16, 16, 23, 23}, {21, 6, 16, 13, 25, 21}, {7, 10, 
            13, 21, 23, 25}, {13, 4, 13, 21, 23, 25}, {10, 10, 13, 18, 21, 
            27}, {16, 4, 13, 18, 21, 27}, {21, 4, 13, 13, 21, 27}, {21, 4, 
            13, 13, 23, 25}, {21, 7, 13, 10, 25, 23}, {21, 7, 13, 13, 25, 
            23}, {21, 7, 13, 16, 23, 25}, {19, 10, 13, 18, 23, 25}, {19, 10, 
            13, 15, 25, 23}, {23, 7, 16, 7, 25, 21}, {23, 10, 16, 4, 25, 
            21}, {23, 13, 19, 1, 25, 18}, {23, 10, 16, 7, 25, 21}, {23, 7, 
            16, 10, 25, 21}, {23, 10, 18, 10, 25, 19}, {21, 4, 13, 16, 23, 
            25}, {23, 1, 16, 13, 21, 25}, {21, 7, 13, 13, 21, 27}, {10, 18, 
            13, 10, 21, 27}, {13, 18, 13, 7, 21, 27}, {16, 16, 13, 6, 21, 
            27}, {19, 13, 13, 6, 21, 27}, {19, 13, 13, 6, 25, 23}, {19, 13, 
            13, 12, 25, 23}, {19, 13, 13, 15, 23, 25}, {19, 15, 16, 15, 23, 
            23}, {21, 13, 16, 9, 25, 21}, {19, 15, 16, 12, 25, 21}, {21, 13, 
            16, 3, 25, 21}, {21, 10, 13, 7, 21, 27}, {21, 10, 13, 7, 25, 
            23}, {21, 10, 13, 10, 25, 23}, {21, 10, 13, 13, 23, 25}, {21, 10, 
            13, 10, 21, 27}, {19, 13, 13, 12, 21, 27}, {16, 16, 13, 12, 21, 
            27}, {13, 18, 13, 10, 21, 27}, {10, 18, 13, 13, 21, 27}, {13, 16, 
            13, 15, 21, 27}, {23, 1, 16, 13, 19, 27}, {23, 10, 16, 4, 19, 
            27}, {23, 7, 16, 13, 19, 27}, {21, 10, 16, 15, 19, 27}, {23, 10, 
            16, 10, 19, 27}, {21, 13, 16, 12, 19, 27}, {23, 10, 16, 13, 21, 
            25}, {21, 13, 16, 15, 21, 25}, {23, 7, 16, 16, 21, 25}, {21, 10, 
            16, 18, 21, 25}, {23, 1, 16, 16, 21, 25}, {18, 16, 16, 15, 21, 
            25}, {16, 4, 13, 21, 23, 25}, {19, 4, 10, 18, 21, 27}, {19, 10, 
            4, 18, 21, 27}, {19, 10, 10, 18, 21, 27}, {10, 13, 13, 18, 21, 
            27}, {13, 13, 13, 18, 21, 27}, {16, 10, 13, 18, 21, 27}, {19, 10, 
            13, 15, 21, 27}, {10, 16, 7, 18, 21, 27}, {13, 16, 4, 18, 21, 
            27}, {10, 16, 10, 18, 21, 27}, {13, 16, 10, 18, 21, 27}, {7, 13, 
            13, 21, 23, 25}, {13, 13, 13, 21, 23, 25}, {16, 10, 13, 21, 23, 
            25}, {4, 16, 13, 18, 27, 21}, {10, 10, 13, 18, 27, 21}, {18, 10, 
            13, 10, 27, 21}, {18, 10, 13, 13, 27, 21}, {16, 13, 13, 15, 27, 
            21}, {4, 21, 13, 13, 27, 21}, {7, 21, 13, 13, 27, 21}, {4, 21, 
            13, 13, 25, 23}, {7, 21, 13, 10, 23, 25}, {10, 21, 13, 7, 23, 
            25}, {10, 21, 13, 7, 27, 21}, {13, 19, 13, 6, 27, 21}, {16, 16, 
            13, 6, 27, 21}, {18, 13, 13, 7, 27, 21}, {18, 13, 13, 10, 27, 
            21}, {16, 16, 13, 12, 27, 21}, {13, 19, 13, 12, 27, 21}, {16, 18, 
            16, 15, 25, 21}, {10, 21, 13, 10, 27, 21}, {13, 19, 13, 6, 23, 
            25}, {13, 19, 13, 12, 23, 25}, {13, 19, 13, 15, 25, 23}, {16, 16, 
            13, 15, 25, 23}, {16, 16, 13, 15, 23, 25}, {13, 21, 16, 9, 21, 
            25}, {15, 19, 16, 15, 23, 23}, {15, 19, 16, 12, 21, 25}, {13, 21, 
            16, 3, 21, 25}, {10, 21, 13, 10, 23, 25}, {10, 21, 13, 13, 25, 
            23}, {7, 21, 13, 13, 23, 25}, {7, 21, 13, 16, 25, 23}, {10, 19, 
            13, 18, 25, 23}, {13, 16, 13, 18, 23, 25}, {10, 19, 13, 15, 23, 
            25}, {4, 21, 13, 16, 25, 23}, {7, 23, 16, 7, 21, 25}, {10, 23, 
            16, 4, 21, 25}, {13, 23, 19, 1, 18, 25}, {10, 23, 16, 7, 21, 
            25}, {7, 23, 16, 10, 21, 25}, {10, 23, 18, 10, 19, 25}, {13, 7, 
            13, 21, 25, 23}, {13, 12, 18, 19, 27, 16}, {16, 12, 16, 21, 23, 
            23}, {13, 10, 13, 18, 27, 21}, {16, 10, 7, 18, 27, 21}, {16, 13, 
            4, 18, 27, 21}, {16, 10, 10, 18, 27, 21}, {16, 13, 10, 18, 27, 
            21}, {10, 16, 13, 18, 27, 21}, {13, 13, 13, 18, 27, 21}, {10, 19, 
            13, 15, 27, 21}, {4, 19, 10, 18, 27, 21}, {10, 19, 4, 18, 27, 
            21}, {10, 19, 10, 18, 27, 21}, {4, 16, 13, 21, 25, 23}, {10, 16, 
            13, 21, 25, 23}, {13, 13, 13, 21, 25, 23}, {16, 13, 13, 18, 25, 
            23}, {10, 10, 16, 20, 19, 27}, {13, 10, 16, 20, 19, 27}, {16, 7, 
            16, 20, 19, 27}, {3, 13, 16, 21, 23, 23}, {3, 21, 16, 13, 23, 
            23}, {6, 21, 16, 10, 21, 25}, {6, 10, 16, 21, 21, 25}, {3, 16, 
            16, 21, 23, 23}, {3, 21, 16, 16, 23, 23}, {6, 21, 16, 13, 21, 
            25}, {9, 21, 16, 13, 21, 25}, {12, 19, 16, 15, 21, 25}, {9, 21, 
            16, 16, 23, 23}, {12, 19, 16, 18, 23, 23}, {6, 13, 16, 21, 21, 
            25}, {15, 13, 16, 21, 21, 25}, {18, 10, 16, 21, 21, 25}, {15, 16, 
            16, 18, 21, 25}, {9, 16, 13, 18, 19, 27}, {9, 13, 16, 19, 18, 
            27}};

acdzineq  =  {5 x1 + 2 x2 + 2 x3 + 2 x4 - 4 x5 ≤ 
            241, 5 x1 + 2 x2 + 2 x3 - 4 x4 + 2 x5 ≤ 241, 
          5 x1 + 2 x2 - 4 x3 + 2 x4 + 2 x5 ≤ 241, 
          5 x1 - 4 x2 + 2 x3 + 2 x4 + 2 x5 ≤ 241, 
          2 x1 + 5 x2 + 2 x3 + 2 x4 - 4 x6 ≤ 241, 
          2 x1 + 5 x2 + 2 x3 - 4 x4 + 2 x6 ≤ 241, 
          2 x1 + 5 x2 - 4 x3 + 2 x4 + 2 x6 ≤ 241, 
          2 x1 + 2 x2 + 5 x3 + 2 x5 - 4 x6 ≤ 241, 
          2 x1 + 2 x2 + 5 x3 - 4 x5 + 2 x6 ≤ 241, 
          2 x1 + 2 x2 + 5 x4 + 2 x5 - 4 x6 ≤ 241, 
          2 x1 + 2 x2 + 5 x4 - 4 x5 + 2 x6 ≤ 241, 
          2 x1 + 2 x3 + 2 x4 + 5 x5 - 4 x6 ≤ 241, 
          2 x1 + 2 x3 - 4 x4 + 5 x5 + 2 x6 ≤ 241, 
          2 x1 - 4 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 241, 
          2 x1 - 4 x2 + 5 x3 + 2 x5 + 2 x6 ≤ 241, 
          2 x1 - 4 x2 + 5 x4 + 2 x5 + 2 x6 ≤ 241, 
          2 x2 + 2 x3 + 2 x4 - 4 x5 + 5 x6 ≤ 241, 
          2 x2 + 2 x3 - 4 x4 + 2 x5 + 5 x6 ≤ 241, 
          2 x2 - 4 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 
            241, -4 x2 + 2 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 
            241, -4 x1 + 5 x2 + 2 x3 + 2 x4 + 2 x6 ≤ 
            241, -4 x1 + 2 x2 + 5 x3 + 2 x5 + 2 x6 ≤ 
            241, -4 x1 + 2 x2 + 5 x4 + 2 x5 + 2 x6 ≤ 
            241, -4 x1 + 2 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 241, 
          5 x1 + 2 x2 + 2 x4 - 10 x5 + 2 x6 ≤ 241, 
          5 x1 + 2 x2 - 10 x3 + 2 x4 + 2 x6 ≤ 241, 
          5 x1 + 2 x3 - 10 x4 + 2 x5 + 2 x6 ≤ 241, 
          5 x1 - 10 x2 + 2 x3 + 2 x5 + 2 x6 ≤ 241, 
          2 x1 + 5 x2 + 2 x4 + 2 x5 - 10 x6 ≤ 241, 
          2 x1 + 5 x2 - 10 x3 + 2 x4 + 2 x5 ≤ 241, 
          2 x1 + 2 x2 + 2 x3 + 5 x4 - 10 x6 ≤ 241, 
          2 x1 + 2 x2 + 2 x3 + 5 x4 - 10 x5 ≤ 241, 
          2 x1 + 2 x2 + 2 x3 + 5 x5 - 10 x6 ≤ 241, 
          2 x1 + 2 x2 + 2 x3 - 10 x5 + 5 x6 ≤ 241, 
          2 x1 + 2 x2 + 2 x3 - 10 x4 + 5 x5 ≤ 241, 
          2 x1 + 2 x2 + 2 x3 - 10 x4 + 5 x6 ≤ 241, 
          2 x1 + 5 x3 + 2 x4 + 2 x5 - 10 x6 ≤ 241, 
          2 x1 - 10 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 241, 
          2 x1 - 10 x2 + 5 x3 + 2 x4 + 2 x5 ≤ 241, 
          2 x1 - 10 x2 + 2 x4 + 2 x5 + 5 x6 ≤ 241, 
          5 x2 + 2 x3 - 10 x4 + 2 x5 + 2 x6 ≤ 241, 
          2 x2 + 5 x3 + 2 x4 - 10 x5 + 2 x6 ≤ 241, 
          2 x2 - 10 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 
            241, -10 x2 + 2 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 
            241, -10 x1 + 5 x2 + 2 x3 + 2 x5 + 2 x6 ≤ 
            241, -10 x1 + 2 x2 + 5 x3 + 2 x4 + 2 x6 ≤ 
            241, -10 x1 + 2 x2 + 2 x4 + 5 x5 + 2 x6 ≤ 
            241, -10 x1 + 2 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 
            241, x1 - 2 x2 - 2 x3 - 2 x4 - 8 x5 - 
              4 x6 ≤ -143, 
          x1 - 2 x2 - 2 x3 - 8 x4 - 2 x5 - 4 x6 ≤ -143, 
          x1 - 2 x2 - 8 x3 - 2 x4 - 2 x5 - 4 x6 ≤ -143, 
          x1 - 8 x2 - 2 x3 - 2 x4 - 2 x5 - 
              4 x6 ≤ -143, -2 x1 + x2 - 2 x3 - 2 x4 - 
              4 x5 - 8 x6 ≤ -143, -2 x1 + x2 - 2 x3 - 
              8 x4 - 4 x5 - 2 x6 ≤ -143, -2 x1 + x2 - 
              8 x3 - 2 x4 - 4 x5 - 
              2 x6 ≤ -143, -2 x1 - 2 x2 + x3 - 4 x4 - 
              2 x5 - 8 x6 ≤ -143, -2 x1 - 2 x2 + x3 - 
              4 x4 - 8 x5 - 2 x6 ≤ -143, -2 x1 - 
              2 x2 - 4 x3 + x4 - 2 x5 - 
              8 x6 ≤ -143, -2 x1 - 2 x2 - 4 x3 + x4 - 
              8 x5 - 2 x6 ≤ -143, -2 x1 - 4 x2 - 
              2 x3 - 2 x4 + x5 - 8 x6 ≤ -143, -2 x1 - 
              4 x2 - 2 x3 - 8 x4 + x5 - 
              2 x6 ≤ -143, -2 x1 - 4 x2 - 8 x3 - 
              2 x4 + x5 - 2 x6 ≤ -143, -2 x1 - 8 x2 + 
              x3 - 4 x4 - 2 x5 - 2 x6 ≤ -143, -2 x1 - 
              8 x2 - 4 x3 + x4 - 2 x5 - 
              2 x6 ≤ -143, -4 x1 - 2 x2 - 2 x3 - 
              2 x4 - 8 x5 + x6 ≤ -143, -4 x1 - 2 x2 - 
              2 x3 - 8 x4 - 2 x5 + x6 ≤ -143, -4 x1 - 
              2 x2 - 8 x3 - 2 x4 - 2 x5 + 
              x6 ≤ -143, -4 x1 - 8 x2 - 2 x3 - 2 x4 - 
              2 x5 + x6 ≤ -143, -8 x1 + x2 - 2 x3 - 
              2 x4 - 4 x5 - 2 x6 ≤ -143, -8 x1 - 
              2 x2 + x3 - 4 x4 - 2 x5 - 
              2 x6 ≤ -143, -8 x1 - 2 x2 - 4 x3 + x4 - 
              2 x5 - 2 x6 ≤ -143, -8 x1 - 4 x2 - 
              2 x3 - 2 x4 + x5 - 2 x6 ≤ -143, 
          3 x1 - 6 x5 - 2 x6 ≤ 43, 
          3 x1 - 6 x4 - 2 x6 ≤ 43, 
          3 x1 - 6 x3 - 2 x6 ≤ 43, 
          3 x1 - 6 x2 - 2 x6 ≤ 43, 
          3 x2 - 2 x5 - 6 x6 ≤ 43, 
          3 x2 - 6 x4 - 2 x5 ≤ 43, 
          3 x2 - 6 x3 - 2 x5 ≤ 43, 
          3 x3 - 2 x4 - 6 x6 ≤ 43, 
          3 x3 - 2 x4 - 6 x5 ≤ 
            43, -2 x3 + 3 x4 - 6 x6 ≤ 
            43, -2 x3 + 3 x4 - 6 x5 ≤ 
            43, -2 x2 + 3 x5 - 6 x6 ≤ 
            43, -2 x2 - 6 x4 + 3 x5 ≤ 
            43, -2 x2 - 6 x3 + 3 x5 ≤ 
            43, -6 x2 + 3 x3 - 2 x4 ≤ 
            43, -6 x2 - 2 x3 + 3 x4 ≤ 
            43, -2 x1 - 6 x5 + 3 x6 ≤ 
            43, -2 x1 - 6 x4 + 3 x6 ≤ 
            43, -2 x1 - 6 x3 + 3 x6 ≤ 
            43, -2 x1 - 6 x2 + 3 x6 ≤ 
            43, -6 x1 + 3 x2 - 2 x5 ≤ 
            43, -6 x1 + 3 x3 - 2 x4 ≤ 
            43, -6 x1 - 2 x3 + 3 x4 ≤ 
            43, -6 x1 - 2 x2 + 3 x5 ≤ 43, 
          23 x1 + 14 x2 + 2 x3 - 4 x4 + 14 x5 + 8 x6 ≤ 1287, 
          23 x1 + 14 x2 - 4 x3 + 2 x4 + 14 x5 + 8 x6 ≤ 1287, 
          23 x1 + 2 x2 + 14 x3 + 14 x4 - 4 x5 + 8 x6 ≤ 1287, 
          23 x1 - 4 x2 + 14 x3 + 14 x4 + 2 x5 + 8 x6 ≤ 1287, 
          14 x1 + 23 x2 + 2 x3 - 4 x4 + 8 x5 + 14 x6 ≤ 1287, 
          14 x1 + 23 x2 - 4 x3 + 2 x4 + 8 x5 + 14 x6 ≤ 1287, 
          14 x1 + 8 x2 + 2 x3 - 4 x4 + 23 x5 + 14 x6 ≤ 1287, 
          14 x1 + 8 x2 - 4 x3 + 2 x4 + 23 x5 + 14 x6 ≤ 1287, 
          14 x1 + 2 x2 + 23 x3 + 8 x4 - 4 x5 + 14 x6 ≤ 1287, 
          14 x1 + 2 x2 + 8 x3 + 23 x4 - 4 x5 + 14 x6 ≤ 1287, 
          14 x1 - 4 x2 + 23 x3 + 8 x4 + 2 x5 + 14 x6 ≤ 1287, 
          14 x1 - 4 x2 + 8 x3 + 23 x4 + 2 x5 + 14 x6 ≤ 1287, 
          8 x1 + 14 x2 + 2 x3 - 4 x4 + 14 x5 + 23 x6 ≤ 1287, 
          8 x1 + 14 x2 - 4 x3 + 2 x4 + 14 x5 + 23 x6 ≤ 1287, 
          8 x1 + 2 x2 + 14 x3 + 14 x4 - 4 x5 + 23 x6 ≤ 1287, 
          8 x1 - 4 x2 + 14 x3 + 14 x4 + 2 x5 + 23 x6 ≤ 1287, 
          2 x1 + 23 x2 + 14 x3 + 14 x4 + 8 x5 - 4 x6 ≤ 1287, 
          2 x1 + 14 x2 + 23 x3 + 8 x4 + 14 x5 - 4 x6 ≤ 1287, 
          2 x1 + 14 x2 + 8 x3 + 23 x4 + 14 x5 - 4 x6 ≤ 1287, 
          2 x1 + 8 x2 + 14 x3 + 14 x4 + 23 x5 - 4 x6 ≤ 
            1287, -4 x1 + 23 x2 + 14 x3 + 14 x4 + 8 x5 + 
              2 x6 ≤ 
            1287, -4 x1 + 14 x2 + 23 x3 + 8 x4 + 14 x5 + 
              2 x6 ≤ 
            1287, -4 x1 + 14 x2 + 8 x3 + 23 x4 + 14 x5 + 
              2 x6 ≤ 
            1287, -4 x1 + 8 x2 + 14 x3 + 14 x4 + 23 x5 + 
              2 x6 ≤ 
            1287, -x3 - x4 - 3 x6 ≤ -29, -x3 - x4 - 
              3 x5 ≤ -29, -x2 - x5 - 
              3 x6 ≤ -29, -x2 - 3 x4 - 
              x5 ≤ -29, -x2 - 3 x3 - 
              x5 ≤ -29, -3 x2 - x3 - 
              x4 ≤ -29, -x1 - 3 x5 - 
              x6 ≤ -29, -x1 - 3 x4 - 
              x6 ≤ -29, -x1 - 3 x3 - 
              x6 ≤ -29, -x1 - 3 x2 - 
              x6 ≤ -29, -3 x1 - x3 - 
              x4 ≤ -29, -3 x1 - x2 - 
              x5 ≤ -29, 
          x1 + x2 + x3 + x4 + x5 + x6 ≤ 
            117, -x3 - x4 - x5 - 3 x6 ≤ -52, -x3 - 
              x4 - 3 x5 - x6 ≤ -52, -x2 - x4 - x5 - 
              3 x6 ≤ -52, -x2 - 3 x4 - x5 - 
              x6 ≤ -52, -x2 - x3 - x5 - 
              3 x6 ≤ -52, -x2 - x3 - x4 - 
              3 x6 ≤ -52, -x2 - 3 x3 - x5 - 
              x6 ≤ -52, -3 x2 - x3 - x4 - 
              x6 ≤ -52, -x1 - x4 - 3 x5 - 
              x6 ≤ -52, -x1 - 3 x4 - x5 - 
              x6 ≤ -52, -x1 - x3 - 3 x5 - 
              x6 ≤ -52, -x1 - x3 - x4 - 
              3 x5 ≤ -52, -x1 - 3 x3 - x5 - 
              x6 ≤ -52, -x1 - x2 - 3 x4 - 
              x6 ≤ -52, -x1 - x2 - 3 x4 - 
              x5 ≤ -52, -x1 - x2 - 3 x3 - 
              x6 ≤ -52, -x1 - x2 - 3 x3 - 
              x5 ≤ -52, -x1 - 3 x2 - x4 - 
              x6 ≤ -52, -x1 - 3 x2 - x3 - 
              x6 ≤ -52, -x1 - 3 x2 - x3 - 
              x4 ≤ -52, -3 x1 - x3 - x4 - 
              x5 ≤ -52, -3 x1 - x2 - x4 - 
              x5 ≤ -52, -3 x1 - x2 - x3 - 
              x5 ≤ -52, -3 x1 - x2 - x3 - 
              x4 ≤ -52, -2 x3 - 4 x4 - 3 x5 - 
              6 x6 ≤ -153, -2 x3 - 4 x4 - 6 x5 - 
              3 x6 ≤ -153, -2 x2 - 3 x4 - 4 x5 - 
              6 x6 ≤ -153, -2 x2 - 6 x4 - 4 x5 - 
              3 x6 ≤ -153, -3 x2 - 4 x3 - 2 x4 - 
              6 x6 ≤ -153, -4 x2 - 3 x3 - 2 x5 - 
              6 x6 ≤ -153, -4 x2 - 6 x3 - 2 x5 - 
              3 x6 ≤ -153, -6 x2 - 4 x3 - 2 x4 - 
              3 x6 ≤ -153, -2 x1 - 3 x4 - 6 x5 - 
              4 x6 ≤ -153, -2 x1 - 6 x4 - 3 x5 - 
              4 x6 ≤ -153, -2 x1 - 3 x2 - 6 x3 - 
              4 x6 ≤ -153, -2 x1 - 6 x2 - 3 x3 - 
              4 x6 ≤ -153, -3 x1 - 4 x3 - 2 x4 - 
              6 x5 ≤ -153, -3 x1 - 2 x2 - 6 x3 - 
              4 x5 ≤ -153, -3 x1 - 4 x2 - 6 x4 - 
              2 x5 ≤ -153, -3 x1 - 6 x2 - 2 x3 - 
              4 x4 ≤ -153, -4 x1 - 3 x3 - 6 x5 - 
              2 x6 ≤ -153, -4 x1 - 6 x3 - 3 x5 - 
              2 x6 ≤ -153, -4 x1 - 3 x2 - 6 x4 - 
              2 x6 ≤ -153, -4 x1 - 6 x2 - 3 x4 - 
              2 x6 ≤ -153, -6 x1 - 4 x3 - 2 x4 - 
              3 x5 ≤ -153, -6 x1 - 2 x2 - 3 x3 - 
              4 x5 ≤ -153, -6 x1 - 3 x2 - 2 x3 - 
              4 x4 ≤ -153, -6 x1 - 4 x2 - 3 x4 - 
              2 x5 ≤ -153, 
          10 x1 + 7 x2 + 4 x3 + 2 x4 + 4 x5 + 2 x6 ≤ 591, 
          10 x1 + 4 x2 + 7 x3 + 4 x4 + 2 x5 + 2 x6 ≤ 591, 
          10 x1 + 4 x2 + 2 x3 + 4 x4 + 7 x5 + 2 x6 ≤ 591, 
          10 x1 + 2 x2 + 4 x3 + 7 x4 + 4 x5 + 2 x6 ≤ 591, 
          7 x1 + 10 x2 + 4 x3 + 2 x4 + 2 x5 + 4 x6 ≤ 591, 
          7 x1 + 4 x2 + 10 x3 + 2 x4 + 2 x5 + 4 x6 ≤ 591, 
          7 x1 + 2 x2 + 2 x3 + 10 x4 + 4 x5 + 4 x6 ≤ 591, 
          7 x1 + 2 x2 + 2 x3 + 4 x4 + 10 x5 + 4 x6 ≤ 591, 
          4 x1 + 10 x2 + 7 x3 + 4 x4 + 2 x5 + 2 x6 ≤ 591, 
          4 x1 + 10 x2 + 2 x3 + 4 x4 + 2 x5 + 7 x6 ≤ 591, 
          4 x1 + 7 x2 + 10 x3 + 2 x4 + 4 x5 + 2 x6 ≤ 591, 
          4 x1 + 4 x2 + 2 x3 + 10 x4 + 7 x5 + 2 x6 ≤ 591, 
          4 x1 + 4 x2 + 2 x3 + 10 x4 + 2 x5 + 7 x6 ≤ 591, 
          4 x1 + 2 x2 + 10 x3 + 2 x4 + 4 x5 + 7 x6 ≤ 591, 
          4 x1 + 2 x2 + 4 x3 + 7 x4 + 10 x5 + 2 x6 ≤ 591, 
          4 x1 + 2 x2 + 4 x3 + 2 x4 + 10 x5 + 7 x6 ≤ 591, 
          2 x1 + 10 x2 + 4 x3 + 7 x4 + 2 x5 + 4 x6 ≤ 591, 
          2 x1 + 7 x2 + 2 x3 + 10 x4 + 4 x5 + 4 x6 ≤ 591, 
          2 x1 + 7 x2 + 2 x3 + 4 x4 + 4 x5 + 10 x6 ≤ 591, 
          2 x1 + 4 x2 + 10 x3 + 2 x4 + 7 x5 + 4 x6 ≤ 591, 
          2 x1 + 4 x2 + 4 x3 + 7 x4 + 2 x5 + 10 x6 ≤ 591, 
          2 x1 + 4 x2 + 4 x3 + 2 x4 + 7 x5 + 10 x6 ≤ 591, 
          2 x1 + 2 x2 + 7 x3 + 4 x4 + 10 x5 + 4 x6 ≤ 591, 
          2 x1 + 2 x2 + 7 x3 + 4 x4 + 4 x5 + 10 x6 ≤ 
            591, -x2 - 2 x3 - 2 x4 - x5 - 
              4 x6 ≤ -104, -2 x2 - x3 - x4 - 2 x5 - 
              4 x6 ≤ -104, -x1 - 2 x3 - 2 x4 - 4 x5 - 
              x6 ≤ -104, -x1 - 2 x2 - 4 x4 - 2 x5 - 
              x6 ≤ -104, -x1 - 2 x2 - 4 x3 - 2 x5 - 
              x6 ≤ -104, -x1 - 4 x2 - 2 x3 - 2 x4 - 
              x6 ≤ -104, -2 x1 - x3 - x4 - 4 x5 - 
              2 x6 ≤ -104, -2 x1 - x2 - 4 x4 - x5 - 
              2 x6 ≤ -104, -2 x1 - x2 - 4 x3 - x5 - 
              2 x6 ≤ -104, -2 x1 - 4 x2 - x3 - x4 - 
              2 x6 ≤ -104, -4 x1 - x2 - 2 x3 - 2 x4 - 
              x5 ≤ -104, -4 x1 - 2 x2 - x3 - x4 - 
              2 x5 ≤ -104, -x3 - x4 - x5 - 
              2 x6 ≤ -51, -x3 - x4 - 2 x5 - 
              x6 ≤ -51, -x2 - x4 - x5 - 
              2 x6 ≤ -51, -x2 - 2 x4 - x5 - 
              x6 ≤ -51, -x2 - x3 - x5 - 
              2 x6 ≤ -51, -x2 - x3 - x4 - 
              2 x6 ≤ -51, -x2 - 2 x3 - x5 - 
              x6 ≤ -51, -2 x2 - x3 - x4 - 
              x6 ≤ -51, -x1 - x4 - 2 x5 - 
              x6 ≤ -51, -x1 - 2 x4 - x5 - 
              x6 ≤ -51, -x1 - x3 - 2 x5 - 
              x6 ≤ -51, -x1 - x3 - x4 - 
              2 x5 ≤ -51, -x1 - 2 x3 - x5 - 
              x6 ≤ -51, -x1 - x2 - 2 x4 - 
              x6 ≤ -51, -x1 - x2 - 2 x4 - 
              x5 ≤ -51, -x1 - x2 - 2 x3 - 
              x6 ≤ -51, -x1 - x2 - 2 x3 - 
              x5 ≤ -51, -x1 - 2 x2 - x4 - 
              x6 ≤ -51, -x1 - 2 x2 - x3 - 
              x6 ≤ -51, -x1 - 2 x2 - x3 - 
              x4 ≤ -51, -2 x1 - x3 - x4 - 
              x5 ≤ -51, -2 x1 - x2 - x4 - 
              x5 ≤ -51, -2 x1 - x2 - x3 - 
              x5 ≤ -51, -2 x1 - x2 - x3 - 
              x4 ≤ -51, -3 x3 - 3 x4 - 3 x5 - 
              5 x6 ≤ -149, -3 x3 - 3 x4 - 5 x5 - 
              3 x6 ≤ -149, -3 x2 - 3 x4 - 3 x5 - 
              5 x6 ≤ -149, -3 x2 - 5 x4 - 3 x5 - 
              3 x6 ≤ -149, -3 x2 - 3 x3 - 3 x5 - 
              5 x6 ≤ -149, -3 x2 - 3 x3 - 3 x4 - 
              5 x6 ≤ -149, -3 x2 - 5 x3 - 3 x5 - 
              3 x6 ≤ -149, -5 x2 - 3 x3 - 3 x4 - 
              3 x6 ≤ -149, -3 x1 - 3 x4 - 5 x5 - 
              3 x6 ≤ -149, -3 x1 - 5 x4 - 3 x5 - 
              3 x6 ≤ -149, -3 x1 - 3 x3 - 5 x5 - 
              3 x6 ≤ -149, -3 x1 - 3 x3 - 3 x4 - 
              5 x5 ≤ -149, -3 x1 - 5 x3 - 3 x5 - 
              3 x6 ≤ -149, -3 x1 - 3 x2 - 5 x4 - 
              3 x6 ≤ -149, -3 x1 - 3 x2 - 5 x4 - 
              3 x5 ≤ -149, -3 x1 - 3 x2 - 5 x3 - 
              3 x6 ≤ -149, -3 x1 - 3 x2 - 5 x3 - 
              3 x5 ≤ -149, -3 x1 - 5 x2 - 3 x4 - 
              3 x6 ≤ -149, -3 x1 - 5 x2 - 3 x3 - 
              3 x6 ≤ -149, -3 x1 - 5 x2 - 3 x3 - 
              3 x4 ≤ -149, -5 x1 - 3 x3 - 3 x4 - 
              3 x5 ≤ -149, -5 x1 - 3 x2 - 3 x4 - 
              3 x5 ≤ -149, -5 x1 - 3 x2 - 3 x3 - 
              3 x5 ≤ -149, -5 x1 - 3 x2 - 3 x3 - 
              3 x4 ≤ -149, 
          x1 + x2 - 2 x3 - 2 x4 - 2 x5 - 4 x6 ≤ -56, 
          x1 + x2 - 2 x3 - 2 x4 - 4 x5 - 2 x6 ≤ -56, 
          x1 - 2 x2 + x3 - 2 x4 - 2 x5 - 4 x6 ≤ -56, 
          x1 - 2 x2 + x3 - 4 x4 - 2 x5 - 2 x6 ≤ -56, 
          x1 - 2 x2 - 2 x3 + x4 - 2 x5 - 4 x6 ≤ -56, 
          x1 - 2 x2 - 2 x3 - 2 x4 + x5 - 4 x6 ≤ -56, 
          x1 - 2 x2 - 4 x3 + x4 - 2 x5 - 2 x6 ≤ -56, 
          x1 - 4 x2 - 2 x3 - 2 x4 + x5 - 
              2 x6 ≤ -56, -2 x1 + x2 + x3 - 2 x4 - 
              4 x5 - 2 x6 ≤ -56, -2 x1 + x2 + x3 - 
              4 x4 - 2 x5 - 2 x6 ≤ -56, -2 x1 + x2 - 
              2 x3 + x4 - 4 x5 - 2 x6 ≤ -56, -2 x1 + 
              x2 - 2 x3 - 2 x4 - 4 x5 + 
              x6 ≤ -56, -2 x1 + x2 - 4 x3 + x4 - 2 x5 - 
              2 x6 ≤ -56, -2 x1 - 2 x2 + x3 - 4 x4 + 
              x5 - 2 x6 ≤ -56, -2 x1 - 2 x2 + x3 - 
              4 x4 - 2 x5 + x6 ≤ -56, -2 x1 - 2 x2 - 
              4 x3 + x4 + x5 - 2 x6 ≤ -56, -2 x1 - 
              2 x2 - 4 x3 + x4 - 2 x5 + 
              x6 ≤ -56, -2 x1 - 4 x2 + x3 - 2 x4 + x5 - 
              2 x6 ≤ -56, -2 x1 - 4 x2 - 2 x3 + x4 + 
              x5 - 2 x6 ≤ -56, -2 x1 - 4 x2 - 2 x3 - 
              2 x4 + x5 + x6 ≤ -56, -4 x1 + x2 - 2 x3 - 
              2 x4 - 2 x5 + x6 ≤ -56, -4 x1 - 2 x2 + 
              x3 - 2 x4 - 2 x5 + x6 ≤ -56, -4 x1 - 
              2 x2 - 2 x3 + x4 - 2 x5 + 
              x6 ≤ -56, -4 x1 - 2 x2 - 2 x3 - 2 x4 + 
              x5 + x6 ≤ -56, 
          3 x1 - 2 x3 - 6 x4 - 12 x5 - 8 x6 ≤ -211, 
          3 x1 - 2 x2 - 12 x4 - 6 x5 - 8 x6 ≤ -211, 
          3 x1 - 6 x2 - 12 x3 - 2 x5 - 8 x6 ≤ -211, 
          3 x1 - 12 x2 - 6 x3 - 2 x4 - 8 x6 ≤ -211, 
          3 x2 - 2 x3 - 6 x4 - 8 x5 - 
              12 x6 ≤ -211, -2 x2 + 3 x3 - 8 x4 - 
              6 x5 - 12 x6 ≤ -211, -6 x2 - 8 x3 + 
              3 x4 - 2 x5 - 12 x6 ≤ -211, -8 x2 - 
              6 x3 - 2 x4 + 3 x5 - 
              12 x6 ≤ -211, -2 x1 + 3 x2 - 12 x4 - 
              8 x5 - 6 x6 ≤ -211, -2 x1 + 3 x3 - 
              8 x4 - 12 x5 - 6 x6 ≤ -211, -2 x1 - 
              8 x2 - 12 x3 + 3 x5 - 
              6 x6 ≤ -211, -2 x1 - 12 x2 - 8 x3 + 
              3 x4 - 6 x6 ≤ -211, -6 x1 + 3 x2 - 
              12 x3 - 8 x5 - 2 x6 ≤ -211, -6 x1 - 
              8 x3 + 3 x4 - 12 x5 - 
              2 x6 ≤ -211, -6 x1 - 8 x2 - 12 x4 + 
              3 x5 - 2 x6 ≤ -211, -6 x1 - 12 x2 + 
              3 x3 - 8 x4 - 2 x6 ≤ -211, -8 x1 - 
              6 x3 - 2 x4 - 12 x5 + 
              3 x6 ≤ -211, -8 x1 - 2 x2 - 12 x3 - 
              6 x5 + 3 x6 ≤ -211, -8 x1 - 6 x2 - 
              12 x4 - 2 x5 + 3 x6 ≤ -211, -8 x1 - 
              12 x2 - 2 x3 - 6 x4 + 
              3 x6 ≤ -211, -12 x1 + 3 x2 - 6 x3 - 
              2 x4 - 8 x5 ≤ -211, -12 x1 - 2 x2 - 
              8 x3 + 3 x4 - 6 x5 ≤ -211, -12 x1 - 
              6 x2 + 3 x3 - 8 x4 - 
              2 x5 ≤ -211, -12 x1 - 8 x2 - 2 x3 - 
              6 x4 + 3 x5 ≤ -211, 
          15 x1 + 12 x2 + 6 x3 + 6 x5 + 4 x6 ≤ 901, 
          15 x1 + 6 x2 + 12 x3 + 6 x4 + 4 x6 ≤ 901, 
          15 x1 + 6 x2 + 6 x4 + 12 x5 + 4 x6 ≤ 901, 
          15 x1 + 6 x3 + 12 x4 + 6 x5 + 4 x6 ≤ 901, 
          12 x1 + 15 x2 + 6 x3 + 4 x5 + 6 x6 ≤ 901, 
          12 x1 + 6 x2 + 15 x3 + 4 x4 + 6 x6 ≤ 901, 
          12 x1 + 4 x2 + 6 x4 + 15 x5 + 6 x6 ≤ 901, 
          12 x1 + 4 x3 + 15 x4 + 6 x5 + 6 x6 ≤ 901, 
          6 x1 + 15 x2 + 12 x3 + 6 x4 + 4 x5 ≤ 901, 
          6 x1 + 15 x2 + 6 x4 + 4 x5 + 12 x6 ≤ 901, 
          6 x1 + 12 x2 + 15 x3 + 4 x4 + 6 x5 ≤ 901, 
          6 x1 + 6 x2 + 4 x3 + 15 x4 + 12 x5 ≤ 901, 
          6 x1 + 6 x2 + 4 x3 + 15 x4 + 12 x6 ≤ 901, 
          6 x1 + 4 x2 + 6 x3 + 12 x4 + 15 x5 ≤ 901, 
          6 x1 + 4 x2 + 6 x3 + 15 x5 + 12 x6 ≤ 901, 
          6 x1 + 15 x3 + 4 x4 + 6 x5 + 12 x6 ≤ 901, 
          4 x1 + 12 x2 + 6 x4 + 6 x5 + 15 x6 ≤ 901, 
          4 x1 + 6 x2 + 6 x3 + 12 x4 + 15 x6 ≤ 901, 
          4 x1 + 6 x2 + 6 x3 + 12 x5 + 15 x6 ≤ 901, 
          4 x1 + 12 x3 + 6 x4 + 6 x5 + 15 x6 ≤ 901, 
          15 x2 + 6 x3 + 12 x4 + 4 x5 + 6 x6 ≤ 901, 
          12 x2 + 4 x3 + 15 x4 + 6 x5 + 6 x6 ≤ 901, 
          6 x2 + 15 x3 + 4 x4 + 12 x5 + 6 x6 ≤ 901, 
          4 x2 + 12 x3 + 6 x4 + 15 x5 + 6 x6 ≤ 901, 
          15 x1 + 10 x2 + 6 x3 + 6 x5 + 4 x6 ≤ 863, 
          15 x1 + 6 x2 + 10 x3 + 6 x4 + 4 x6 ≤ 863, 
          15 x1 + 6 x2 + 6 x4 + 10 x5 + 4 x6 ≤ 863, 
          15 x1 + 6 x3 + 10 x4 + 6 x5 + 4 x6 ≤ 863, 
          10 x1 + 15 x2 + 6 x3 + 4 x5 + 6 x6 ≤ 863, 
          10 x1 + 6 x2 + 15 x3 + 4 x4 + 6 x6 ≤ 863, 
          10 x1 + 4 x2 + 6 x4 + 15 x5 + 6 x6 ≤ 863, 
          10 x1 + 4 x3 + 15 x4 + 6 x5 + 6 x6 ≤ 863, 
          6 x1 + 15 x2 + 10 x3 + 6 x4 + 4 x5 ≤ 863, 
          6 x1 + 15 x2 + 6 x4 + 4 x5 + 10 x6 ≤ 863, 
          6 x1 + 10 x2 + 15 x3 + 4 x4 + 6 x5 ≤ 863, 
          6 x1 + 6 x2 + 4 x3 + 15 x4 + 10 x5 ≤ 863, 
          6 x1 + 6 x2 + 4 x3 + 15 x4 + 10 x6 ≤ 863, 
          6 x1 + 4 x2 + 6 x3 + 10 x4 + 15 x5 ≤ 863, 
          6 x1 + 4 x2 + 6 x3 + 15 x5 + 10 x6 ≤ 863, 
          6 x1 + 15 x3 + 4 x4 + 6 x5 + 10 x6 ≤ 863, 
          4 x1 + 10 x2 + 6 x4 + 6 x5 + 15 x6 ≤ 863, 
          4 x1 + 6 x2 + 6 x3 + 10 x4 + 15 x6 ≤ 863, 
          4 x1 + 6 x2 + 6 x3 + 10 x5 + 15 x6 ≤ 863, 
          4 x1 + 10 x3 + 6 x4 + 6 x5 + 15 x6 ≤ 863, 
          15 x2 + 6 x3 + 10 x4 + 4 x5 + 6 x6 ≤ 863, 
          10 x2 + 4 x3 + 15 x4 + 6 x5 + 6 x6 ≤ 863, 
          6 x2 + 15 x3 + 4 x4 + 10 x5 + 6 x6 ≤ 863, 
          4 x2 + 10 x3 + 6 x4 + 15 x5 + 6 x6 ≤ 863, 
          x1 - 2 x2 - 6 x3 - 8 x4 - 2 x5 - 4 x6 ≤ -195, 
          x1 - 2 x2 - 8 x3 - 6 x4 - 2 x5 - 4 x6 ≤ -195, 
          x1 - 6 x2 - 2 x3 - 2 x4 - 8 x5 - 4 x6 ≤ -195, 
          x1 - 8 x2 - 2 x3 - 2 x4 - 6 x5 - 
              4 x6 ≤ -195, -2 x1 + x2 - 6 x3 - 8 x4 - 
              4 x5 - 2 x6 ≤ -195, -2 x1 + x2 - 8 x3 - 
              6 x4 - 4 x5 - 2 x6 ≤ -195, -2 x1 - 
              4 x2 - 6 x3 - 8 x4 + x5 - 
              2 x6 ≤ -195, -2 x1 - 4 x2 - 8 x3 - 
              6 x4 + x5 - 2 x6 ≤ -195, -2 x1 - 6 x2 + 
              x3 - 4 x4 - 8 x5 - 2 x6 ≤ -195, -2 x1 - 
              6 x2 - 4 x3 + x4 - 8 x5 - 
              2 x6 ≤ -195, -2 x1 - 8 x2 + x3 - 4 x4 - 
              6 x5 - 2 x6 ≤ -195, -2 x1 - 8 x2 - 
              4 x3 + x4 - 6 x5 - 2 x6 ≤ -195, -4 x1 - 
              2 x2 - 6 x3 - 8 x4 - 2 x5 + 
              x6 ≤ -195, -4 x1 - 2 x2 - 8 x3 - 6 x4 - 
              2 x5 + x6 ≤ -195, -4 x1 - 6 x2 - 2 x3 - 
              2 x4 - 8 x5 + x6 ≤ -195, -4 x1 - 8 x2 - 
              2 x3 - 2 x4 - 6 x5 + x6 ≤ -195, -6 x1 + 
              x2 - 2 x3 - 2 x4 - 4 x5 - 
              8 x6 ≤ -195, -6 x1 - 2 x2 + x3 - 4 x4 - 
              2 x5 - 8 x6 ≤ -195, -6 x1 - 2 x2 - 
              4 x3 + x4 - 2 x5 - 8 x6 ≤ -195, -6 x1 - 
              4 x2 - 2 x3 - 2 x4 + x5 - 
              8 x6 ≤ -195, -8 x1 + x2 - 2 x3 - 2 x4 - 
              4 x5 - 6 x6 ≤ -195, -8 x1 - 2 x2 + x3 - 
              4 x4 - 2 x5 - 6 x6 ≤ -195, -8 x1 - 
              2 x2 - 4 x3 + x4 - 2 x5 - 
              6 x6 ≤ -195, -8 x1 - 4 x2 - 2 x3 - 
              2 x4 + x5 - 6 x6 ≤ -195, 
          7 x1 + 4 x2 - 2 x4 + 4 x5 + 2 x6 ≤ 363, 
          7 x1 + 4 x2 - 2 x3 + 4 x5 + 2 x6 ≤ 363, 
          7 x1 + 4 x3 + 4 x4 - 2 x5 + 2 x6 ≤ 363, 
          7 x1 - 2 x2 + 4 x3 + 4 x4 + 2 x6 ≤ 363, 
          4 x1 + 7 x2 - 2 x4 + 2 x5 + 4 x6 ≤ 363, 
          4 x1 + 7 x2 - 2 x3 + 2 x5 + 4 x6 ≤ 363, 
          4 x1 + 2 x2 - 2 x4 + 7 x5 + 4 x6 ≤ 363, 
          4 x1 + 2 x2 - 2 x3 + 7 x5 + 4 x6 ≤ 363, 
          4 x1 + 7 x3 + 2 x4 - 2 x5 + 4 x6 ≤ 363, 
          4 x1 + 2 x3 + 7 x4 - 2 x5 + 4 x6 ≤ 363, 
          4 x1 - 2 x2 + 7 x3 + 2 x4 + 4 x6 ≤ 363, 
          4 x1 - 2 x2 + 2 x3 + 7 x4 + 4 x6 ≤ 363, 
          2 x1 + 4 x2 - 2 x4 + 4 x5 + 7 x6 ≤ 363, 
          2 x1 + 4 x2 - 2 x3 + 4 x5 + 7 x6 ≤ 363, 
          2 x1 + 4 x3 + 4 x4 - 2 x5 + 7 x6 ≤ 363, 
          2 x1 - 2 x2 + 4 x3 + 4 x4 + 7 x6 ≤ 363, 
          7 x2 + 4 x3 + 4 x4 + 2 x5 - 2 x6 ≤ 363, 
          4 x2 + 7 x3 + 2 x4 + 4 x5 - 2 x6 ≤ 363, 
          4 x2 + 2 x3 + 7 x4 + 4 x5 - 2 x6 ≤ 363, 
          2 x2 + 4 x3 + 4 x4 + 7 x5 - 2 x6 ≤ 
            363, -2 x1 + 7 x2 + 4 x3 + 4 x4 + 2 x5 ≤ 
            363, -2 x1 + 4 x2 + 7 x3 + 2 x4 + 4 x5 ≤ 
            363, -2 x1 + 4 x2 + 2 x3 + 7 x4 + 4 x5 ≤ 
            363, -2 x1 + 2 x2 + 4 x3 + 4 x4 + 7 x5 ≤ 363, 
          3 x1 - 6 x3 - 18 x4 - 24 x5 - 20 x6 ≤ -707, 
          3 x1 - 6 x2 - 24 x4 - 18 x5 - 20 x6 ≤ -707, 
          3 x1 - 18 x2 - 24 x3 - 6 x5 - 20 x6 ≤ -707, 
          3 x1 - 24 x2 - 18 x3 - 6 x4 - 20 x6 ≤ -707, 
          3 x2 - 6 x3 - 18 x4 - 20 x5 - 
              24 x6 ≤ -707, -6 x2 + 3 x3 - 20 x4 - 
              18 x5 - 24 x6 ≤ -707, -18 x2 - 20 x3 + 
              3 x4 - 6 x5 - 24 x6 ≤ -707, -20 x2 - 
              18 x3 - 6 x4 + 3 x5 - 
              24 x6 ≤ -707, -6 x1 + 3 x2 - 24 x4 - 
              20 x5 - 18 x6 ≤ -707, -6 x1 + 3 x3 - 
              20 x4 - 24 x5 - 18 x6 ≤ -707, -6 x1 - 
              20 x2 - 24 x3 + 3 x5 - 
              18 x6 ≤ -707, -6 x1 - 24 x2 - 20 x3 + 
              3 x4 - 18 x6 ≤ -707, -18 x1 + 3 x2 - 
              24 x3 - 20 x5 - 6 x6 ≤ -707, -18 x1 - 
              20 x3 + 3 x4 - 24 x5 - 
              6 x6 ≤ -707, -18 x1 - 20 x2 - 24 x4 + 
              3 x5 - 6 x6 ≤ -707, -18 x1 - 24 x2 + 
              3 x3 - 20 x4 - 6 x6 ≤ -707, -20 x1 - 
              18 x3 - 6 x4 - 24 x5 + 
              3 x6 ≤ -707, -20 x1 - 6 x2 - 24 x3 - 
              18 x5 + 3 x6 ≤ -707, -20 x1 - 18 x2 - 
              24 x4 - 6 x5 + 3 x6 ≤ -707, -20 x1 - 
              24 x2 - 6 x3 - 18 x4 + 
              3 x6 ≤ -707, -24 x1 + 3 x2 - 18 x3 - 
              6 x4 - 20 x5 ≤ -707, -24 x1 - 6 x2 - 
              20 x3 + 3 x4 - 18 x5 ≤ -707, -24 x1 - 
              18 x2 + 3 x3 - 20 x4 - 
              6 x5 ≤ -707, -24 x1 - 20 x2 - 6 x3 - 
              18 x4 + 3 x5 ≤ -707, 
          9 x1 - 2 x3 - 6 x4 - 8 x5 - 12 x6 ≤ -85, 
          9 x1 - 2 x2 - 8 x4 - 6 x5 - 12 x6 ≤ -85, 
          9 x1 - 6 x2 - 8 x3 - 2 x5 - 12 x6 ≤ -85, 
          9 x1 - 8 x2 - 6 x3 - 2 x4 - 12 x6 ≤ -85, 
          9 x2 - 2 x3 - 6 x4 - 12 x5 - 
              8 x6 ≤ -85, -2 x2 + 9 x3 - 12 x4 - 
              6 x5 - 8 x6 ≤ -85, -6 x2 - 12 x3 + 
              9 x4 - 2 x5 - 8 x6 ≤ -85, -12 x2 - 
              6 x3 - 2 x4 + 9 x5 - 
              8 x6 ≤ -85, -2 x1 + 9 x2 - 8 x4 - 
              12 x5 - 6 x6 ≤ -85, -2 x1 + 9 x3 - 
              12 x4 - 8 x5 - 6 x6 ≤ -85, -2 x1 - 
              8 x2 - 12 x3 + 9 x4 - 
              6 x6 ≤ -85, -2 x1 - 12 x2 - 8 x3 + 
              9 x5 - 6 x6 ≤ -85, -6 x1 + 9 x2 - 
              8 x3 - 12 x5 - 2 x6 ≤ -85, -6 x1 - 
              12 x3 + 9 x4 - 8 x5 - 
              2 x6 ≤ -85, -6 x1 - 8 x2 + 9 x3 - 
              12 x4 - 2 x6 ≤ -85, -6 x1 - 12 x2 - 
              8 x4 + 9 x5 - 2 x6 ≤ -85, -8 x1 + 
              9 x2 - 6 x3 - 2 x4 - 
              12 x5 ≤ -85, -8 x1 - 2 x2 - 12 x3 + 
              9 x4 - 6 x5 ≤ -85, -8 x1 - 6 x2 + 
              9 x3 - 12 x4 - 2 x5 ≤ -85, -8 x1 - 
              12 x2 - 2 x3 - 6 x4 + 
              9 x5 ≤ -85, -12 x1 - 6 x3 - 2 x4 - 
              8 x5 + 9 x6 ≤ -85, -12 x1 - 2 x2 - 
              8 x3 - 6 x5 + 9 x6 ≤ -85, -12 x1 - 
              6 x2 - 8 x4 - 2 x5 + 
              9 x6 ≤ -85, -12 x1 - 8 x2 - 2 x3 - 
              6 x4 + 9 x6 ≤ -85, 
          9 x1 - 24 x3 - 18 x4 - 2 x5 - 2 x6 ≤ -79, 
          9 x1 - 2 x2 - 18 x3 - 24 x4 - 2 x6 ≤ -79, 
          9 x1 - 18 x2 - 2 x3 - 24 x5 - 2 x6 ≤ -79, 
          9 x1 - 24 x2 - 2 x4 - 18 x5 - 2 x6 ≤ -79, 
          9 x2 - 24 x3 - 18 x4 - 2 x5 - 
              2 x6 ≤ -79, -2 x2 - 18 x3 - 24 x4 + 
              9 x5 - 2 x6 ≤ -79, -18 x2 - 2 x3 + 
              9 x4 - 24 x5 - 2 x6 ≤ -79, -24 x2 + 
              9 x3 - 2 x4 - 18 x5 - 
              2 x6 ≤ -79, -2 x1 + 9 x2 - 18 x3 - 
              24 x4 - 2 x5 ≤ -79, -2 x1 - 18 x3 - 
              24 x4 - 2 x5 + 9 x6 ≤ -79, -2 x1 - 
              2 x2 - 24 x3 - 18 x4 + 
              9 x5 ≤ -79, -2 x1 - 2 x2 - 24 x3 - 
              18 x4 + 9 x6 ≤ -79, -2 x1 - 18 x2 + 
              9 x3 - 2 x4 - 24 x5 ≤ -79, -2 x1 - 
              18 x2 - 2 x4 - 24 x5 + 
              9 x6 ≤ -79, -2 x1 - 24 x2 - 2 x3 + 
              9 x4 - 18 x5 ≤ -79, -2 x1 - 24 x2 - 
              2 x3 - 18 x5 + 9 x6 ≤ -79, -18 x1 + 
              9 x2 - 2 x3 - 2 x5 - 
              24 x6 ≤ -79, -18 x1 - 2 x3 + 9 x4 - 
              2 x5 - 24 x6 ≤ -79, -18 x1 - 2 x2 + 
              9 x3 - 2 x4 - 24 x6 ≤ -79, -18 x1 - 
              2 x2 - 2 x4 + 9 x5 - 
              24 x6 ≤ -79, -24 x1 + 9 x2 - 2 x4 - 
              2 x5 - 18 x6 ≤ -79, -24 x1 + 9 x3 - 
              2 x4 - 2 x5 - 18 x6 ≤ -79, -24 x1 - 
              2 x2 - 2 x3 + 9 x4 - 
              18 x6 ≤ -79, -24 x1 - 2 x2 - 2 x3 + 
              9 x5 - 18 x6 ≤ -79, 
          11 x1 - 16 x2 - 88 x3 - 70 x4 - 22 x5 - 
              38 x6 ≤ -1981, 
          11 x1 - 22 x2 - 70 x3 - 88 x4 - 16 x5 - 
              38 x6 ≤ -1981, 
          11 x1 - 70 x2 - 22 x3 - 16 x4 - 88 x5 - 
              38 x6 ≤ -1981, 
          11 x1 - 88 x2 - 16 x3 - 22 x4 - 70 x5 - 
              38 x6 ≤ -1981, -16 x1 + 11 x2 - 88 x3 - 
              70 x4 - 38 x5 - 22 x6 ≤ -1981, -16 x1 - 
              38 x2 - 70 x3 - 88 x4 + 11 x5 - 
              22 x6 ≤ -1981, -16 x1 - 70 x2 - 38 x3 + 
              11 x4 - 88 x5 - 22 x6 ≤ -1981, -16 x1 - 
              88 x2 + 11 x3 - 38 x4 - 70 x5 - 
              22 x6 ≤ -1981, -22 x1 + 11 x2 - 70 x3 - 
              88 x4 - 38 x5 - 16 x6 ≤ -1981, -22 x1 - 
              38 x2 - 88 x3 - 70 x4 + 11 x5 - 
              16 x6 ≤ -1981, -22 x1 - 70 x2 + 11 x3 - 
              38 x4 - 88 x5 - 16 x6 ≤ -1981, -22 x1 - 
              88 x2 - 38 x3 + 11 x4 - 70 x5 - 
              16 x6 ≤ -1981, -38 x1 - 16 x2 - 70 x3 - 
              88 x4 - 22 x5 + 11 x6 ≤ -1981, -38 x1 - 
              22 x2 - 88 x3 - 70 x4 - 16 x5 + 
              11 x6 ≤ -1981, -38 x1 - 70 x2 - 16 x3 - 
              22 x4 - 88 x5 + 11 x6 ≤ -1981, -38 x1 - 
              88 x2 - 22 x3 - 16 x4 - 70 x5 + 
              11 x6 ≤ -1981, -70 x1 + 11 x2 - 22 x3 - 
              16 x4 - 38 x5 - 88 x6 ≤ -1981, -70 x1 - 
              16 x2 - 38 x3 + 11 x4 - 22 x5 - 
              88 x6 ≤ -1981, -70 x1 - 22 x2 + 11 x3 - 
              38 x4 - 16 x5 - 88 x6 ≤ -1981, -70 x1 - 
              38 x2 - 16 x3 - 22 x4 + 11 x5 - 
              88 x6 ≤ -1981, -88 x1 + 11 x2 - 16 x3 - 
              22 x4 - 38 x5 - 70 x6 ≤ -1981, -88 x1 - 
              16 x2 + 11 x3 - 38 x4 - 22 x5 - 
              70 x6 ≤ -1981, -88 x1 - 22 x2 - 38 x3 + 
              11 x4 - 16 x5 - 70 x6 ≤ -1981, -88 x1 - 
              38 x2 - 22 x3 - 16 x4 + 11 x5 - 
              70 x6 ≤ -1981, -3 x2 - 15 x3 - 13 x4 - 
              4 x5 - 7 x6 ≤ -413, -4 x2 - 13 x3 - 
              15 x4 - 3 x5 - 7 x6 ≤ -413, -13 x2 - 
              4 x3 - 3 x4 - 15 x5 - 
              7 x6 ≤ -413, -15 x2 - 3 x3 - 4 x4 - 
              13 x5 - 7 x6 ≤ -413, -3 x1 - 15 x3 - 
              13 x4 - 7 x5 - 4 x6 ≤ -413, -3 x1 - 
              7 x2 - 13 x3 - 15 x4 - 
              4 x6 ≤ -413, -3 x1 - 13 x2 - 7 x3 - 
              15 x5 - 4 x6 ≤ -413, -3 x1 - 15 x2 - 
              7 x4 - 13 x5 - 4 x6 ≤ -413, -4 x1 - 
              13 x3 - 15 x4 - 7 x5 - 
              3 x6 ≤ -413, -4 x1 - 7 x2 - 15 x3 - 
              13 x4 - 3 x6 ≤ -413, -4 x1 - 13 x2 - 
              7 x4 - 15 x5 - 3 x6 ≤ -413, -4 x1 - 
              15 x2 - 7 x3 - 13 x5 - 
              3 x6 ≤ -413, -7 x1 - 3 x2 - 13 x3 - 
              15 x4 - 4 x5 ≤ -413, -7 x1 - 4 x2 - 
              15 x3 - 13 x4 - 3 x5 ≤ -413, -7 x1 - 
              13 x2 - 3 x3 - 4 x4 - 
              15 x5 ≤ -413, -7 x1 - 15 x2 - 4 x3 - 
              3 x4 - 13 x5 ≤ -413, -13 x1 - 4 x3 - 
              3 x4 - 7 x5 - 15 x6 ≤ -413, -13 x1 - 
              3 x2 - 7 x3 - 4 x5 - 
              15 x6 ≤ -413, -13 x1 - 4 x2 - 7 x4 - 
              3 x5 - 15 x6 ≤ -413, -13 x1 - 7 x2 - 
              3 x3 - 4 x4 - 15 x6 ≤ -413, -15 x1 - 
              3 x3 - 4 x4 - 7 x5 - 
              13 x6 ≤ -413, -15 x1 - 3 x2 - 7 x4 - 
              4 x5 - 13 x6 ≤ -413, -15 x1 - 4 x2 - 
              7 x3 - 3 x5 - 13 x6 ≤ -413, -15 x1 - 
              7 x2 - 4 x3 - 3 x4 - 13 x6 ≤ -413, 
          x1 - 2 x2 - 11 x3 - 9 x4 - 3 x5 - 5 x6 ≤ -268, 
          x1 - 3 x2 - 9 x3 - 11 x4 - 2 x5 - 5 x6 ≤ -268, 
          x1 - 9 x2 - 3 x3 - 2 x4 - 11 x5 - 5 x6 ≤ -268, 
          x1 - 11 x2 - 2 x3 - 3 x4 - 9 x5 - 
              5 x6 ≤ -268, -2 x1 + x2 - 11 x3 - 9 x4 - 
              5 x5 - 3 x6 ≤ -268, -2 x1 - 5 x2 - 
              9 x3 - 11 x4 + x5 - 3 x6 ≤ -268, -2 x1 - 
              9 x2 - 5 x3 + x4 - 11 x5 - 
              3 x6 ≤ -268, -2 x1 - 11 x2 + x3 - 5 x4 - 
              9 x5 - 3 x6 ≤ -268, -3 x1 + x2 - 9 x3 - 
              11 x4 - 5 x5 - 2 x6 ≤ -268, -3 x1 - 
              5 x2 - 11 x3 - 9 x4 + x5 - 
              2 x6 ≤ -268, -3 x1 - 9 x2 + x3 - 5 x4 - 
              11 x5 - 2 x6 ≤ -268, -3 x1 - 11 x2 - 
              5 x3 + x4 - 9 x5 - 2 x6 ≤ -268, -5 x1 - 
              2 x2 - 9 x3 - 11 x4 - 3 x5 + 
              x6 ≤ -268, -5 x1 - 3 x2 - 11 x3 - 9 x4 - 
              2 x5 + x6 ≤ -268, -5 x1 - 9 x2 - 2 x3 - 
              3 x4 - 11 x5 + x6 ≤ -268, -5 x1 - 
              11 x2 - 3 x3 - 2 x4 - 9 x5 + 
              x6 ≤ -268, -9 x1 + x2 - 3 x3 - 2 x4 - 
              5 x5 - 11 x6 ≤ -268, -9 x1 - 2 x2 - 
              5 x3 + x4 - 3 x5 - 11 x6 ≤ -268, -9 x1 - 
              3 x2 + x3 - 5 x4 - 2 x5 - 
              11 x6 ≤ -268, -9 x1 - 5 x2 - 2 x3 - 
              3 x4 + x5 - 11 x6 ≤ -268, -11 x1 + x2 - 
              2 x3 - 3 x4 - 5 x5 - 
              9 x6 ≤ -268, -11 x1 - 2 x2 + x3 - 5 x4 - 
              3 x5 - 9 x6 ≤ -268, -11 x1 - 3 x2 - 
              5 x3 + x4 - 2 x5 - 9 x6 ≤ -268, -11 x1 - 
              5 x2 - 3 x3 - 2 x4 + x5 - 9 x6 ≤ -268, 
          3 x1 - 12 x3 - 6 x4 - 2 x5 ≤ -35, 
          3 x1 - 2 x2 - 6 x3 - 12 x4 ≤ -35, 
          3 x1 - 6 x2 - 2 x3 - 12 x5 ≤ -35, 
          3 x1 - 12 x2 - 2 x4 - 6 x5 ≤ -35, 
          3 x2 - 12 x3 - 6 x4 - 2 x6 ≤ -35, -6 x3 - 
              12 x4 + 3 x5 - 2 x6 ≤ -35, -6 x3 - 
              12 x4 - 2 x5 + 3 x6 ≤ -35, -2 x2 - 
              12 x3 - 6 x4 + 3 x6 ≤ -35, -6 x2 + 
              3 x4 - 12 x5 - 2 x6 ≤ -35, -6 x2 - 
              2 x4 - 12 x5 + 3 x6 ≤ -35, -12 x2 + 
              3 x3 - 6 x5 - 2 x6 ≤ -35, -12 x2 - 
              2 x3 - 6 x5 + 3 x6 ≤ -35, -2 x1 + 
              3 x2 - 6 x3 - 12 x4 ≤ -35, -2 x1 - 
              12 x3 - 6 x4 + 3 x5 ≤ -35, -2 x1 - 
              6 x2 + 3 x3 - 12 x5 ≤ -35, -2 x1 - 
              12 x2 + 3 x4 - 6 x5 ≤ -35, -6 x1 + 
              3 x2 - 2 x3 - 12 x6 ≤ -35, -6 x1 + 
              3 x4 - 2 x5 - 12 x6 ≤ -35, -6 x1 - 
              2 x4 + 3 x5 - 12 x6 ≤ -35, -6 x1 - 
              2 x2 + 3 x3 - 12 x6 ≤ -35, -12 x1 + 
              3 x2 - 2 x4 - 6 x6 ≤ -35, -12 x1 + 
              3 x3 - 2 x5 - 6 x6 ≤ -35, -12 x1 - 
              2 x3 + 3 x5 - 6 x6 ≤ -35, -12 x1 - 
              2 x2 + 3 x4 - 6 x6 ≤ -35, 
          3 x1 - 8 x3 - 6 x4 - 2 x5 ≤ -31, 
          3 x1 - 2 x2 - 6 x3 - 8 x4 ≤ -31, 
          3 x1 - 6 x2 - 2 x3 - 8 x5 ≤ -31, 
          3 x1 - 8 x2 - 2 x4 - 6 x5 ≤ -31, 
          3 x2 - 8 x3 - 6 x4 - 2 x6 ≤ -31, -6 x3 - 
              8 x4 + 3 x5 - 2 x6 ≤ -31, -6 x3 - 
              8 x4 - 2 x5 + 3 x6 ≤ -31, -2 x2 - 
              8 x3 - 6 x4 + 3 x6 ≤ -31, -6 x2 + 
              3 x4 - 8 x5 - 2 x6 ≤ -31, -6 x2 - 
              2 x4 - 8 x5 + 3 x6 ≤ -31, -8 x2 + 
              3 x3 - 6 x5 - 2 x6 ≤ -31, -8 x2 - 
              2 x3 - 6 x5 + 3 x6 ≤ -31, -2 x1 + 
              3 x2 - 6 x3 - 8 x4 ≤ -31, -2 x1 - 
              8 x3 - 6 x4 + 3 x5 ≤ -31, -2 x1 - 
              6 x2 + 3 x3 - 8 x5 ≤ -31, -2 x1 - 
              8 x2 + 3 x4 - 6 x5 ≤ -31, -6 x1 + 
              3 x2 - 2 x3 - 8 x6 ≤ -31, -6 x1 + 
              3 x4 - 2 x5 - 8 x6 ≤ -31, -6 x1 - 
              2 x4 + 3 x5 - 8 x6 ≤ -31, -6 x1 - 
              2 x2 + 3 x3 - 8 x6 ≤ -31, -8 x1 + 
              3 x2 - 2 x4 - 6 x6 ≤ -31, -8 x1 + 
              3 x3 - 2 x5 - 6 x6 ≤ -31, -8 x1 - 
              2 x3 + 3 x5 - 6 x6 ≤ -31, -8 x1 - 
              2 x2 + 3 x4 - 6 x6 ≤ -31, 
          3 x1 - 2 x3 - 2 x4 - 2 x5 ≤ 33, 
          3 x1 - 2 x2 - 2 x4 - 2 x5 ≤ 33, 
          3 x1 - 2 x2 - 2 x3 - 2 x5 ≤ 33, 
          3 x1 - 2 x2 - 2 x3 - 2 x4 ≤ 33, 
          3 x2 - 2 x3 - 2 x4 - 2 x6 ≤ 
            33, -2 x3 - 2 x4 + 3 x5 - 2 x6 ≤ 
            33, -2 x3 - 2 x4 - 2 x5 + 3 x6 ≤ 
            33, -2 x2 + 3 x3 - 2 x5 - 2 x6 ≤ 
            33, -2 x2 + 3 x4 - 2 x5 - 2 x6 ≤ 
            33, -2 x2 - 2 x4 - 2 x5 + 3 x6 ≤ 
            33, -2 x2 - 2 x3 - 2 x5 + 3 x6 ≤ 
            33, -2 x2 - 2 x3 - 2 x4 + 3 x6 ≤ 
            33, -2 x1 + 3 x2 - 2 x4 - 2 x6 ≤ 
            33, -2 x1 + 3 x2 - 2 x3 - 2 x6 ≤ 
            33, -2 x1 + 3 x2 - 2 x3 - 2 x4 ≤ 
            33, -2 x1 + 3 x3 - 2 x5 - 2 x6 ≤ 
            33, -2 x1 + 3 x4 - 2 x5 - 2 x6 ≤ 
            33, -2 x1 - 2 x4 + 3 x5 - 2 x6 ≤ 
            33, -2 x1 - 2 x3 + 3 x5 - 2 x6 ≤ 
            33, -2 x1 - 2 x3 - 2 x4 + 3 x5 ≤ 
            33, -2 x1 - 2 x2 + 3 x3 - 2 x6 ≤ 
            33, -2 x1 - 2 x2 + 3 x3 - 2 x5 ≤ 
            33, -2 x1 - 2 x2 + 3 x4 - 2 x6 ≤ 
            33, -2 x1 - 2 x2 + 3 x4 - 2 x5 ≤ 33, 
          14 x1 + 8 x2 + 2 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 717, 
          14 x1 + 2 x2 + 8 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 717, 
          14 x1 + 2 x2 + 2 x3 + 8 x4 + 2 x5 + 5 x6 ≤ 717, 
          14 x1 + 2 x2 + 2 x3 + 2 x4 + 8 x5 + 5 x6 ≤ 717, 
          8 x1 + 14 x2 + 2 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 717, 
          8 x1 + 5 x2 + 2 x3 + 2 x4 + 14 x5 + 2 x6 ≤ 717, 
          8 x1 + 2 x2 + 14 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 717, 
          8 x1 + 2 x2 + 5 x3 + 14 x4 + 2 x5 + 2 x6 ≤ 717, 
          5 x1 + 8 x2 + 2 x3 + 2 x4 + 2 x5 + 14 x6 ≤ 717, 
          5 x1 + 2 x2 + 8 x3 + 2 x4 + 2 x5 + 14 x6 ≤ 717, 
          5 x1 + 2 x2 + 2 x3 + 8 x4 + 2 x5 + 14 x6 ≤ 717, 
          5 x1 + 2 x2 + 2 x3 + 2 x4 + 8 x5 + 14 x6 ≤ 717, 
          2 x1 + 14 x2 + 8 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 717, 
          2 x1 + 14 x2 + 2 x3 + 8 x4 + 5 x5 + 2 x6 ≤ 717, 
          2 x1 + 14 x2 + 2 x3 + 2 x4 + 5 x5 + 8 x6 ≤ 717, 
          2 x1 + 8 x2 + 14 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 717, 
          2 x1 + 8 x2 + 5 x3 + 14 x4 + 2 x5 + 2 x6 ≤ 717, 
          2 x1 + 5 x2 + 8 x3 + 2 x4 + 14 x5 + 2 x6 ≤ 717, 
          2 x1 + 5 x2 + 2 x3 + 8 x4 + 14 x5 + 2 x6 ≤ 717, 
          2 x1 + 5 x2 + 2 x3 + 2 x4 + 14 x5 + 8 x6 ≤ 717, 
          2 x1 + 2 x2 + 14 x3 + 5 x4 + 8 x5 + 2 x6 ≤ 717, 
          2 x1 + 2 x2 + 14 x3 + 5 x4 + 2 x5 + 8 x6 ≤ 717, 
          2 x1 + 2 x2 + 5 x3 + 14 x4 + 8 x5 + 2 x6 ≤ 717, 
          2 x1 + 2 x2 + 5 x3 + 14 x4 + 2 x5 + 8 x6 ≤ 717, 
          3 x1 - 6 x3 - 6 x4 - 2 x5 ≤ -23, 
          3 x1 - 2 x2 - 6 x3 - 6 x4 ≤ -23, 
          3 x1 - 6 x2 - 2 x4 - 6 x5 ≤ -23, 
          3 x1 - 6 x2 - 2 x3 - 6 x5 ≤ -23, 
          3 x2 - 6 x3 - 6 x4 - 2 x6 ≤ -23, -6 x3 - 
              6 x4 + 3 x5 - 2 x6 ≤ -23, -6 x3 - 
              6 x4 - 2 x5 + 3 x6 ≤ -23, -2 x2 - 
              6 x3 - 6 x4 + 3 x6 ≤ -23, -6 x2 + 
              3 x3 - 6 x5 - 2 x6 ≤ -23, -6 x2 + 
              3 x4 - 6 x5 - 2 x6 ≤ -23, -6 x2 - 
              2 x4 - 6 x5 + 3 x6 ≤ -23, -6 x2 - 
              2 x3 - 6 x5 + 3 x6 ≤ -23, -2 x1 + 
              3 x2 - 6 x3 - 6 x4 ≤ -23, -2 x1 - 
              6 x3 - 6 x4 + 3 x5 ≤ -23, -2 x1 - 
              6 x2 + 3 x3 - 6 x5 ≤ -23, -2 x1 - 
              6 x2 + 3 x4 - 6 x5 ≤ -23, -6 x1 + 
              3 x2 - 2 x4 - 6 x6 ≤ -23, -6 x1 + 
              3 x2 - 2 x3 - 6 x6 ≤ -23, -6 x1 + 
              3 x3 - 2 x5 - 6 x6 ≤ -23, -6 x1 + 
              3 x4 - 2 x5 - 6 x6 ≤ -23, -6 x1 - 
              2 x4 + 3 x5 - 6 x6 ≤ -23, -6 x1 - 
              2 x3 + 3 x5 - 6 x6 ≤ -23, -6 x1 - 
              2 x2 + 3 x3 - 6 x6 ≤ -23, -6 x1 - 
              2 x2 + 3 x4 - 6 x6 ≤ -23, 
          15 x1 + 6 x2 - 4 x5 ≤ 515, 
          15 x1 + 6 x3 - 4 x4 ≤ 515, 
          15 x1 - 4 x3 + 6 x4 ≤ 515, 
          15 x1 - 4 x2 + 6 x5 ≤ 515, 
          6 x1 + 15 x2 - 4 x6 ≤ 515, 
          6 x1 + 15 x3 - 4 x6 ≤ 515, 
          6 x1 + 15 x4 - 4 x6 ≤ 515, 
          6 x1 + 15 x5 - 4 x6 ≤ 515, 
          15 x2 + 6 x3 - 4 x4 ≤ 515, 
          15 x2 - 4 x3 + 6 x4 ≤ 515, 
          6 x2 + 15 x3 - 4 x5 ≤ 515, 
          6 x2 + 15 x4 - 4 x5 ≤ 515, 
          6 x2 - 4 x5 + 15 x6 ≤ 515, 
          6 x3 - 4 x4 + 15 x5 ≤ 515, 
          6 x3 - 4 x4 + 15 x6 ≤ 
            515, -4 x3 + 6 x4 + 15 x5 ≤ 
            515, -4 x3 + 6 x4 + 15 x6 ≤ 
            515, -4 x2 + 15 x3 + 6 x5 ≤ 
            515, -4 x2 + 15 x4 + 6 x5 ≤ 
            515, -4 x2 + 6 x5 + 15 x6 ≤ 
            515, -4 x1 + 15 x2 + 6 x6 ≤ 
            515, -4 x1 + 15 x3 + 6 x6 ≤ 
            515, -4 x1 + 15 x4 + 6 x6 ≤ 
            515, -4 x1 + 15 x5 + 6 x6 ≤ 515, 
          3 x1 - 4 x2 - 6 x3 - 6 x4 - 6 x5 - 
              10 x6 ≤ -325, 
          3 x1 - 6 x2 - 4 x3 - 6 x4 - 6 x5 - 
              10 x6 ≤ -325, 
          3 x1 - 6 x2 - 6 x3 - 4 x4 - 6 x5 - 
              10 x6 ≤ -325, 
          3 x1 - 6 x2 - 6 x3 - 6 x4 - 4 x5 - 
              10 x6 ≤ -325, -4 x1 + 3 x2 - 6 x3 - 
              6 x4 - 10 x5 - 6 x6 ≤ -325, -4 x1 - 
              6 x2 + 3 x3 - 10 x4 - 6 x5 - 
              6 x6 ≤ -325, -4 x1 - 6 x2 - 10 x3 + 
              3 x4 - 6 x5 - 6 x6 ≤ -325, -4 x1 - 
              10 x2 - 6 x3 - 6 x4 + 3 x5 - 
              6 x6 ≤ -325, -6 x1 + 3 x2 - 4 x3 - 
              6 x4 - 10 x5 - 6 x6 ≤ -325, -6 x1 + 
              3 x2 - 6 x3 - 4 x4 - 10 x5 - 
              6 x6 ≤ -325, -6 x1 + 3 x2 - 6 x3 - 
              6 x4 - 10 x5 - 4 x6 ≤ -325, -6 x1 - 
              4 x2 + 3 x3 - 10 x4 - 6 x5 - 
              6 x6 ≤ -325, -6 x1 - 4 x2 - 10 x3 + 
              3 x4 - 6 x5 - 6 x6 ≤ -325, -6 x1 - 
              6 x2 + 3 x3 - 10 x4 - 4 x5 - 
              6 x6 ≤ -325, -6 x1 - 6 x2 + 3 x3 - 
              10 x4 - 6 x5 - 4 x6 ≤ -325, -6 x1 - 
              6 x2 - 10 x3 + 3 x4 - 4 x5 - 
              6 x6 ≤ -325, -6 x1 - 6 x2 - 10 x3 + 
              3 x4 - 6 x5 - 4 x6 ≤ -325, -6 x1 - 
              10 x2 - 4 x3 - 6 x4 + 3 x5 - 
              6 x6 ≤ -325, -6 x1 - 10 x2 - 6 x3 - 
              4 x4 + 3 x5 - 6 x6 ≤ -325, -6 x1 - 
              10 x2 - 6 x3 - 6 x4 + 3 x5 - 
              4 x6 ≤ -325, -10 x1 - 4 x2 - 6 x3 - 
              6 x4 - 6 x5 + 3 x6 ≤ -325, -10 x1 - 
              6 x2 - 4 x3 - 6 x4 - 6 x5 + 
              3 x6 ≤ -325, -10 x1 - 6 x2 - 6 x3 - 
              4 x4 - 6 x5 + 3 x6 ≤ -325, -10 x1 - 
              6 x2 - 6 x3 - 6 x4 - 4 x5 + 3 x6 ≤ -325, 
          5 x1 - 2 x2 - 4 x3 - 4 x4 - 4 x5 - 
              8 x6 ≤ -139, 
          5 x1 - 4 x2 - 2 x3 - 4 x4 - 4 x5 - 
              8 x6 ≤ -139, 
          5 x1 - 4 x2 - 4 x3 - 2 x4 - 4 x5 - 
              8 x6 ≤ -139, 
          5 x1 - 4 x2 - 4 x3 - 4 x4 - 2 x5 - 
              8 x6 ≤ -139, -2 x1 + 5 x2 - 4 x3 - 
              4 x4 - 8 x5 - 4 x6 ≤ -139, -2 x1 - 
              4 x2 + 5 x3 - 8 x4 - 4 x5 - 
              4 x6 ≤ -139, -2 x1 - 4 x2 - 8 x3 + 
              5 x4 - 4 x5 - 4 x6 ≤ -139, -2 x1 - 
              8 x2 - 4 x3 - 4 x4 + 5 x5 - 
              4 x6 ≤ -139, -4 x1 + 5 x2 - 2 x3 - 
              4 x4 - 8 x5 - 4 x6 ≤ -139, -4 x1 + 
              5 x2 - 4 x3 - 2 x4 - 8 x5 - 
              4 x6 ≤ -139, -4 x1 + 5 x2 - 4 x3 - 
              4 x4 - 8 x5 - 2 x6 ≤ -139, -4 x1 - 
              2 x2 + 5 x3 - 8 x4 - 4 x5 - 
              4 x6 ≤ -139, -4 x1 - 2 x2 - 8 x3 + 
              5 x4 - 4 x5 - 4 x6 ≤ -139, -4 x1 - 
              4 x2 + 5 x3 - 8 x4 - 2 x5 - 
              4 x6 ≤ -139, -4 x1 - 4 x2 + 5 x3 - 
              8 x4 - 4 x5 - 2 x6 ≤ -139, -4 x1 - 
              4 x2 - 8 x3 + 5 x4 - 2 x5 - 
              4 x6 ≤ -139, -4 x1 - 4 x2 - 8 x3 + 
              5 x4 - 4 x5 - 2 x6 ≤ -139, -4 x1 - 
              8 x2 - 2 x3 - 4 x4 + 5 x5 - 
              4 x6 ≤ -139, -4 x1 - 8 x2 - 4 x3 - 
              2 x4 + 5 x5 - 4 x6 ≤ -139, -4 x1 - 
              8 x2 - 4 x3 - 4 x4 + 5 x5 - 
              2 x6 ≤ -139, -8 x1 - 2 x2 - 4 x3 - 
              4 x4 - 4 x5 + 5 x6 ≤ -139, -8 x1 - 
              4 x2 - 2 x3 - 4 x4 - 4 x5 + 
              5 x6 ≤ -139, -8 x1 - 4 x2 - 4 x3 - 
              2 x4 - 4 x5 + 5 x6 ≤ -139, -8 x1 - 
              4 x2 - 4 x3 - 4 x4 - 2 x5 + 5 x6 ≤ -139, 
          13 x1 + 6 x2 + 4 x3 + 4 x4 + 4 x5 ≤ 653, 
          13 x1 + 4 x2 + 6 x3 + 4 x4 + 4 x5 ≤ 653, 
          13 x1 + 4 x2 + 4 x3 + 6 x4 + 4 x5 ≤ 653, 
          13 x1 + 4 x2 + 4 x3 + 4 x4 + 6 x5 ≤ 653, 
          6 x1 + 13 x2 + 4 x3 + 4 x4 + 4 x6 ≤ 653, 
          6 x1 + 4 x2 + 13 x3 + 4 x5 + 4 x6 ≤ 653, 
          6 x1 + 4 x2 + 13 x4 + 4 x5 + 4 x6 ≤ 653, 
          6 x1 + 4 x3 + 4 x4 + 13 x5 + 4 x6 ≤ 653, 
          4 x1 + 13 x2 + 6 x3 + 4 x4 + 4 x6 ≤ 653, 
          4 x1 + 13 x2 + 4 x3 + 6 x4 + 4 x6 ≤ 653, 
          4 x1 + 13 x2 + 4 x3 + 4 x4 + 6 x6 ≤ 653, 
          4 x1 + 6 x2 + 13 x3 + 4 x5 + 4 x6 ≤ 653, 
          4 x1 + 6 x2 + 13 x4 + 4 x5 + 4 x6 ≤ 653, 
          4 x1 + 4 x2 + 13 x3 + 6 x5 + 4 x6 ≤ 653, 
          4 x1 + 4 x2 + 13 x3 + 4 x5 + 6 x6 ≤ 653, 
          4 x1 + 4 x2 + 13 x4 + 6 x5 + 4 x6 ≤ 653, 
          4 x1 + 4 x2 + 13 x4 + 4 x5 + 6 x6 ≤ 653, 
          4 x1 + 6 x3 + 4 x4 + 13 x5 + 4 x6 ≤ 653, 
          4 x1 + 4 x3 + 6 x4 + 13 x5 + 4 x6 ≤ 653, 
          4 x1 + 4 x3 + 4 x4 + 13 x5 + 6 x6 ≤ 653, 
          6 x2 + 4 x3 + 4 x4 + 4 x5 + 13 x6 ≤ 653, 
          4 x2 + 6 x3 + 4 x4 + 4 x5 + 13 x6 ≤ 653, 
          4 x2 + 4 x3 + 6 x4 + 4 x5 + 13 x6 ≤ 653, 
          4 x2 + 4 x3 + 4 x4 + 6 x5 + 13 x6 ≤ 
            653, -x3 - x4 - 2 x6 ≤ -28, -x3 - x4 - 
              2 x5 ≤ -28, -x2 - x5 - 
              2 x6 ≤ -28, -x2 - 2 x4 - 
              x5 ≤ -28, -x2 - 2 x3 - 
              x5 ≤ -28, -2 x2 - x3 - 
              x4 ≤ -28, -x1 - 2 x5 - 
              x6 ≤ -28, -x1 - 2 x4 - 
              x6 ≤ -28, -x1 - 2 x3 - 
              x6 ≤ -28, -x1 - 2 x2 - 
              x6 ≤ -28, -2 x1 - x3 - 
              x4 ≤ -28, -2 x1 - x2 - 
              x5 ≤ -28, -x3 - 2 x4 - 2 x5 - 
              3 x6 ≤ -88, -x3 - 2 x4 - 3 x5 - 
              2 x6 ≤ -88, -x2 - 2 x4 - 2 x5 - 
              3 x6 ≤ -88, -x2 - 3 x4 - 2 x5 - 
              2 x6 ≤ -88, -2 x2 - 2 x3 - x5 - 
              3 x6 ≤ -88, -2 x2 - 2 x3 - x4 - 
              3 x6 ≤ -88, -2 x2 - 3 x3 - x5 - 
              2 x6 ≤ -88, -3 x2 - 2 x3 - x4 - 
              2 x6 ≤ -88, -x1 - 2 x4 - 3 x5 - 
              2 x6 ≤ -88, -x1 - 3 x4 - 2 x5 - 
              2 x6 ≤ -88, -x1 - 2 x2 - 3 x3 - 
              2 x6 ≤ -88, -x1 - 3 x2 - 2 x3 - 
              2 x6 ≤ -88, -2 x1 - 2 x3 - 3 x5 - 
              x6 ≤ -88, -2 x1 - 2 x3 - x4 - 
              3 x5 ≤ -88, -2 x1 - 3 x3 - 2 x5 - 
              x6 ≤ -88, -2 x1 - x2 - 3 x3 - 
              2 x5 ≤ -88, -2 x1 - 2 x2 - 3 x4 - 
              x6 ≤ -88, -2 x1 - 2 x2 - 3 x4 - 
              x5 ≤ -88, -2 x1 - 3 x2 - 2 x4 - 
              x6 ≤ -88, -2 x1 - 3 x2 - x3 - 
              2 x4 ≤ -88, -3 x1 - 2 x3 - x4 - 
              2 x5 ≤ -88, -3 x1 - x2 - 2 x3 - 
              2 x5 ≤ -88, -3 x1 - 2 x2 - 2 x4 - 
              x5 ≤ -88, -3 x1 - 2 x2 - x3 - 
              2 x4 ≤ -88, -x2 - 2 x3 - 2 x4 - 2 x5 - 
              4 x6 ≤ -127, -2 x2 - x3 - 2 x4 - 2 x5 - 
              4 x6 ≤ -127, -2 x2 - 2 x3 - x4 - 2 x5 - 
              4 x6 ≤ -127, -2 x2 - 2 x3 - 2 x4 - x5 - 
              4 x6 ≤ -127, -x1 - 2 x3 - 2 x4 - 4 x5 - 
              2 x6 ≤ -127, -x1 - 2 x2 - 4 x4 - 2 x5 - 
              2 x6 ≤ -127, -x1 - 2 x2 - 4 x3 - 2 x5 - 
              2 x6 ≤ -127, -x1 - 4 x2 - 2 x3 - 2 x4 - 
              2 x6 ≤ -127, -2 x1 - x3 - 2 x4 - 4 x5 - 
              2 x6 ≤ -127, -2 x1 - 2 x3 - x4 - 4 x5 - 
              2 x6 ≤ -127, -2 x1 - 2 x3 - 2 x4 - 
              4 x5 - x6 ≤ -127, -2 x1 - x2 - 4 x4 - 
              2 x5 - 2 x6 ≤ -127, -2 x1 - x2 - 4 x3 - 
              2 x5 - 2 x6 ≤ -127, -2 x1 - 2 x2 - 
              4 x4 - x5 - 2 x6 ≤ -127, -2 x1 - 2 x2 - 
              4 x4 - 2 x5 - x6 ≤ -127, -2 x1 - 2 x2 - 
              4 x3 - x5 - 2 x6 ≤ -127, -2 x1 - 2 x2 - 
              4 x3 - 2 x5 - x6 ≤ -127, -2 x1 - 4 x2 - 
              x3 - 2 x4 - 2 x6 ≤ -127, -2 x1 - 4 x2 - 
              2 x3 - x4 - 2 x6 ≤ -127, -2 x1 - 4 x2 - 
              2 x3 - 2 x4 - x6 ≤ -127, -4 x1 - x2 - 
              2 x3 - 2 x4 - 2 x5 ≤ -127, -4 x1 - 
              2 x2 - x3 - 2 x4 - 2 x5 ≤ -127, -4 x1 - 
              2 x2 - 2 x3 - x4 - 2 x5 ≤ -127, -4 x1 - 
              2 x2 - 2 x3 - 2 x4 - x5 ≤ -127, 
          x1 - x2 - 2 x3 - 2 x4 - 2 x5 - 4 x6 ≤ -106, 
          x1 - 2 x2 - x3 - 2 x4 - 2 x5 - 4 x6 ≤ -106, 
          x1 - 2 x2 - 2 x3 - x4 - 2 x5 - 4 x6 ≤ -106, 
          x1 - 2 x2 - 2 x3 - 2 x4 - x5 - 
              4 x6 ≤ -106, -x1 + x2 - 2 x3 - 2 x4 - 
              4 x5 - 2 x6 ≤ -106, -x1 - 2 x2 + x3 - 
              4 x4 - 2 x5 - 2 x6 ≤ -106, -x1 - 2 x2 - 
              4 x3 + x4 - 2 x5 - 2 x6 ≤ -106, -x1 - 
              4 x2 - 2 x3 - 2 x4 + x5 - 
              2 x6 ≤ -106, -2 x1 + x2 - x3 - 2 x4 - 
              4 x5 - 2 x6 ≤ -106, -2 x1 + x2 - 2 x3 - 
              x4 - 4 x5 - 2 x6 ≤ -106, -2 x1 + x2 - 
              2 x3 - 2 x4 - 4 x5 - x6 ≤ -106, -2 x1 - 
              x2 + x3 - 4 x4 - 2 x5 - 
              2 x6 ≤ -106, -2 x1 - x2 - 4 x3 + x4 - 
              2 x5 - 2 x6 ≤ -106, -2 x1 - 2 x2 + x3 - 
              4 x4 - x5 - 2 x6 ≤ -106, -2 x1 - 2 x2 + 
              x3 - 4 x4 - 2 x5 - x6 ≤ -106, -2 x1 - 
              2 x2 - 4 x3 + x4 - x5 - 
              2 x6 ≤ -106, -2 x1 - 2 x2 - 4 x3 + x4 - 
              2 x5 - x6 ≤ -106, -2 x1 - 4 x2 - x3 - 
              2 x4 + x5 - 2 x6 ≤ -106, -2 x1 - 4 x2 - 
              2 x3 - x4 + x5 - 2 x6 ≤ -106, -2 x1 - 
              4 x2 - 2 x3 - 2 x4 + x5 - 
              x6 ≤ -106, -4 x1 - x2 - 2 x3 - 2 x4 - 
              2 x5 + x6 ≤ -106, -4 x1 - 2 x2 - x3 - 
              2 x4 - 2 x5 + x6 ≤ -106, -4 x1 - 2 x2 - 
              2 x3 - x4 - 2 x5 + x6 ≤ -106, -4 x1 - 
              2 x2 - 2 x3 - 2 x4 - x5 + x6 ≤ -106, 
          x1 - 2 x2 - 2 x3 - 2 x4 - 4 x5 - 4 x6 ≤ -139, 
          x1 - 2 x2 - 2 x3 - 4 x4 - 2 x5 - 4 x6 ≤ -139, 
          x1 - 2 x2 - 4 x3 - 2 x4 - 2 x5 - 4 x6 ≤ -139, 
          x1 - 4 x2 - 2 x3 - 2 x4 - 2 x5 - 
              4 x6 ≤ -139, -2 x1 + x2 - 2 x3 - 2 x4 - 
              4 x5 - 4 x6 ≤ -139, -2 x1 + x2 - 2 x3 - 
              4 x4 - 4 x5 - 2 x6 ≤ -139, -2 x1 + x2 - 
              4 x3 - 2 x4 - 4 x5 - 
              2 x6 ≤ -139, -2 x1 - 2 x2 + x3 - 4 x4 - 
              2 x5 - 4 x6 ≤ -139, -2 x1 - 2 x2 + x3 - 
              4 x4 - 4 x5 - 2 x6 ≤ -139, -2 x1 - 
              2 x2 - 4 x3 + x4 - 2 x5 - 
              4 x6 ≤ -139, -2 x1 - 2 x2 - 4 x3 + x4 - 
              4 x5 - 2 x6 ≤ -139, -2 x1 - 4 x2 + x3 - 
              4 x4 - 2 x5 - 2 x6 ≤ -139, -2 x1 - 
              4 x2 - 2 x3 - 2 x4 + x5 - 
              4 x6 ≤ -139, -2 x1 - 4 x2 - 2 x3 - 
              4 x4 + x5 - 2 x6 ≤ -139, -2 x1 - 4 x2 - 
              4 x3 + x4 - 2 x5 - 2 x6 ≤ -139, -2 x1 - 
              4 x2 - 4 x3 - 2 x4 + x5 - 
              2 x6 ≤ -139, -4 x1 + x2 - 2 x3 - 2 x4 - 
              4 x5 - 2 x6 ≤ -139, -4 x1 - 2 x2 + x3 - 
              4 x4 - 2 x5 - 2 x6 ≤ -139, -4 x1 - 
              2 x2 - 2 x3 - 2 x4 - 4 x5 + 
              x6 ≤ -139, -4 x1 - 2 x2 - 2 x3 - 4 x4 - 
              2 x5 + x6 ≤ -139, -4 x1 - 2 x2 - 4 x3 + 
              x4 - 2 x5 - 2 x6 ≤ -139, -4 x1 - 2 x2 - 
              4 x3 - 2 x4 - 2 x5 + x6 ≤ -139, -4 x1 - 
              4 x2 - 2 x3 - 2 x4 + x5 - 
              2 x6 ≤ -139, -4 x1 - 4 x2 - 2 x3 - 
              2 x4 - 2 x5 + x6 ≤ -139, 
          3 x1 - 6 x3 - 8 x4 ≤ -3, 
          3 x1 - 8 x3 - 6 x4 ≤ -3, 
          3 x1 - 6 x2 - 8 x5 ≤ -3, 
          3 x1 - 8 x2 - 6 x5 ≤ -3, 
          3 x2 - 6 x3 - 8 x4 ≤ -3, 
          3 x2 - 8 x3 - 6 x4 ≤ -3, -6 x3 - 8 x4 + 
              3 x5 ≤ -3, -6 x3 - 8 x4 + 
              3 x6 ≤ -3, -8 x3 - 6 x4 + 
              3 x5 ≤ -3, -8 x3 - 6 x4 + 
              3 x6 ≤ -3, -6 x2 + 3 x3 - 
              8 x5 ≤ -3, -6 x2 + 3 x4 - 
              8 x5 ≤ -3, -6 x2 - 8 x5 + 
              3 x6 ≤ -3, -8 x2 + 3 x3 - 
              6 x5 ≤ -3, -8 x2 + 3 x4 - 
              6 x5 ≤ -3, -8 x2 - 6 x5 + 
              3 x6 ≤ -3, -6 x1 + 3 x2 - 
              8 x6 ≤ -3, -6 x1 + 3 x3 - 
              8 x6 ≤ -3, -6 x1 + 3 x4 - 
              8 x6 ≤ -3, -6 x1 + 3 x5 - 
              8 x6 ≤ -3, -8 x1 + 3 x2 - 
              6 x6 ≤ -3, -8 x1 + 3 x3 - 
              6 x6 ≤ -3, -8 x1 + 3 x4 - 
              6 x6 ≤ -3, -8 x1 + 3 x5 - 
              6 x6 ≤ -3, 
          9 x1 + 6 x2 - 6 x3 + 4 x5 + 6 x6 ≤ 523, 
          9 x1 + 4 x2 - 6 x4 + 6 x5 + 6 x6 ≤ 523, 
          9 x1 + 4 x3 + 6 x4 - 6 x5 + 6 x6 ≤ 523, 
          9 x1 - 6 x2 + 6 x3 + 4 x4 + 6 x6 ≤ 523, 
          6 x1 + 9 x2 - 6 x3 + 6 x5 + 4 x6 ≤ 523, 
          6 x1 + 6 x2 - 6 x4 + 9 x5 + 4 x6 ≤ 523, 
          6 x1 + 6 x2 - 6 x4 + 4 x5 + 9 x6 ≤ 523, 
          6 x1 + 4 x2 - 6 x3 + 6 x5 + 9 x6 ≤ 523, 
          6 x1 + 6 x3 + 9 x4 - 6 x5 + 4 x6 ≤ 523, 
          6 x1 + 6 x3 + 4 x4 - 6 x5 + 9 x6 ≤ 523, 
          6 x1 - 6 x2 + 9 x3 + 6 x4 + 4 x6 ≤ 523, 
          6 x1 - 6 x2 + 4 x3 + 6 x4 + 9 x6 ≤ 523, 
          4 x1 + 9 x2 - 6 x4 + 6 x5 + 6 x6 ≤ 523, 
          4 x1 + 6 x2 - 6 x3 + 9 x5 + 6 x6 ≤ 523, 
          4 x1 + 9 x3 + 6 x4 - 6 x5 + 6 x6 ≤ 523, 
          4 x1 - 6 x2 + 6 x3 + 9 x4 + 6 x6 ≤ 523, 
          9 x2 + 4 x3 + 6 x4 + 6 x5 - 6 x6 ≤ 523, 
          6 x2 + 6 x3 + 9 x4 + 4 x5 - 6 x6 ≤ 523, 
          6 x2 + 6 x3 + 4 x4 + 9 x5 - 6 x6 ≤ 523, 
          4 x2 + 9 x3 + 6 x4 + 6 x5 - 6 x6 ≤ 
            523, -6 x1 + 9 x2 + 6 x3 + 4 x4 + 6 x5 ≤ 
            523, -6 x1 + 6 x2 + 9 x3 + 6 x4 + 4 x5 ≤ 
            523, -6 x1 + 6 x2 + 4 x3 + 6 x4 + 9 x5 ≤ 
            523, -6 x1 + 4 x2 + 6 x3 + 9 x4 + 6 x5 ≤ 523, 
          81 x1 + 54 x2 - 18 x3 + 48 x5 + 32 x6 ≤ 4529, 
          81 x1 + 48 x2 - 18 x4 + 54 x5 + 32 x6 ≤ 4529, 
          81 x1 + 48 x3 + 54 x4 - 18 x5 + 32 x6 ≤ 4529, 
          81 x1 - 18 x2 + 54 x3 + 48 x4 + 32 x6 ≤ 4529, 
          54 x1 + 81 x2 - 18 x3 + 32 x5 + 48 x6 ≤ 4529, 
          54 x1 + 32 x2 - 18 x4 + 81 x5 + 48 x6 ≤ 4529, 
          54 x1 + 32 x3 + 81 x4 - 18 x5 + 48 x6 ≤ 4529, 
          54 x1 - 18 x2 + 81 x3 + 32 x4 + 48 x6 ≤ 4529, 
          48 x1 + 81 x2 - 18 x4 + 32 x5 + 54 x6 ≤ 4529, 
          48 x1 + 32 x2 - 18 x3 + 81 x5 + 54 x6 ≤ 4529, 
          48 x1 + 81 x3 + 32 x4 - 18 x5 + 54 x6 ≤ 4529, 
          48 x1 - 18 x2 + 32 x3 + 81 x4 + 54 x6 ≤ 4529, 
          32 x1 + 54 x2 - 18 x4 + 48 x5 + 81 x6 ≤ 4529, 
          32 x1 + 48 x2 - 18 x3 + 54 x5 + 81 x6 ≤ 4529, 
          32 x1 + 54 x3 + 48 x4 - 18 x5 + 81 x6 ≤ 4529, 
          32 x1 - 18 x2 + 48 x3 + 54 x4 + 81 x6 ≤ 4529, 
          81 x2 + 48 x3 + 54 x4 + 32 x5 - 18 x6 ≤ 4529, 
          54 x2 + 32 x3 + 81 x4 + 48 x5 - 18 x6 ≤ 4529, 
          48 x2 + 81 x3 + 32 x4 + 54 x5 - 18 x6 ≤ 4529, 
          32 x2 + 54 x3 + 48 x4 + 81 x5 - 18 x6 ≤ 
            4529, -18 x1 + 81 x2 + 54 x3 + 48 x4 + 
              32 x5 ≤ 
            4529, -18 x1 + 54 x2 + 81 x3 + 32 x4 + 
              48 x5 ≤ 
            4529, -18 x1 + 48 x2 + 32 x3 + 81 x4 + 
              54 x5 ≤ 
            4529, -18 x1 + 32 x2 + 48 x3 + 54 x4 + 
              81 x5 ≤ 4529, 
          14 x1 + 11 x2 + 2 x3 + 2 x4 + 8 x5 + 8 x6 ≤ 915, 
          14 x1 + 8 x2 + 2 x3 + 2 x4 + 11 x5 + 8 x6 ≤ 915, 
          14 x1 + 2 x2 + 11 x3 + 8 x4 + 2 x5 + 8 x6 ≤ 915, 
          14 x1 + 2 x2 + 8 x3 + 11 x4 + 2 x5 + 8 x6 ≤ 915, 
          11 x1 + 14 x2 + 2 x3 + 2 x4 + 8 x5 + 8 x6 ≤ 915, 
          11 x1 + 8 x2 + 2 x3 + 2 x4 + 14 x5 + 8 x6 ≤ 915, 
          11 x1 + 2 x2 + 14 x3 + 8 x4 + 2 x5 + 8 x6 ≤ 915, 
          11 x1 + 2 x2 + 8 x3 + 14 x4 + 2 x5 + 8 x6 ≤ 915, 
          8 x1 + 14 x2 + 2 x3 + 2 x4 + 8 x5 + 11 x6 ≤ 915, 
          8 x1 + 11 x2 + 2 x3 + 2 x4 + 8 x5 + 14 x6 ≤ 915, 
          8 x1 + 8 x2 + 2 x3 + 2 x4 + 14 x5 + 11 x6 ≤ 915, 
          8 x1 + 8 x2 + 2 x3 + 2 x4 + 11 x5 + 14 x6 ≤ 915, 
          8 x1 + 2 x2 + 14 x3 + 8 x4 + 2 x5 + 11 x6 ≤ 915, 
          8 x1 + 2 x2 + 11 x3 + 8 x4 + 2 x5 + 14 x6 ≤ 915, 
          8 x1 + 2 x2 + 8 x3 + 14 x4 + 2 x5 + 11 x6 ≤ 915, 
          8 x1 + 2 x2 + 8 x3 + 11 x4 + 2 x5 + 14 x6 ≤ 915, 
          2 x1 + 14 x2 + 11 x3 + 8 x4 + 8 x5 + 2 x6 ≤ 915, 
          2 x1 + 14 x2 + 8 x3 + 11 x4 + 8 x5 + 2 x6 ≤ 915, 
          2 x1 + 11 x2 + 14 x3 + 8 x4 + 8 x5 + 2 x6 ≤ 915, 
          2 x1 + 11 x2 + 8 x3 + 14 x4 + 8 x5 + 2 x6 ≤ 915, 
          2 x1 + 8 x2 + 14 x3 + 8 x4 + 11 x5 + 2 x6 ≤ 915, 
          2 x1 + 8 x2 + 11 x3 + 8 x4 + 14 x5 + 2 x6 ≤ 915, 
          2 x1 + 8 x2 + 8 x3 + 14 x4 + 11 x5 + 2 x6 ≤ 915, 
          2 x1 + 8 x2 + 8 x3 + 11 x4 + 14 x5 + 2 x6 ≤ 915, 
          x1 - 2 x5 ≤ 25, x1 - 2 x4 ≤ 25, 
          x1 - 2 x3 ≤ 25, x1 - 2 x2 ≤ 25, 
          x2 - 2 x6 ≤ 25, x2 - 2 x4 ≤ 25, 
          x2 - 2 x3 ≤ 25, x3 - 2 x6 ≤ 25, 
          x3 - 2 x5 ≤ 25, x4 - 2 x6 ≤ 25, 
          x4 - 2 x5 ≤ 25, 
          x5 - 2 x6 ≤ 25, -2 x5 + x6 ≤ 
            25, -2 x4 + x5 ≤ 25, -2 x4 + x6 ≤ 
            25, -2 x3 + x5 ≤ 25, -2 x3 + x6 ≤ 
            25, -2 x2 + x3 ≤ 25, -2 x2 + x4 ≤ 
            25, -2 x2 + x6 ≤ 25, -2 x1 + x2 ≤ 
            25, -2 x1 + x3 ≤ 25, -2 x1 + x4 ≤ 
            25, -2 x1 + x5 ≤ 25, 
          9 x1 - 24 x3 - 18 x4 - 2 x5 ≤ -41, 
          9 x1 - 2 x2 - 18 x3 - 24 x4 ≤ -41, 
          9 x1 - 18 x2 - 2 x3 - 24 x5 ≤ -41, 
          9 x1 - 24 x2 - 2 x4 - 18 x5 ≤ -41, 
          9 x2 - 24 x3 - 18 x4 - 2 x6 ≤ -41, -18 x3 - 
              24 x4 + 9 x5 - 2 x6 ≤ -41, -18 x3 - 
              24 x4 - 2 x5 + 9 x6 ≤ -41, -2 x2 - 
              24 x3 - 18 x4 + 9 x6 ≤ -41, -18 x2 + 
              9 x4 - 24 x5 - 2 x6 ≤ -41, -18 x2 - 
              2 x4 - 24 x5 + 9 x6 ≤ -41, -24 x2 + 
              9 x3 - 18 x5 - 2 x6 ≤ -41, -24 x2 - 
              2 x3 - 18 x5 + 9 x6 ≤ -41, -2 x1 + 
              9 x2 - 18 x3 - 24 x4 ≤ -41, -2 x1 - 
              24 x3 - 18 x4 + 9 x5 ≤ -41, -2 x1 - 
              18 x2 + 9 x3 - 24 x5 ≤ -41, -2 x1 - 
              24 x2 + 9 x4 - 18 x5 ≤ -41, -18 x1 + 
              9 x2 - 2 x3 - 24 x6 ≤ -41, -18 x1 + 
              9 x4 - 2 x5 - 24 x6 ≤ -41, -18 x1 - 
              2 x4 + 9 x5 - 24 x6 ≤ -41, -18 x1 - 
              2 x2 + 9 x3 - 24 x6 ≤ -41, -24 x1 + 
              9 x2 - 2 x4 - 18 x6 ≤ -41, -24 x1 + 
              9 x3 - 2 x5 - 18 x6 ≤ -41, -24 x1 - 
              2 x3 + 9 x5 - 18 x6 ≤ -41, -24 x1 - 
              2 x2 + 9 x4 - 18 x6 ≤ -41, 
          3 x1 - 4 x3 - 6 x4 ≤ 23, 
          3 x1 - 6 x3 - 4 x4 ≤ 23, 
          3 x1 - 4 x2 - 6 x5 ≤ 23, 
          3 x1 - 6 x2 - 4 x5 ≤ 23, 
          3 x2 - 4 x3 - 6 x4 ≤ 23, 
          3 x2 - 6 x3 - 4 x4 ≤ 
            23, -4 x3 - 6 x4 + 3 x5 ≤ 
            23, -4 x3 - 6 x4 + 3 x6 ≤ 
            23, -6 x3 - 4 x4 + 3 x5 ≤ 
            23, -6 x3 - 4 x4 + 3 x6 ≤ 
            23, -4 x2 + 3 x3 - 6 x5 ≤ 
            23, -4 x2 + 3 x4 - 6 x5 ≤ 
            23, -4 x2 - 6 x5 + 3 x6 ≤ 
            23, -6 x2 + 3 x3 - 4 x5 ≤ 
            23, -6 x2 + 3 x4 - 4 x5 ≤ 
            23, -6 x2 - 4 x5 + 3 x6 ≤ 
            23, -4 x1 + 3 x2 - 6 x6 ≤ 
            23, -4 x1 + 3 x3 - 6 x6 ≤ 
            23, -4 x1 + 3 x4 - 6 x6 ≤ 
            23, -4 x1 + 3 x5 - 6 x6 ≤ 
            23, -6 x1 + 3 x2 - 4 x6 ≤ 
            23, -6 x1 + 3 x3 - 4 x6 ≤ 
            23, -6 x1 + 3 x4 - 4 x6 ≤ 
            23, -6 x1 + 3 x5 - 4 x6 ≤ 23, 
          15 x1 + 6 x2 + 4 x3 + 4 x4 + 6 x5 ≤ 743, 
          15 x1 + 4 x2 + 6 x3 + 6 x4 + 4 x5 ≤ 743, 
          6 x1 + 15 x2 + 4 x3 + 4 x4 + 6 x6 ≤ 743, 
          6 x1 + 4 x2 + 15 x3 + 4 x5 + 6 x6 ≤ 743, 
          6 x1 + 4 x2 + 15 x4 + 4 x5 + 6 x6 ≤ 743, 
          6 x1 + 4 x3 + 4 x4 + 15 x5 + 6 x6 ≤ 743, 
          4 x1 + 15 x2 + 6 x3 + 6 x4 + 4 x6 ≤ 743, 
          4 x1 + 6 x2 + 15 x3 + 6 x5 + 4 x6 ≤ 743, 
          4 x1 + 6 x2 + 15 x4 + 6 x5 + 4 x6 ≤ 743, 
          4 x1 + 6 x3 + 6 x4 + 15 x5 + 4 x6 ≤ 743, 
          6 x2 + 4 x3 + 4 x4 + 6 x5 + 15 x6 ≤ 743, 
          4 x2 + 6 x3 + 6 x4 + 4 x5 + 15 x6 ≤ 743, 
          9 x1 + 6 x2 - 2 x3 + 4 x5 + 6 x6 ≤ 527, 
          9 x1 + 4 x2 - 2 x4 + 6 x5 + 6 x6 ≤ 527, 
          9 x1 + 4 x3 + 6 x4 - 2 x5 + 6 x6 ≤ 527, 
          9 x1 - 2 x2 + 6 x3 + 4 x4 + 6 x6 ≤ 527, 
          6 x1 + 9 x2 - 2 x3 + 6 x5 + 4 x6 ≤ 527, 
          6 x1 + 6 x2 - 2 x4 + 9 x5 + 4 x6 ≤ 527, 
          6 x1 + 6 x2 - 2 x4 + 4 x5 + 9 x6 ≤ 527, 
          6 x1 + 4 x2 - 2 x3 + 6 x5 + 9 x6 ≤ 527, 
          6 x1 + 6 x3 + 9 x4 - 2 x5 + 4 x6 ≤ 527, 
          6 x1 + 6 x3 + 4 x4 - 2 x5 + 9 x6 ≤ 527, 
          6 x1 - 2 x2 + 9 x3 + 6 x4 + 4 x6 ≤ 527, 
          6 x1 - 2 x2 + 4 x3 + 6 x4 + 9 x6 ≤ 527, 
          4 x1 + 9 x2 - 2 x4 + 6 x5 + 6 x6 ≤ 527, 
          4 x1 + 6 x2 - 2 x3 + 9 x5 + 6 x6 ≤ 527, 
          4 x1 + 9 x3 + 6 x4 - 2 x5 + 6 x6 ≤ 527, 
          4 x1 - 2 x2 + 6 x3 + 9 x4 + 6 x6 ≤ 527, 
          9 x2 + 4 x3 + 6 x4 + 6 x5 - 2 x6 ≤ 527, 
          6 x2 + 6 x3 + 9 x4 + 4 x5 - 2 x6 ≤ 527, 
          6 x2 + 6 x3 + 4 x4 + 9 x5 - 2 x6 ≤ 527, 
          4 x2 + 9 x3 + 6 x4 + 6 x5 - 2 x6 ≤ 
            527, -2 x1 + 9 x2 + 6 x3 + 4 x4 + 6 x5 ≤ 
            527, -2 x1 + 6 x2 + 9 x3 + 6 x4 + 4 x5 ≤ 
            527, -2 x1 + 6 x2 + 4 x3 + 6 x4 + 9 x5 ≤ 
            527, -2 x1 + 4 x2 + 6 x3 + 9 x4 + 6 x5 ≤ 527, 
          11 x1 + 8 x2 + 2 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 636, 
          11 x1 + 2 x2 + 8 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 636, 
          11 x1 + 2 x2 + 2 x3 + 8 x4 + 2 x5 + 5 x6 ≤ 636, 
          11 x1 + 2 x2 + 2 x3 + 2 x4 + 8 x5 + 5 x6 ≤ 636, 
          8 x1 + 11 x2 + 2 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 636, 
          8 x1 + 5 x2 + 2 x3 + 2 x4 + 11 x5 + 2 x6 ≤ 636, 
          8 x1 + 2 x2 + 11 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 636, 
          8 x1 + 2 x2 + 5 x3 + 11 x4 + 2 x5 + 2 x6 ≤ 636, 
          5 x1 + 8 x2 + 2 x3 + 2 x4 + 2 x5 + 11 x6 ≤ 636, 
          5 x1 + 2 x2 + 8 x3 + 2 x4 + 2 x5 + 11 x6 ≤ 636, 
          5 x1 + 2 x2 + 2 x3 + 8 x4 + 2 x5 + 11 x6 ≤ 636, 
          5 x1 + 2 x2 + 2 x3 + 2 x4 + 8 x5 + 11 x6 ≤ 636, 
          2 x1 + 11 x2 + 8 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 636, 
          2 x1 + 11 x2 + 2 x3 + 8 x4 + 5 x5 + 2 x6 ≤ 636, 
          2 x1 + 11 x2 + 2 x3 + 2 x4 + 5 x5 + 8 x6 ≤ 636, 
          2 x1 + 8 x2 + 11 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 636, 
          2 x1 + 8 x2 + 5 x3 + 11 x4 + 2 x5 + 2 x6 ≤ 636, 
          2 x1 + 5 x2 + 8 x3 + 2 x4 + 11 x5 + 2 x6 ≤ 636, 
          2 x1 + 5 x2 + 2 x3 + 8 x4 + 11 x5 + 2 x6 ≤ 636, 
          2 x1 + 5 x2 + 2 x3 + 2 x4 + 11 x5 + 8 x6 ≤ 636, 
          2 x1 + 2 x2 + 11 x3 + 5 x4 + 8 x5 + 2 x6 ≤ 636, 
          2 x1 + 2 x2 + 11 x3 + 5 x4 + 2 x5 + 8 x6 ≤ 636, 
          2 x1 + 2 x2 + 5 x3 + 11 x4 + 8 x5 + 2 x6 ≤ 636, 
          2 x1 + 2 x2 + 5 x3 + 11 x4 + 2 x5 + 8 x6 ≤ 636, 
          3 x1 - 2 x5 ≤ 79, 3 x1 - 2 x4 ≤ 79, 
          3 x1 - 2 x3 ≤ 79, 3 x1 - 2 x2 ≤ 79, 
          3 x2 - 2 x6 ≤ 79, 3 x2 - 2 x4 ≤ 79, 
          3 x2 - 2 x3 ≤ 79, 3 x3 - 2 x6 ≤ 79, 
          3 x3 - 2 x5 ≤ 79, 3 x4 - 2 x6 ≤ 79, 
          3 x4 - 2 x5 ≤ 79, 
          3 x5 - 2 x6 ≤ 79, -2 x5 + 3 x6 ≤ 
            79, -2 x4 + 3 x5 ≤ 
            79, -2 x4 + 3 x6 ≤ 
            79, -2 x3 + 3 x5 ≤ 
            79, -2 x3 + 3 x6 ≤ 
            79, -2 x2 + 3 x3 ≤ 
            79, -2 x2 + 3 x4 ≤ 
            79, -2 x2 + 3 x6 ≤ 
            79, -2 x1 + 3 x2 ≤ 
            79, -2 x1 + 3 x3 ≤ 
            79, -2 x1 + 3 x4 ≤ 
            79, -2 x1 + 3 x5 ≤ 79, 
          6 x1 + 3 x2 + 2 x3 + 2 x4 + 3 x5 ≤ 334, 
          6 x1 + 2 x2 + 3 x3 + 3 x4 + 2 x5 ≤ 334, 
          3 x1 + 6 x2 + 2 x3 + 2 x4 + 3 x6 ≤ 334, 
          3 x1 + 2 x2 + 6 x3 + 2 x5 + 3 x6 ≤ 334, 
          3 x1 + 2 x2 + 6 x4 + 2 x5 + 3 x6 ≤ 334, 
          3 x1 + 2 x3 + 2 x4 + 6 x5 + 3 x6 ≤ 334, 
          2 x1 + 6 x2 + 3 x3 + 3 x4 + 2 x6 ≤ 334, 
          2 x1 + 3 x2 + 6 x3 + 3 x5 + 2 x6 ≤ 334, 
          2 x1 + 3 x2 + 6 x4 + 3 x5 + 2 x6 ≤ 334, 
          2 x1 + 3 x3 + 3 x4 + 6 x5 + 2 x6 ≤ 334, 
          3 x2 + 2 x3 + 2 x4 + 3 x5 + 6 x6 ≤ 334, 
          2 x2 + 3 x3 + 3 x4 + 2 x5 + 6 x6 ≤ 334, 
          x1 - 2 x5 + x6 ≤ 48, x1 - 2 x4 + x6 ≤ 48, 
          x1 - 2 x3 + x6 ≤ 48, x1 - 2 x2 + x6 ≤ 48, 
          x2 + x5 - 2 x6 ≤ 48, x2 - 2 x4 + x5 ≤ 48, 
          x2 - 2 x3 + x5 ≤ 48, x3 + x4 - 2 x6 ≤ 48, 
          x3 + x4 - 2 x5 ≤ 48, -2 x2 + x3 + x4 ≤ 
            48, -2 x1 + x2 + x5 ≤ 
            48, -2 x1 + x3 + x4 ≤ 48, 
          3 x1 - 2 x3 - 12 x5 - 2 x6 ≤ 5, 
          3 x1 - 12 x3 - 2 x5 - 2 x6 ≤ 5, 
          3 x1 - 2 x2 - 12 x4 - 2 x6 ≤ 5, 
          3 x1 - 12 x2 - 2 x4 - 2 x6 ≤ 5, 
          3 x2 - 2 x3 - 2 x5 - 12 x6 ≤ 5, 
          3 x2 - 12 x3 - 2 x5 - 2 x6 ≤ 
            5, -2 x3 + 3 x4 - 2 x5 - 12 x6 ≤ 
            5, -2 x3 + 3 x4 - 12 x5 - 2 x6 ≤ 
            5, -2 x2 + 3 x3 - 2 x4 - 12 x6 ≤ 
            5, -2 x2 - 2 x4 + 3 x5 - 12 x6 ≤ 
            5, -2 x2 - 12 x4 + 3 x5 - 2 x6 ≤ 
            5, -12 x2 + 3 x3 - 2 x4 - 2 x6 ≤ 
            5, -2 x1 + 3 x2 - 12 x4 - 2 x5 ≤ 
            5, -2 x1 + 3 x3 - 2 x4 - 12 x5 ≤ 
            5, -2 x1 - 2 x4 - 12 x5 + 3 x6 ≤ 
            5, -2 x1 - 12 x4 - 2 x5 + 3 x6 ≤ 
            5, -2 x1 - 2 x2 - 12 x3 + 3 x5 ≤ 
            5, -2 x1 - 2 x2 - 12 x3 + 3 x6 ≤ 
            5, -2 x1 - 12 x2 - 2 x3 + 3 x4 ≤ 
            5, -2 x1 - 12 x2 - 2 x3 + 3 x6 ≤ 
            5, -12 x1 + 3 x2 - 2 x4 - 2 x5 ≤ 
            5, -12 x1 + 3 x3 - 2 x4 - 2 x5 ≤ 
            5, -12 x1 - 2 x2 - 2 x3 + 3 x4 ≤ 
            5, -12 x1 - 2 x2 - 2 x3 + 3 x5 ≤ 5, 
          x1 - 8 x3 - 2 x4 - 2 x5 - 2 x6 ≤ -71, 
          x1 - 2 x2 - 2 x3 - 8 x5 - 2 x6 ≤ -71, 
          x1 - 2 x2 - 2 x3 - 8 x4 - 2 x6 ≤ -71, 
          x1 - 8 x2 - 2 x4 - 2 x5 - 2 x6 ≤ -71, 
          x2 - 8 x3 - 2 x4 - 2 x5 - 
              2 x6 ≤ -71, -2 x2 - 2 x3 + x4 - 8 x5 - 
              2 x6 ≤ -71, -2 x2 - 2 x3 - 8 x4 + x5 - 
              2 x6 ≤ -71, -8 x2 + x3 - 2 x4 - 2 x5 - 
              2 x6 ≤ -71, -2 x1 + x2 - 2 x3 - 2 x5 - 
              8 x6 ≤ -71, -2 x1 + x2 - 2 x3 - 8 x4 - 
              2 x5 ≤ -71, -2 x1 - 2 x3 + x4 - 2 x5 - 
              8 x6 ≤ -71, -2 x1 - 2 x3 - 8 x4 - 
              2 x5 + x6 ≤ -71, -2 x1 - 2 x2 + x3 - 
              2 x4 - 8 x6 ≤ -71, -2 x1 - 2 x2 + x3 - 
              2 x4 - 8 x5 ≤ -71, -2 x1 - 2 x2 - 
              2 x4 + x5 - 8 x6 ≤ -71, -2 x1 - 2 x2 - 
              2 x4 - 8 x5 + x6 ≤ -71, -2 x1 - 2 x2 - 
              8 x3 - 2 x4 + x5 ≤ -71, -2 x1 - 2 x2 - 
              8 x3 - 2 x4 + x6 ≤ -71, -2 x1 - 8 x2 - 
              2 x3 + x4 - 2 x5 ≤ -71, -2 x1 - 8 x2 - 
              2 x3 - 2 x5 + x6 ≤ -71, -8 x1 + x2 - 
              2 x4 - 2 x5 - 2 x6 ≤ -71, -8 x1 + x3 - 
              2 x4 - 2 x5 - 2 x6 ≤ -71, -8 x1 - 
              2 x2 - 2 x3 + x4 - 2 x6 ≤ -71, -8 x1 - 
              2 x2 - 2 x3 + x5 - 2 x6 ≤ -71, 
          10 x1 + 7 x2 - 2 x3 + 6 x5 + 4 x6 ≤ 569, 
          10 x1 + 6 x2 - 2 x4 + 7 x5 + 4 x6 ≤ 569, 
          10 x1 + 6 x3 + 7 x4 - 2 x5 + 4 x6 ≤ 569, 
          10 x1 - 2 x2 + 7 x3 + 6 x4 + 4 x6 ≤ 569, 
          7 x1 + 10 x2 - 2 x3 + 4 x5 + 6 x6 ≤ 569, 
          7 x1 + 4 x2 - 2 x4 + 10 x5 + 6 x6 ≤ 569, 
          7 x1 + 4 x3 + 10 x4 - 2 x5 + 6 x6 ≤ 569, 
          7 x1 - 2 x2 + 10 x3 + 4 x4 + 6 x6 ≤ 569, 
          6 x1 + 10 x2 - 2 x4 + 4 x5 + 7 x6 ≤ 569, 
          6 x1 + 4 x2 - 2 x3 + 10 x5 + 7 x6 ≤ 569, 
          6 x1 + 10 x3 + 4 x4 - 2 x5 + 7 x6 ≤ 569, 
          6 x1 - 2 x2 + 4 x3 + 10 x4 + 7 x6 ≤ 569, 
          4 x1 + 7 x2 - 2 x4 + 6 x5 + 10 x6 ≤ 569, 
          4 x1 + 6 x2 - 2 x3 + 7 x5 + 10 x6 ≤ 569, 
          4 x1 + 7 x3 + 6 x4 - 2 x5 + 10 x6 ≤ 569, 
          4 x1 - 2 x2 + 6 x3 + 7 x4 + 10 x6 ≤ 569, 
          10 x2 + 6 x3 + 7 x4 + 4 x5 - 2 x6 ≤ 569, 
          7 x2 + 4 x3 + 10 x4 + 6 x5 - 2 x6 ≤ 569, 
          6 x2 + 10 x3 + 4 x4 + 7 x5 - 2 x6 ≤ 569, 
          4 x2 + 7 x3 + 6 x4 + 10 x5 - 2 x6 ≤ 
            569, -2 x1 + 10 x2 + 7 x3 + 6 x4 + 4 x5 ≤ 
            569, -2 x1 + 7 x2 + 10 x3 + 4 x4 + 6 x5 ≤ 
            569, -2 x1 + 6 x2 + 4 x3 + 10 x4 + 7 x5 ≤ 
            569, -2 x1 + 4 x2 + 6 x3 + 7 x4 + 10 x5 ≤ 
            569, 3 x1 - 8 x3 - 6 x4 - 6 x5 - 6 x6 ≤ -197, 
          3 x1 - 6 x2 - 6 x3 - 8 x5 - 6 x6 ≤ -197, 
          3 x1 - 6 x2 - 6 x3 - 8 x4 - 6 x6 ≤ -197, 
          3 x1 - 8 x2 - 6 x4 - 6 x5 - 6 x6 ≤ -197, 
          3 x2 - 8 x3 - 6 x4 - 6 x5 - 
              6 x6 ≤ -197, -6 x2 - 6 x3 + 3 x4 - 
              8 x5 - 6 x6 ≤ -197, -6 x2 - 6 x3 - 
              8 x4 + 3 x5 - 6 x6 ≤ -197, -8 x2 + 
              3 x3 - 6 x4 - 6 x5 - 
              6 x6 ≤ -197, -6 x1 + 3 x2 - 6 x3 - 
              6 x5 - 8 x6 ≤ -197, -6 x1 + 3 x2 - 
              6 x3 - 8 x4 - 6 x5 ≤ -197, -6 x1 - 
              6 x3 + 3 x4 - 6 x5 - 
              8 x6 ≤ -197, -6 x1 - 6 x3 - 8 x4 - 
              6 x5 + 3 x6 ≤ -197, -6 x1 - 6 x2 + 
              3 x3 - 6 x4 - 8 x6 ≤ -197, -6 x1 - 
              6 x2 + 3 x3 - 6 x4 - 
              8 x5 ≤ -197, -6 x1 - 6 x2 - 6 x4 + 
              3 x5 - 8 x6 ≤ -197, -6 x1 - 6 x2 - 
              6 x4 - 8 x5 + 3 x6 ≤ -197, -6 x1 - 
              6 x2 - 8 x3 - 6 x4 + 
              3 x5 ≤ -197, -6 x1 - 6 x2 - 8 x3 - 
              6 x4 + 3 x6 ≤ -197, -6 x1 - 8 x2 - 
              6 x3 + 3 x4 - 6 x5 ≤ -197, -6 x1 - 
              8 x2 - 6 x3 - 6 x5 + 
              3 x6 ≤ -197, -8 x1 + 3 x2 - 6 x4 - 
              6 x5 - 6 x6 ≤ -197, -8 x1 + 3 x3 - 
              6 x4 - 6 x5 - 6 x6 ≤ -197, -8 x1 - 
              6 x2 - 6 x3 + 3 x4 - 
              6 x6 ≤ -197, -8 x1 - 6 x2 - 6 x3 + 
              3 x5 - 6 x6 ≤ -197, 
          15 x1 + 6 x2 + 6 x3 + 6 x4 + 4 x5 ≤ 775, 
          15 x1 + 6 x2 + 6 x3 + 4 x4 + 6 x5 ≤ 775, 
          15 x1 + 6 x2 + 4 x3 + 6 x4 + 6 x5 ≤ 775, 
          15 x1 + 4 x2 + 6 x3 + 6 x4 + 6 x5 ≤ 775, 
          6 x1 + 15 x2 + 6 x3 + 6 x4 + 4 x6 ≤ 775, 
          6 x1 + 15 x2 + 6 x3 + 4 x4 + 6 x6 ≤ 775, 
          6 x1 + 15 x2 + 4 x3 + 6 x4 + 6 x6 ≤ 775, 
          6 x1 + 6 x2 + 15 x3 + 6 x5 + 4 x6 ≤ 775, 
          6 x1 + 6 x2 + 15 x3 + 4 x5 + 6 x6 ≤ 775, 
          6 x1 + 6 x2 + 15 x4 + 6 x5 + 4 x6 ≤ 775, 
          6 x1 + 6 x2 + 15 x4 + 4 x5 + 6 x6 ≤ 775, 
          6 x1 + 4 x2 + 15 x3 + 6 x5 + 6 x6 ≤ 775, 
          6 x1 + 4 x2 + 15 x4 + 6 x5 + 6 x6 ≤ 775, 
          6 x1 + 6 x3 + 6 x4 + 15 x5 + 4 x6 ≤ 775, 
          6 x1 + 6 x3 + 4 x4 + 15 x5 + 6 x6 ≤ 775, 
          6 x1 + 4 x3 + 6 x4 + 15 x5 + 6 x6 ≤ 775, 
          4 x1 + 15 x2 + 6 x3 + 6 x4 + 6 x6 ≤ 775, 
          4 x1 + 6 x2 + 15 x3 + 6 x5 + 6 x6 ≤ 775, 
          4 x1 + 6 x2 + 15 x4 + 6 x5 + 6 x6 ≤ 775, 
          4 x1 + 6 x3 + 6 x4 + 15 x5 + 6 x6 ≤ 775, 
          6 x2 + 6 x3 + 6 x4 + 4 x5 + 15 x6 ≤ 775, 
          6 x2 + 6 x3 + 4 x4 + 6 x5 + 15 x6 ≤ 775, 
          6 x2 + 4 x3 + 6 x4 + 6 x5 + 15 x6 ≤ 775, 
          4 x2 + 6 x3 + 6 x4 + 6 x5 + 15 x6 ≤ 775, 
          2 x1 - x2 - 2 x3 - 2 x4 - x5 - 4 x6 ≤ -62, 
          2 x1 - 2 x2 - x3 - x4 - 2 x5 - 
              4 x6 ≤ -62, -x1 + 2 x2 - 2 x3 - 2 x4 - 
              4 x5 - x6 ≤ -62, -x1 - 2 x2 + 2 x3 - 
              4 x4 - 2 x5 - x6 ≤ -62, -x1 - 2 x2 - 
              4 x3 + 2 x4 - 2 x5 - x6 ≤ -62, -x1 - 
              4 x2 - 2 x3 - 2 x4 + 2 x5 - 
              x6 ≤ -62, -2 x1 + 2 x2 - x3 - x4 - 4 x5 - 
              2 x6 ≤ -62, -2 x1 - x2 + 2 x3 - 4 x4 - 
              x5 - 2 x6 ≤ -62, -2 x1 - x2 - 4 x3 + 
              2 x4 - x5 - 2 x6 ≤ -62, -2 x1 - 4 x2 - 
              x3 - x4 + 2 x5 - 2 x6 ≤ -62, -4 x1 - x2 - 
              2 x3 - 2 x4 - x5 + 2 x6 ≤ -62, -4 x1 - 
              2 x2 - x3 - x4 - 2 x5 + 2 x6 ≤ -62, 
          6 x1 + 3 x2 + 2 x3 + 3 x4 + 2 x5 ≤ 334, 
          6 x1 + 2 x2 + 3 x3 + 2 x4 + 3 x5 ≤ 334, 
          3 x1 + 6 x2 + 2 x3 + 3 x4 + 2 x6 ≤ 334, 
          3 x1 + 3 x2 + 6 x4 + 2 x5 + 2 x6 ≤ 334, 
          3 x1 + 2 x2 + 6 x3 + 3 x5 + 2 x6 ≤ 334, 
          3 x1 + 3 x3 + 2 x4 + 6 x5 + 2 x6 ≤ 334, 
          2 x1 + 6 x2 + 3 x3 + 2 x4 + 3 x6 ≤ 334, 
          2 x1 + 3 x2 + 6 x3 + 2 x5 + 3 x6 ≤ 334, 
          2 x1 + 2 x2 + 6 x4 + 3 x5 + 3 x6 ≤ 334, 
          2 x1 + 2 x3 + 3 x4 + 6 x5 + 3 x6 ≤ 334, 
          3 x2 + 3 x3 + 2 x4 + 2 x5 + 6 x6 ≤ 334, 
          2 x2 + 2 x3 + 3 x4 + 3 x5 + 6 x6 ≤ 334, 
          3 x1 - 6 x2 - 6 x3 - 6 x4 - 8 x5 - 
              12 x6 ≤ -401, 
          3 x1 - 6 x2 - 6 x3 - 8 x4 - 6 x5 - 
              12 x6 ≤ -401, 
          3 x1 - 6 x2 - 8 x3 - 6 x4 - 6 x5 - 
              12 x6 ≤ -401, 
          3 x1 - 8 x2 - 6 x3 - 6 x4 - 6 x5 - 
              12 x6 ≤ -401, -6 x1 + 3 x2 - 6 x3 - 
              6 x4 - 12 x5 - 8 x6 ≤ -401, -6 x1 + 
              3 x2 - 6 x3 - 8 x4 - 12 x5 - 
              6 x6 ≤ -401, -6 x1 + 3 x2 - 8 x3 - 
              6 x4 - 12 x5 - 6 x6 ≤ -401, -6 x1 - 
              6 x2 + 3 x3 - 12 x4 - 6 x5 - 
              8 x6 ≤ -401, -6 x1 - 6 x2 + 3 x3 - 
              12 x4 - 8 x5 - 6 x6 ≤ -401, -6 x1 - 
              6 x2 - 12 x3 + 3 x4 - 6 x5 - 
              8 x6 ≤ -401, -6 x1 - 6 x2 - 12 x3 + 
              3 x4 - 8 x5 - 6 x6 ≤ -401, -6 x1 - 
              8 x2 + 3 x3 - 12 x4 - 6 x5 - 
              6 x6 ≤ -401, -6 x1 - 8 x2 - 12 x3 + 
              3 x4 - 6 x5 - 6 x6 ≤ -401, -6 x1 - 
              12 x2 - 6 x3 - 6 x4 + 3 x5 - 
              8 x6 ≤ -401, -6 x1 - 12 x2 - 6 x3 - 
              8 x4 + 3 x5 - 6 x6 ≤ -401, -6 x1 - 
              12 x2 - 8 x3 - 6 x4 + 3 x5 - 
              6 x6 ≤ -401, -8 x1 + 3 x2 - 6 x3 - 
              6 x4 - 12 x5 - 6 x6 ≤ -401, -8 x1 - 
              6 x2 + 3 x3 - 12 x4 - 6 x5 - 
              6 x6 ≤ -401, -8 x1 - 6 x2 - 12 x3 + 
              3 x4 - 6 x5 - 6 x6 ≤ -401, -8 x1 - 
              12 x2 - 6 x3 - 6 x4 + 3 x5 - 
              6 x6 ≤ -401, -12 x1 - 6 x2 - 6 x3 - 
              6 x4 - 8 x5 + 3 x6 ≤ -401, -12 x1 - 
              6 x2 - 6 x3 - 8 x4 - 6 x5 + 
              3 x6 ≤ -401, -12 x1 - 6 x2 - 8 x3 - 
              6 x4 - 6 x5 + 3 x6 ≤ -401, -12 x1 - 
              8 x2 - 6 x3 - 6 x4 - 6 x5 + 3 x6 ≤ -401, 
          5 x1 - 4 x2 - 4 x3 - 4 x4 - 6 x5 - 
              10 x6 ≤ -215, 
          5 x1 - 4 x2 - 4 x3 - 6 x4 - 4 x5 - 
              10 x6 ≤ -215, 
          5 x1 - 4 x2 - 6 x3 - 4 x4 - 4 x5 - 
              10 x6 ≤ -215, 
          5 x1 - 6 x2 - 4 x3 - 4 x4 - 4 x5 - 
              10 x6 ≤ -215, -4 x1 + 5 x2 - 4 x3 - 
              4 x4 - 10 x5 - 6 x6 ≤ -215, -4 x1 + 
              5 x2 - 4 x3 - 6 x4 - 10 x5 - 
              4 x6 ≤ -215, -4 x1 + 5 x2 - 6 x3 - 
              4 x4 - 10 x5 - 4 x6 ≤ -215, -4 x1 - 
              4 x2 + 5 x3 - 10 x4 - 4 x5 - 
              6 x6 ≤ -215, -4 x1 - 4 x2 + 5 x3 - 
              10 x4 - 6 x5 - 4 x6 ≤ -215, -4 x1 - 
              4 x2 - 10 x3 + 5 x4 - 4 x5 - 
              6 x6 ≤ -215, -4 x1 - 4 x2 - 10 x3 + 
              5 x4 - 6 x5 - 4 x6 ≤ -215, -4 x1 - 
              6 x2 + 5 x3 - 10 x4 - 4 x5 - 
              4 x6 ≤ -215, -4 x1 - 6 x2 - 10 x3 + 
              5 x4 - 4 x5 - 4 x6 ≤ -215, -4 x1 - 
              10 x2 - 4 x3 - 4 x4 + 5 x5 - 
              6 x6 ≤ -215, -4 x1 - 10 x2 - 4 x3 - 
              6 x4 + 5 x5 - 4 x6 ≤ -215, -4 x1 - 
              10 x2 - 6 x3 - 4 x4 + 5 x5 - 
              4 x6 ≤ -215, -6 x1 + 5 x2 - 4 x3 - 
              4 x4 - 10 x5 - 4 x6 ≤ -215, -6 x1 - 
              4 x2 + 5 x3 - 10 x4 - 4 x5 - 
              4 x6 ≤ -215, -6 x1 - 4 x2 - 10 x3 + 
              5 x4 - 4 x5 - 4 x6 ≤ -215, -6 x1 - 
              10 x2 - 4 x3 - 4 x4 + 5 x5 - 
              4 x6 ≤ -215, -10 x1 - 4 x2 - 4 x3 - 
              4 x4 - 6 x5 + 5 x6 ≤ -215, -10 x1 - 
              4 x2 - 4 x3 - 6 x4 - 4 x5 + 
              5 x6 ≤ -215, -10 x1 - 4 x2 - 6 x3 - 
              4 x4 - 4 x5 + 5 x6 ≤ -215, -10 x1 - 
              6 x2 - 4 x3 - 4 x4 - 4 x5 + 5 x6 ≤ -215, 
          9 x1 - 2 x5 - 6 x6 ≤ 169, 
          9 x1 - 2 x4 - 6 x6 ≤ 169, 
          9 x1 - 2 x3 - 6 x6 ≤ 169, 
          9 x1 - 2 x2 - 6 x6 ≤ 169, 
          9 x2 - 6 x5 - 2 x6 ≤ 169, 
          9 x2 - 2 x4 - 6 x5 ≤ 169, 
          9 x2 - 2 x3 - 6 x5 ≤ 169, 
          9 x3 - 6 x4 - 2 x6 ≤ 169, 
          9 x3 - 6 x4 - 2 x5 ≤ 
            169, -6 x3 + 9 x4 - 2 x6 ≤ 
            169, -6 x3 + 9 x4 - 2 x5 ≤ 
            169, -2 x2 + 9 x3 - 6 x4 ≤ 
            169, -2 x2 - 6 x3 + 9 x4 ≤ 
            169, -6 x2 + 9 x5 - 2 x6 ≤ 
            169, -6 x2 - 2 x4 + 9 x5 ≤ 
            169, -6 x2 - 2 x3 + 9 x5 ≤ 
            169, -2 x1 + 9 x2 - 6 x5 ≤ 
            169, -2 x1 + 9 x3 - 6 x4 ≤ 
            169, -2 x1 - 6 x3 + 9 x4 ≤ 
            169, -2 x1 - 6 x2 + 9 x5 ≤ 
            169, -6 x1 - 2 x5 + 9 x6 ≤ 
            169, -6 x1 - 2 x4 + 9 x6 ≤ 
            169, -6 x1 - 2 x3 + 9 x6 ≤ 
            169, -6 x1 - 2 x2 + 9 x6 ≤ 169, 
          11 x1 + 2 x2 + 2 x3 + 2 x4 - 4 x6 ≤ 367, 
          11 x1 + 2 x2 + 2 x3 + 2 x5 - 4 x6 ≤ 367, 
          11 x1 + 2 x2 + 2 x4 + 2 x5 - 4 x6 ≤ 367, 
          11 x1 + 2 x3 + 2 x4 + 2 x5 - 4 x6 ≤ 367, 
          2 x1 + 11 x2 + 2 x3 + 2 x4 - 4 x5 ≤ 367, 
          2 x1 + 11 x2 + 2 x3 - 4 x5 + 2 x6 ≤ 367, 
          2 x1 + 11 x2 + 2 x4 - 4 x5 + 2 x6 ≤ 367, 
          2 x1 + 2 x2 + 11 x3 - 4 x4 + 2 x5 ≤ 367, 
          2 x1 + 2 x2 + 11 x3 - 4 x4 + 2 x6 ≤ 367, 
          2 x1 + 2 x2 - 4 x3 + 11 x4 + 2 x5 ≤ 367, 
          2 x1 + 2 x2 - 4 x3 + 11 x4 + 2 x6 ≤ 367, 
          2 x1 + 11 x3 - 4 x4 + 2 x5 + 2 x6 ≤ 367, 
          2 x1 - 4 x3 + 11 x4 + 2 x5 + 2 x6 ≤ 367, 
          2 x1 - 4 x2 + 2 x3 + 2 x4 + 11 x5 ≤ 367, 
          2 x1 - 4 x2 + 2 x3 + 11 x5 + 2 x6 ≤ 367, 
          2 x1 - 4 x2 + 2 x4 + 11 x5 + 2 x6 ≤ 367, 
          11 x2 + 2 x3 + 2 x4 - 4 x5 + 2 x6 ≤ 367, 
          2 x2 + 11 x3 - 4 x4 + 2 x5 + 2 x6 ≤ 367, 
          2 x2 - 4 x3 + 11 x4 + 2 x5 + 2 x6 ≤ 
            367, -4 x2 + 2 x3 + 2 x4 + 11 x5 + 2 x6 ≤ 
            367, -4 x1 + 2 x2 + 2 x3 + 2 x4 + 11 x6 ≤ 
            367, -4 x1 + 2 x2 + 2 x3 + 2 x5 + 11 x6 ≤ 
            367, -4 x1 + 2 x2 + 2 x4 + 2 x5 + 11 x6 ≤ 
            367, -4 x1 + 2 x3 + 2 x4 + 2 x5 + 11 x6 ≤ 
            367, 8 x1 + 5 x2 + 2 x3 + 2 x4 + 2 x5 + 2 x6 ≤ 
            435, 8 x1 + 2 x2 + 5 x3 + 2 x4 + 2 x5 + 2 x6 ≤ 
            435, 8 x1 + 2 x2 + 2 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 
            435, 8 x1 + 2 x2 + 2 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 
            435, 5 x1 + 8 x2 + 2 x3 + 2 x4 + 2 x5 + 2 x6 ≤ 
            435, 5 x1 + 2 x2 + 8 x3 + 2 x4 + 2 x5 + 2 x6 ≤ 
            435, 5 x1 + 2 x2 + 2 x3 + 8 x4 + 2 x5 + 2 x6 ≤ 
            435, 5 x1 + 2 x2 + 2 x3 + 2 x4 + 8 x5 + 2 x6 ≤ 
            435, 2 x1 + 8 x2 + 5 x3 + 2 x4 + 2 x5 + 2 x6 ≤ 
            435, 
          2 x1 + 8 x2 + 2 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 435, 
          2 x1 + 8 x2 + 2 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 435, 
          2 x1 + 5 x2 + 8 x3 + 2 x4 + 2 x5 + 2 x6 ≤ 435, 
          2 x1 + 5 x2 + 2 x3 + 8 x4 + 2 x5 + 2 x6 ≤ 435, 
          2 x1 + 5 x2 + 2 x3 + 2 x4 + 2 x5 + 8 x6 ≤ 435, 
          2 x1 + 2 x2 + 8 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 435, 
          2 x1 + 2 x2 + 8 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 435, 
          2 x1 + 2 x2 + 5 x3 + 2 x4 + 8 x5 + 2 x6 ≤ 435, 
          2 x1 + 2 x2 + 5 x3 + 2 x4 + 2 x5 + 8 x6 ≤ 435, 
          2 x1 + 2 x2 + 2 x3 + 8 x4 + 5 x5 + 2 x6 ≤ 435, 
          2 x1 + 2 x2 + 2 x3 + 8 x4 + 2 x5 + 5 x6 ≤ 435, 
          2 x1 + 2 x2 + 2 x3 + 5 x4 + 8 x5 + 2 x6 ≤ 435, 
          2 x1 + 2 x2 + 2 x3 + 5 x4 + 2 x5 + 8 x6 ≤ 435, 
          2 x1 + 2 x2 + 2 x3 + 2 x4 + 8 x5 + 5 x6 ≤ 435, 
          2 x1 + 2 x2 + 2 x3 + 2 x4 + 5 x5 + 8 x6 ≤ 435, 
          19 x1 + 10 x2 + 4 x3 + 4 x4 + 4 x5 + 4 x6 ≤ 951, 
          19 x1 + 4 x2 + 10 x3 + 4 x4 + 4 x5 + 4 x6 ≤ 951, 
          19 x1 + 4 x2 + 4 x3 + 10 x4 + 4 x5 + 4 x6 ≤ 951, 
          19 x1 + 4 x2 + 4 x3 + 4 x4 + 10 x5 + 4 x6 ≤ 951, 
          10 x1 + 19 x2 + 4 x3 + 4 x4 + 4 x5 + 4 x6 ≤ 951, 
          10 x1 + 4 x2 + 19 x3 + 4 x4 + 4 x5 + 4 x6 ≤ 951, 
          10 x1 + 4 x2 + 4 x3 + 19 x4 + 4 x5 + 4 x6 ≤ 951, 
          10 x1 + 4 x2 + 4 x3 + 4 x4 + 19 x5 + 4 x6 ≤ 951, 
          4 x1 + 19 x2 + 10 x3 + 4 x4 + 4 x5 + 4 x6 ≤ 951, 
          4 x1 + 19 x2 + 4 x3 + 10 x4 + 4 x5 + 4 x6 ≤ 951, 
          4 x1 + 19 x2 + 4 x3 + 4 x4 + 4 x5 + 10 x6 ≤ 951, 
          4 x1 + 10 x2 + 19 x3 + 4 x4 + 4 x5 + 4 x6 ≤ 951, 
          4 x1 + 10 x2 + 4 x3 + 19 x4 + 4 x5 + 4 x6 ≤ 951, 
          4 x1 + 10 x2 + 4 x3 + 4 x4 + 4 x5 + 19 x6 ≤ 951, 
          4 x1 + 4 x2 + 19 x3 + 4 x4 + 10 x5 + 4 x6 ≤ 951, 
          4 x1 + 4 x2 + 19 x3 + 4 x4 + 4 x5 + 10 x6 ≤ 951, 
          4 x1 + 4 x2 + 10 x3 + 4 x4 + 19 x5 + 4 x6 ≤ 951, 
          4 x1 + 4 x2 + 10 x3 + 4 x4 + 4 x5 + 19 x6 ≤ 951, 
          4 x1 + 4 x2 + 4 x3 + 19 x4 + 10 x5 + 4 x6 ≤ 951, 
          4 x1 + 4 x2 + 4 x3 + 19 x4 + 4 x5 + 10 x6 ≤ 951, 
          4 x1 + 4 x2 + 4 x3 + 10 x4 + 19 x5 + 4 x6 ≤ 951, 
          4 x1 + 4 x2 + 4 x3 + 10 x4 + 4 x5 + 19 x6 ≤ 951, 
          4 x1 + 4 x2 + 4 x3 + 4 x4 + 19 x5 + 10 x6 ≤ 951, 
          4 x1 + 4 x2 + 4 x3 + 4 x4 + 10 x5 + 19 x6 ≤ 
            951, -x2 - 4 x3 - 4 x4 - x5 - 
              2 x6 ≤ -120, -4 x2 - x3 - x4 - 4 x5 - 
              2 x6 ≤ -120, -x1 - 4 x3 - 4 x4 - 2 x5 - 
              x6 ≤ -120, -x1 - 2 x2 - 4 x3 - 4 x4 - 
              x6 ≤ -120, -x1 - 4 x2 - 2 x4 - 4 x5 - 
              x6 ≤ -120, -x1 - 4 x2 - 2 x3 - 4 x5 - 
              x6 ≤ -120, -2 x1 - x2 - 4 x3 - 4 x4 - 
              x5 ≤ -120, -2 x1 - 4 x2 - x3 - x4 - 
              4 x5 ≤ -120, -4 x1 - x3 - x4 - 2 x5 - 
              4 x6 ≤ -120, -4 x1 - x2 - 2 x4 - x5 - 
              4 x6 ≤ -120, -4 x1 - x2 - 2 x3 - x5 - 
              4 x6 ≤ -120, -4 x1 - 2 x2 - x3 - x4 - 
              4 x6 ≤ -120, 
          x1 - 2 x3 - 2 x4 - 2 x5 - 2 x6 ≤ -63, 
          x1 - 2 x2 - 2 x4 - 2 x5 - 2 x6 ≤ -63, 
          x1 - 2 x2 - 2 x3 - 2 x5 - 2 x6 ≤ -63, 
          x1 - 2 x2 - 2 x3 - 2 x4 - 2 x6 ≤ -63, 
          x2 - 2 x3 - 2 x4 - 2 x5 - 
              2 x6 ≤ -63, -2 x2 + x3 - 2 x4 - 2 x5 - 
              2 x6 ≤ -63, -2 x2 - 2 x3 + x4 - 2 x5 - 
              2 x6 ≤ -63, -2 x2 - 2 x3 - 2 x4 + x5 - 
              2 x6 ≤ -63, -2 x1 + x2 - 2 x4 - 2 x5 - 
              2 x6 ≤ -63, -2 x1 + x2 - 2 x3 - 2 x5 - 
              2 x6 ≤ -63, -2 x1 + x2 - 2 x3 - 2 x4 - 
              2 x5 ≤ -63, -2 x1 + x3 - 2 x4 - 2 x5 - 
              2 x6 ≤ -63, -2 x1 - 2 x3 + x4 - 2 x5 - 
              2 x6 ≤ -63, -2 x1 - 2 x3 - 2 x4 - 
              2 x5 + x6 ≤ -63, -2 x1 - 2 x2 + x3 - 
              2 x4 - 2 x6 ≤ -63, -2 x1 - 2 x2 + x3 - 
              2 x4 - 2 x5 ≤ -63, -2 x1 - 2 x2 - 
              2 x4 + x5 - 2 x6 ≤ -63, -2 x1 - 2 x2 - 
              2 x4 - 2 x5 + x6 ≤ -63, -2 x1 - 2 x2 - 
              2 x3 + x4 - 2 x6 ≤ -63, -2 x1 - 2 x2 - 
              2 x3 + x4 - 2 x5 ≤ -63, -2 x1 - 2 x2 - 
              2 x3 + x5 - 2 x6 ≤ -63, -2 x1 - 2 x2 - 
              2 x3 - 2 x5 + x6 ≤ -63, -2 x1 - 2 x2 - 
              2 x3 - 2 x4 + x5 ≤ -63, -2 x1 - 2 x2 - 
              2 x3 - 2 x4 + x6 ≤ -63, 
          3 x1 - 6 x2 - 8 x3 - 8 x4 - 6 x5 - 
              12 x6 ≤ -421, 
          3 x1 - 8 x2 - 6 x3 - 6 x4 - 8 x5 - 
              12 x6 ≤ -421, -6 x1 + 3 x2 - 8 x3 - 
              8 x4 - 12 x5 - 6 x6 ≤ -421, -6 x1 - 
              8 x2 + 3 x3 - 12 x4 - 8 x5 - 
              6 x6 ≤ -421, -6 x1 - 8 x2 - 12 x3 + 
              3 x4 - 8 x5 - 6 x6 ≤ -421, -6 x1 - 
              12 x2 - 8 x3 - 8 x4 + 3 x5 - 
              6 x6 ≤ -421, -8 x1 + 3 x2 - 6 x3 - 
              6 x4 - 12 x5 - 8 x6 ≤ -421, -8 x1 - 
              6 x2 + 3 x3 - 12 x4 - 6 x5 - 
              8 x6 ≤ -421, -8 x1 - 6 x2 - 12 x3 + 
              3 x4 - 6 x5 - 8 x6 ≤ -421, -8 x1 - 
              12 x2 - 6 x3 - 6 x4 + 3 x5 - 
              8 x6 ≤ -421, -12 x1 - 6 x2 - 8 x3 - 
              8 x4 - 6 x5 + 3 x6 ≤ -421, -12 x1 - 
              8 x2 - 6 x3 - 6 x4 - 8 x5 + 3 x6 ≤ -421, 
          7 x1 - 2 x2 - 4 x3 - 4 x4 - 2 x5 - 8 x6 ≤ -49, 
          7 x1 - 4 x2 - 2 x3 - 2 x4 - 4 x5 - 
              8 x6 ≤ -49, -2 x1 + 7 x2 - 4 x3 - 
              4 x4 - 8 x5 - 2 x6 ≤ -49, -2 x1 - 
              4 x2 + 7 x3 - 8 x4 - 4 x5 - 
              2 x6 ≤ -49, -2 x1 - 4 x2 - 8 x3 + 
              7 x4 - 4 x5 - 2 x6 ≤ -49, -2 x1 - 
              8 x2 - 4 x3 - 4 x4 + 7 x5 - 
              2 x6 ≤ -49, -4 x1 + 7 x2 - 2 x3 - 
              2 x4 - 8 x5 - 4 x6 ≤ -49, -4 x1 - 
              2 x2 + 7 x3 - 8 x4 - 2 x5 - 
              4 x6 ≤ -49, -4 x1 - 2 x2 - 8 x3 + 
              7 x4 - 2 x5 - 4 x6 ≤ -49, -4 x1 - 
              8 x2 - 2 x3 - 2 x4 + 7 x5 - 
              4 x6 ≤ -49, -8 x1 - 2 x2 - 4 x3 - 
              4 x4 - 2 x5 + 7 x6 ≤ -49, -8 x1 - 
              4 x2 - 2 x3 - 2 x4 - 4 x5 + 7 x6 ≤ -49, 
          15 x1 + 6 x2 + 4 x3 + 6 x4 + 4 x5 ≤ 743, 
          15 x1 + 4 x2 + 6 x3 + 4 x4 + 6 x5 ≤ 743, 
          6 x1 + 15 x2 + 4 x3 + 6 x4 + 4 x6 ≤ 743, 
          6 x1 + 6 x2 + 15 x4 + 4 x5 + 4 x6 ≤ 743, 
          6 x1 + 4 x2 + 15 x3 + 6 x5 + 4 x6 ≤ 743, 
          6 x1 + 6 x3 + 4 x4 + 15 x5 + 4 x6 ≤ 743, 
          4 x1 + 15 x2 + 6 x3 + 4 x4 + 6 x6 ≤ 743, 
          4 x1 + 6 x2 + 15 x3 + 4 x5 + 6 x6 ≤ 743, 
          4 x1 + 4 x2 + 15 x4 + 6 x5 + 6 x6 ≤ 743, 
          4 x1 + 4 x3 + 6 x4 + 15 x5 + 6 x6 ≤ 743, 
          6 x2 + 6 x3 + 4 x4 + 4 x5 + 15 x6 ≤ 743, 
          4 x2 + 4 x3 + 6 x4 + 6 x5 + 15 x6 ≤ 743, 
          x1 + x2 + x5 - 2 x6 ≤ 67, 
          x1 + x2 - 2 x5 + x6 ≤ 67, 
          x1 + x3 + x4 - 2 x6 ≤ 67, 
          x1 + x3 - 2 x4 + x6 ≤ 67, 
          x1 - 2 x3 + x4 + x6 ≤ 67, 
          x1 - 2 x2 + x5 + x6 ≤ 67, 
          x2 + x3 + x4 - 2 x5 ≤ 67, 
          x2 + x3 - 2 x4 + x5 ≤ 67, 
          x2 - 2 x3 + x4 + x5 ≤ 
            67, -2 x2 + x3 + x4 + x5 ≤ 
            67, -2 x1 + x2 + x5 + x6 ≤ 
            67, -2 x1 + x3 + x4 + x6 ≤ 67, 
          19 x1 + 10 x2 + 4 x3 + 4 x4 + 4 x6 ≤ 911, 
          19 x1 + 4 x2 + 10 x3 + 4 x5 + 4 x6 ≤ 911, 
          19 x1 + 4 x2 + 10 x4 + 4 x5 + 4 x6 ≤ 911, 
          19 x1 + 4 x3 + 4 x4 + 10 x5 + 4 x6 ≤ 911, 
          10 x1 + 19 x2 + 4 x3 + 4 x4 + 4 x5 ≤ 911, 
          10 x1 + 4 x2 + 19 x3 + 4 x4 + 4 x5 ≤ 911, 
          10 x1 + 4 x2 + 4 x3 + 19 x4 + 4 x5 ≤ 911, 
          10 x1 + 4 x2 + 4 x3 + 4 x4 + 19 x5 ≤ 911, 
          4 x1 + 19 x2 + 10 x3 + 4 x5 + 4 x6 ≤ 911, 
          4 x1 + 19 x2 + 10 x4 + 4 x5 + 4 x6 ≤ 911, 
          4 x1 + 10 x2 + 19 x3 + 4 x4 + 4 x6 ≤ 911, 
          4 x1 + 10 x2 + 4 x3 + 19 x4 + 4 x6 ≤ 911, 
          4 x1 + 10 x2 + 4 x3 + 4 x4 + 19 x6 ≤ 911, 
          4 x1 + 4 x2 + 10 x3 + 19 x5 + 4 x6 ≤ 911, 
          4 x1 + 4 x2 + 10 x3 + 4 x5 + 19 x6 ≤ 911, 
          4 x1 + 4 x2 + 10 x4 + 19 x5 + 4 x6 ≤ 911, 
          4 x1 + 4 x2 + 10 x4 + 4 x5 + 19 x6 ≤ 911, 
          4 x1 + 19 x3 + 4 x4 + 10 x5 + 4 x6 ≤ 911, 
          4 x1 + 4 x3 + 19 x4 + 10 x5 + 4 x6 ≤ 911, 
          4 x1 + 4 x3 + 4 x4 + 10 x5 + 19 x6 ≤ 911, 
          19 x2 + 4 x3 + 4 x4 + 4 x5 + 10 x6 ≤ 911, 
          4 x2 + 19 x3 + 4 x4 + 4 x5 + 10 x6 ≤ 911, 
          4 x2 + 4 x3 + 19 x4 + 4 x5 + 10 x6 ≤ 911, 
          4 x2 + 4 x3 + 4 x4 + 19 x5 + 10 x6 ≤ 
            911, -x3 - x5 - 3 x6 ≤ -32, -x3 - 3 x5 - 
              x6 ≤ -32, -3 x3 - x5 - 
              x6 ≤ -32, -x2 - x4 - 
              3 x6 ≤ -32, -x2 - 3 x4 - 
              x6 ≤ -32, -3 x2 - x4 - 
              x6 ≤ -32, -x1 - x4 - 
              3 x5 ≤ -32, -x1 - 3 x4 - 
              x5 ≤ -32, -x1 - x2 - 
              3 x3 ≤ -32, -x1 - 3 x2 - 
              x3 ≤ -32, -3 x1 - x4 - 
              x5 ≤ -32, -3 x1 - x2 - 
              x3 ≤ -32, -2 x2 - 3 x3 - 3 x4 - 3 x5 - 
              5 x6 ≤ -199, -3 x2 - 2 x3 - 3 x4 - 
              3 x5 - 5 x6 ≤ -199, -3 x2 - 3 x3 - 
              2 x4 - 3 x5 - 5 x6 ≤ -199, -3 x2 - 
              3 x3 - 3 x4 - 2 x5 - 
              5 x6 ≤ -199, -2 x1 - 3 x3 - 3 x4 - 
              5 x5 - 3 x6 ≤ -199, -2 x1 - 3 x2 - 
              5 x4 - 3 x5 - 3 x6 ≤ -199, -2 x1 - 
              3 x2 - 5 x3 - 3 x5 - 
              3 x6 ≤ -199, -2 x1 - 5 x2 - 3 x3 - 
              3 x4 - 3 x6 ≤ -199, -3 x1 - 2 x3 - 
              3 x4 - 5 x5 - 3 x6 ≤ -199, -3 x1 - 
              3 x3 - 2 x4 - 5 x5 - 
              3 x6 ≤ -199, -3 x1 - 3 x3 - 3 x4 - 
              5 x5 - 2 x6 ≤ -199, -3 x1 - 2 x2 - 
              5 x4 - 3 x5 - 3 x6 ≤ -199, -3 x1 - 
              2 x2 - 5 x3 - 3 x5 - 
              3 x6 ≤ -199, -3 x1 - 3 x2 - 5 x4 - 
              2 x5 - 3 x6 ≤ -199, -3 x1 - 3 x2 - 
              5 x4 - 3 x5 - 2 x6 ≤ -199, -3 x1 - 
              3 x2 - 5 x3 - 2 x5 - 
              3 x6 ≤ -199, -3 x1 - 3 x2 - 5 x3 - 
              3 x5 - 2 x6 ≤ -199, -3 x1 - 5 x2 - 
              2 x3 - 3 x4 - 3 x6 ≤ -199, -3 x1 - 
              5 x2 - 3 x3 - 2 x4 - 
              3 x6 ≤ -199, -3 x1 - 5 x2 - 3 x3 - 
              3 x4 - 2 x6 ≤ -199, -5 x1 - 2 x2 - 
              3 x3 - 3 x4 - 3 x5 ≤ -199, -5 x1 - 
              3 x2 - 2 x3 - 3 x4 - 
              3 x5 ≤ -199, -5 x1 - 3 x2 - 3 x3 - 
              2 x4 - 3 x5 ≤ -199, -5 x1 - 3 x2 - 
              3 x3 - 3 x4 - 2 x5 ≤ -199, 
          3 x1 - 2 x3 - 12 x5 ≤ 43, 
          3 x1 - 12 x3 - 2 x5 ≤ 43, 
          3 x1 - 2 x2 - 12 x4 ≤ 43, 
          3 x1 - 12 x2 - 2 x4 ≤ 43, 
          3 x2 - 2 x3 - 12 x6 ≤ 43, 
          3 x2 - 12 x3 - 2 x6 ≤ 43, 
          3 x4 - 2 x5 - 12 x6 ≤ 43, 
          3 x4 - 12 x5 - 2 x6 ≤ 
            43, -2 x4 + 3 x5 - 12 x6 ≤ 
            43, -2 x4 - 12 x5 + 3 x6 ≤ 
            43, -12 x4 + 3 x5 - 2 x6 ≤ 
            43, -12 x4 - 2 x5 + 3 x6 ≤ 
            43, -2 x2 + 3 x3 - 12 x6 ≤ 
            43, -2 x2 - 12 x3 + 3 x6 ≤ 
            43, -12 x2 + 3 x3 - 2 x6 ≤ 
            43, -12 x2 - 2 x3 + 3 x6 ≤ 
            43, -2 x1 + 3 x2 - 12 x4 ≤ 
            43, -2 x1 + 3 x3 - 12 x5 ≤ 
            43, -2 x1 - 12 x3 + 3 x5 ≤ 
            43, -2 x1 - 12 x2 + 3 x4 ≤ 
            43, -12 x1 + 3 x2 - 2 x4 ≤ 
            43, -12 x1 + 3 x3 - 2 x5 ≤ 
            43, -12 x1 - 2 x3 + 3 x5 ≤ 
            43, -12 x1 - 2 x2 + 3 x4 ≤ 43, 
          5 x1 - 4 x2 - 6 x3 - 10 x4 - 12 x5 - 
              16 x6 ≤ -469, 
          5 x1 - 6 x2 - 4 x3 - 12 x4 - 10 x5 - 
              16 x6 ≤ -469, 
          5 x1 - 10 x2 - 12 x3 - 4 x4 - 6 x5 - 
              16 x6 ≤ -469, 
          5 x1 - 12 x2 - 10 x3 - 6 x4 - 4 x5 - 
              16 x6 ≤ -469, -4 x1 + 5 x2 - 6 x3 - 
              10 x4 - 16 x5 - 12 x6 ≤ -469, -4 x1 - 
              6 x2 + 5 x3 - 16 x4 - 10 x5 - 
              12 x6 ≤ -469, -4 x1 - 10 x2 - 16 x3 + 
              5 x4 - 6 x5 - 12 x6 ≤ -469, -4 x1 - 
              16 x2 - 10 x3 - 6 x4 + 5 x5 - 
              12 x6 ≤ -469, -6 x1 + 5 x2 - 4 x3 - 
              12 x4 - 16 x5 - 10 x6 ≤ -469, -6 x1 - 
              4 x2 + 5 x3 - 16 x4 - 12 x5 - 
              10 x6 ≤ -469, -6 x1 - 12 x2 - 16 x3 + 
              5 x4 - 4 x5 - 10 x6 ≤ -469, -6 x1 - 
              16 x2 - 12 x3 - 4 x4 + 5 x5 - 
              10 x6 ≤ -469, -10 x1 + 5 x2 - 12 x3 - 
              4 x4 - 16 x5 - 6 x6 ≤ -469, -10 x1 - 
              4 x2 - 16 x3 + 5 x4 - 12 x5 - 
              6 x6 ≤ -469, -10 x1 - 12 x2 + 5 x3 - 
              16 x4 - 4 x5 - 6 x6 ≤ -469, -10 x1 - 
              16 x2 - 4 x3 - 12 x4 + 5 x5 - 
              6 x6 ≤ -469, -12 x1 + 5 x2 - 10 x3 - 
              6 x4 - 16 x5 - 4 x6 ≤ -469, -12 x1 - 
              6 x2 - 16 x3 + 5 x4 - 10 x5 - 
              4 x6 ≤ -469, -12 x1 - 10 x2 + 5 x3 - 
              16 x4 - 6 x5 - 4 x6 ≤ -469, -12 x1 - 
              16 x2 - 6 x3 - 10 x4 + 5 x5 - 
              4 x6 ≤ -469, -16 x1 - 4 x2 - 10 x3 - 
              6 x4 - 12 x5 + 5 x6 ≤ -469, -16 x1 - 
              6 x2 - 12 x3 - 4 x4 - 10 x5 + 
              5 x6 ≤ -469, -16 x1 - 10 x2 - 4 x3 - 
              12 x4 - 6 x5 + 5 x6 ≤ -469, -16 x1 - 
              12 x2 - 6 x3 - 10 x4 - 4 x5 + 5 x6 ≤ -469, 
          23 x1 + 14 x2 + 2 x3 - 4 x4 + 14 x5 + 14 x6 ≤ 
            1383, 23 x1 + 14 x2 - 4 x3 + 2 x4 + 14 x5 + 
              14 x6 ≤ 1383, 
          23 x1 + 2 x2 + 14 x3 + 14 x4 - 4 x5 + 14 x6 ≤ 
            1383, 23 x1 - 4 x2 + 14 x3 + 14 x4 + 2 x5 + 
              14 x6 ≤ 1383, 
          14 x1 + 23 x2 + 2 x3 - 4 x4 + 14 x5 + 14 x6 ≤ 
            1383, 14 x1 + 23 x2 - 4 x3 + 2 x4 + 14 x5 + 
              14 x6 ≤ 1383, 
          14 x1 + 14 x2 + 2 x3 - 4 x4 + 23 x5 + 14 x6 ≤ 
            1383, 14 x1 + 14 x2 + 2 x3 - 4 x4 + 14 x5 + 
              23 x6 ≤ 1383, 
          14 x1 + 14 x2 - 4 x3 + 2 x4 + 23 x5 + 14 x6 ≤ 
            1383, 14 x1 + 14 x2 - 4 x3 + 2 x4 + 14 x5 + 
              23 x6 ≤ 1383, 
          14 x1 + 2 x2 + 23 x3 + 14 x4 - 4 x5 + 14 x6 ≤ 
            1383, 14 x1 + 2 x2 + 14 x3 + 23 x4 - 4 x5 + 
              14 x6 ≤ 1383, 
          14 x1 + 2 x2 + 14 x3 + 14 x4 - 4 x5 + 23 x6 ≤ 
            1383, 14 x1 - 4 x2 + 23 x3 + 14 x4 + 2 x5 + 
              14 x6 ≤ 1383, 
          14 x1 - 4 x2 + 14 x3 + 23 x4 + 2 x5 + 14 x6 ≤ 
            1383, 14 x1 - 4 x2 + 14 x3 + 14 x4 + 2 x5 + 
              23 x6 ≤ 1383, 
          2 x1 + 23 x2 + 14 x3 + 14 x4 + 14 x5 - 4 x6 ≤ 
            1383, 2 x1 + 14 x2 + 23 x3 + 14 x4 + 14 x5 - 
              4 x6 ≤ 1383, 
          2 x1 + 14 x2 + 14 x3 + 23 x4 + 14 x5 - 4 x6 ≤ 
            1383, 2 x1 + 14 x2 + 14 x3 + 14 x4 + 23 x5 - 
              4 x6 ≤ 
            1383, -4 x1 + 23 x2 + 14 x3 + 14 x4 + 14 x5 + 
              2 x6 ≤ 
            1383, -4 x1 + 14 x2 + 23 x3 + 14 x4 + 14 x5 + 
              2 x6 ≤ 
            1383, -4 x1 + 14 x2 + 14 x3 + 23 x4 + 14 x5 + 
              2 x6 ≤ 
            1383, -4 x1 + 14 x2 + 14 x3 + 14 x4 + 23 x5 + 
              2 x6 ≤ 1383, 
          27 x1 + 18 x2 - 6 x3 + 16 x5 + 18 x6 ≤ 1633, 
          27 x1 + 16 x2 - 6 x4 + 18 x5 + 18 x6 ≤ 1633, 
          27 x1 + 16 x3 + 18 x4 - 6 x5 + 18 x6 ≤ 1633, 
          27 x1 - 6 x2 + 18 x3 + 16 x4 + 18 x6 ≤ 1633, 
          18 x1 + 27 x2 - 6 x3 + 18 x5 + 16 x6 ≤ 1633, 
          18 x1 + 18 x2 - 6 x4 + 27 x5 + 16 x6 ≤ 1633, 
          18 x1 + 18 x2 - 6 x4 + 16 x5 + 27 x6 ≤ 1633, 
          18 x1 + 16 x2 - 6 x3 + 18 x5 + 27 x6 ≤ 1633, 
          18 x1 + 18 x3 + 27 x4 - 6 x5 + 16 x6 ≤ 1633, 
          18 x1 + 18 x3 + 16 x4 - 6 x5 + 27 x6 ≤ 1633, 
          18 x1 - 6 x2 + 27 x3 + 18 x4 + 16 x6 ≤ 1633, 
          18 x1 - 6 x2 + 16 x3 + 18 x4 + 27 x6 ≤ 1633, 
          16 x1 + 27 x2 - 6 x4 + 18 x5 + 18 x6 ≤ 1633, 
          16 x1 + 18 x2 - 6 x3 + 27 x5 + 18 x6 ≤ 1633, 
          16 x1 + 27 x3 + 18 x4 - 6 x5 + 18 x6 ≤ 1633, 
          16 x1 - 6 x2 + 18 x3 + 27 x4 + 18 x6 ≤ 1633, 
          27 x2 + 16 x3 + 18 x4 + 18 x5 - 6 x6 ≤ 1633, 
          18 x2 + 18 x3 + 27 x4 + 16 x5 - 6 x6 ≤ 1633, 
          18 x2 + 18 x3 + 16 x4 + 27 x5 - 6 x6 ≤ 1633, 
          16 x2 + 27 x3 + 18 x4 + 18 x5 - 6 x6 ≤ 
            1633, -6 x1 + 27 x2 + 18 x3 + 16 x4 + 18 x5 ≤ 
            1633, -6 x1 + 18 x2 + 27 x3 + 18 x4 + 16 x5 ≤ 
            1633, -6 x1 + 18 x2 + 16 x3 + 18 x4 + 27 x5 ≤ 
            1633, -6 x1 + 16 x2 + 18 x3 + 27 x4 + 18 x5 ≤ 
            1633, 25 x1 + 16 x2 + 10 x3 + 4 x4 + 10 x5 + 
              4 x6 ≤ 1419, 
          25 x1 + 10 x2 + 16 x3 + 10 x4 + 4 x5 + 4 x6 ≤ 
            1419, 25 x1 + 10 x2 + 4 x3 + 10 x4 + 16 x5 + 
              4 x6 ≤ 1419, 
          25 x1 + 4 x2 + 10 x3 + 16 x4 + 10 x5 + 4 x6 ≤ 
            1419, 16 x1 + 25 x2 + 10 x3 + 4 x4 + 4 x5 + 
              10 x6 ≤ 1419, 
          16 x1 + 10 x2 + 25 x3 + 4 x4 + 4 x5 + 10 x6 ≤ 
            1419, 16 x1 + 4 x2 + 4 x3 + 25 x4 + 10 x5 + 
              10 x6 ≤ 1419, 
          16 x1 + 4 x2 + 4 x3 + 10 x4 + 25 x5 + 10 x6 ≤ 
            1419, 10 x1 + 25 x2 + 16 x3 + 10 x4 + 4 x5 + 
              4 x6 ≤ 1419, 
          10 x1 + 25 x2 + 4 x3 + 10 x4 + 4 x5 + 16 x6 ≤ 
            1419, 10 x1 + 16 x2 + 25 x3 + 4 x4 + 10 x5 + 
              4 x6 ≤ 1419, 
          10 x1 + 10 x2 + 4 x3 + 25 x4 + 16 x5 + 4 x6 ≤ 
            1419, 10 x1 + 10 x2 + 4 x3 + 25 x4 + 4 x5 + 
              16 x6 ≤ 1419, 
          10 x1 + 4 x2 + 25 x3 + 4 x4 + 10 x5 + 16 x6 ≤ 
            1419, 10 x1 + 4 x2 + 10 x3 + 16 x4 + 25 x5 + 
              4 x6 ≤ 1419, 
          10 x1 + 4 x2 + 10 x3 + 4 x4 + 25 x5 + 16 x6 ≤ 
            1419, 4 x1 + 25 x2 + 10 x3 + 16 x4 + 4 x5 + 
              10 x6 ≤ 1419, 
          4 x1 + 16 x2 + 4 x3 + 25 x4 + 10 x5 + 10 x6 ≤ 
            1419, 4 x1 + 16 x2 + 4 x3 + 10 x4 + 10 x5 + 
              25 x6 ≤ 1419, 
          4 x1 + 10 x2 + 25 x3 + 4 x4 + 16 x5 + 10 x6 ≤ 
            1419, 4 x1 + 10 x2 + 10 x3 + 16 x4 + 4 x5 + 
              25 x6 ≤ 1419, 
          4 x1 + 10 x2 + 10 x3 + 4 x4 + 16 x5 + 25 x6 ≤ 
            1419, 4 x1 + 4 x2 + 16 x3 + 10 x4 + 25 x5 + 
              10 x6 ≤ 1419, 
          4 x1 + 4 x2 + 16 x3 + 10 x4 + 10 x5 + 25 x6 ≤ 
            1419, 25 x1 + 14 x2 + 10 x3 + 4 x4 + 10 x5 + 
              4 x6 ≤ 1381, 
          25 x1 + 10 x2 + 14 x3 + 10 x4 + 4 x5 + 4 x6 ≤ 
            1381, 25 x1 + 10 x2 + 4 x3 + 10 x4 + 14 x5 + 
              4 x6 ≤ 1381, 
          25 x1 + 4 x2 + 10 x3 + 14 x4 + 10 x5 + 4 x6 ≤ 
            1381, 14 x1 + 25 x2 + 10 x3 + 4 x4 + 4 x5 + 
              10 x6 ≤ 1381, 
          14 x1 + 10 x2 + 25 x3 + 4 x4 + 4 x5 + 10 x6 ≤ 
            1381, 14 x1 + 4 x2 + 4 x3 + 25 x4 + 10 x5 + 
              10 x6 ≤ 1381, 
          14 x1 + 4 x2 + 4 x3 + 10 x4 + 25 x5 + 10 x6 ≤ 
            1381, 10 x1 + 25 x2 + 14 x3 + 10 x4 + 4 x5 + 
              4 x6 ≤ 1381, 
          10 x1 + 25 x2 + 4 x3 + 10 x4 + 4 x5 + 14 x6 ≤ 
            1381, 10 x1 + 14 x2 + 25 x3 + 4 x4 + 10 x5 + 
              4 x6 ≤ 1381, 
          10 x1 + 10 x2 + 4 x3 + 25 x4 + 14 x5 + 4 x6 ≤ 
            1381, 10 x1 + 10 x2 + 4 x3 + 25 x4 + 4 x5 + 
              14 x6 ≤ 1381, 
          10 x1 + 4 x2 + 25 x3 + 4 x4 + 10 x5 + 14 x6 ≤ 
            1381, 10 x1 + 4 x2 + 10 x3 + 14 x4 + 25 x5 + 
              4 x6 ≤ 1381, 
          10 x1 + 4 x2 + 10 x3 + 4 x4 + 25 x5 + 14 x6 ≤ 
            1381, 4 x1 + 25 x2 + 10 x3 + 14 x4 + 4 x5 + 
              10 x6 ≤ 1381, 
          4 x1 + 14 x2 + 4 x3 + 25 x4 + 10 x5 + 10 x6 ≤ 
            1381, 4 x1 + 14 x2 + 4 x3 + 10 x4 + 10 x5 + 
              25 x6 ≤ 1381, 
          4 x1 + 10 x2 + 25 x3 + 4 x4 + 14 x5 + 10 x6 ≤ 
            1381, 4 x1 + 10 x2 + 10 x3 + 14 x4 + 4 x5 + 
              25 x6 ≤ 1381, 
          4 x1 + 10 x2 + 10 x3 + 4 x4 + 14 x5 + 25 x6 ≤ 
            1381, 4 x1 + 4 x2 + 14 x3 + 10 x4 + 25 x5 + 
              10 x6 ≤ 1381, 
          4 x1 + 4 x2 + 14 x3 + 10 x4 + 10 x5 + 25 x6 ≤ 
            1381, 27 x1 + 18 x2 - 6 x3 + 16 x5 + 16 x6 ≤ 
            1595, 27 x1 + 16 x2 - 6 x4 + 18 x5 + 16 x6 ≤ 
            1595, 
          27 x1 + 16 x3 + 18 x4 - 6 x5 + 16 x6 ≤ 1595, 
          27 x1 - 6 x2 + 18 x3 + 16 x4 + 16 x6 ≤ 1595, 
          18 x1 + 27 x2 - 6 x3 + 16 x5 + 16 x6 ≤ 1595, 
          18 x1 + 16 x2 - 6 x4 + 27 x5 + 16 x6 ≤ 1595, 
          18 x1 + 16 x3 + 27 x4 - 6 x5 + 16 x6 ≤ 1595, 
          18 x1 - 6 x2 + 27 x3 + 16 x4 + 16 x6 ≤ 1595, 
          16 x1 + 27 x2 - 6 x4 + 16 x5 + 18 x6 ≤ 1595, 
          16 x1 + 18 x2 - 6 x4 + 16 x5 + 27 x6 ≤ 1595, 
          16 x1 + 16 x2 - 6 x3 + 27 x5 + 18 x6 ≤ 1595, 
          16 x1 + 16 x2 - 6 x3 + 18 x5 + 27 x6 ≤ 1595, 
          16 x1 + 27 x3 + 16 x4 - 6 x5 + 18 x6 ≤ 1595, 
          16 x1 + 18 x3 + 16 x4 - 6 x5 + 27 x6 ≤ 1595, 
          16 x1 - 6 x2 + 16 x3 + 27 x4 + 18 x6 ≤ 1595, 
          16 x1 - 6 x2 + 16 x3 + 18 x4 + 27 x6 ≤ 1595, 
          27 x2 + 16 x3 + 18 x4 + 16 x5 - 6 x6 ≤ 1595, 
          18 x2 + 16 x3 + 27 x4 + 16 x5 - 6 x6 ≤ 1595, 
          16 x2 + 27 x3 + 16 x4 + 18 x5 - 6 x6 ≤ 1595, 
          16 x2 + 18 x3 + 16 x4 + 27 x5 - 6 x6 ≤ 
            1595, -6 x1 + 27 x2 + 18 x3 + 16 x4 + 16 x5 ≤ 
            1595, -6 x1 + 18 x2 + 27 x3 + 16 x4 + 16 x5 ≤ 
            1595, -6 x1 + 16 x2 + 16 x3 + 27 x4 + 18 x5 ≤ 
            1595, -6 x1 + 16 x2 + 16 x3 + 18 x4 + 27 x5 ≤ 
            1595, 8 x1 + 5 x2 + 2 x3 + 2 x4 + 4 x5 + 2 x6 ≤ 
            467, 8 x1 + 4 x2 + 2 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 
            467, 8 x1 + 2 x2 + 5 x3 + 4 x4 + 2 x5 + 2 x6 ≤ 
            467, 8 x1 + 2 x2 + 4 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 
            467, 5 x1 + 8 x2 + 2 x3 + 2 x4 + 2 x5 + 4 x6 ≤ 
            467, 5 x1 + 2 x2 + 8 x3 + 2 x4 + 2 x5 + 4 x6 ≤ 
            467, 5 x1 + 2 x2 + 2 x3 + 8 x4 + 2 x5 + 4 x6 ≤ 
            467, 5 x1 + 2 x2 + 2 x3 + 2 x4 + 8 x5 + 4 x6 ≤ 
            467, 
          4 x1 + 8 x2 + 2 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 467, 
          4 x1 + 2 x2 + 8 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 467, 
          4 x1 + 2 x2 + 2 x3 + 8 x4 + 2 x5 + 5 x6 ≤ 467, 
          4 x1 + 2 x2 + 2 x3 + 2 x4 + 8 x5 + 5 x6 ≤ 467, 
          2 x1 + 8 x2 + 5 x3 + 4 x4 + 2 x5 + 2 x6 ≤ 467, 
          2 x1 + 8 x2 + 4 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 467, 
          2 x1 + 5 x2 + 8 x3 + 2 x4 + 4 x5 + 2 x6 ≤ 467, 
          2 x1 + 5 x2 + 2 x3 + 8 x4 + 4 x5 + 2 x6 ≤ 467, 
          2 x1 + 5 x2 + 2 x3 + 2 x4 + 4 x5 + 8 x6 ≤ 467, 
          2 x1 + 4 x2 + 8 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 467, 
          2 x1 + 4 x2 + 2 x3 + 8 x4 + 5 x5 + 2 x6 ≤ 467, 
          2 x1 + 4 x2 + 2 x3 + 2 x4 + 5 x5 + 8 x6 ≤ 467, 
          2 x1 + 2 x2 + 5 x3 + 4 x4 + 8 x5 + 2 x6 ≤ 467, 
          2 x1 + 2 x2 + 5 x3 + 4 x4 + 2 x5 + 8 x6 ≤ 467, 
          2 x1 + 2 x2 + 4 x3 + 5 x4 + 8 x5 + 2 x6 ≤ 467, 
          2 x1 + 2 x2 + 4 x3 + 5 x4 + 2 x5 + 8 x6 ≤ 467, 
          x1 - 2 x2 - 3 x3 - 3 x4 - 3 x5 - 5 x6 ≤ -176, 
          x1 - 3 x2 - 2 x3 - 3 x4 - 3 x5 - 5 x6 ≤ -176, 
          x1 - 3 x2 - 3 x3 - 2 x4 - 3 x5 - 5 x6 ≤ -176, 
          x1 - 3 x2 - 3 x3 - 3 x4 - 2 x5 - 
              5 x6 ≤ -176, -2 x1 + x2 - 3 x3 - 3 x4 - 
              5 x5 - 3 x6 ≤ -176, -2 x1 - 3 x2 + x3 - 
              5 x4 - 3 x5 - 3 x6 ≤ -176, -2 x1 - 
              3 x2 - 5 x3 + x4 - 3 x5 - 
              3 x6 ≤ -176, -2 x1 - 5 x2 - 3 x3 - 
              3 x4 + x5 - 3 x6 ≤ -176, -3 x1 + x2 - 
              2 x3 - 3 x4 - 5 x5 - 
              3 x6 ≤ -176, -3 x1 + x2 - 3 x3 - 2 x4 - 
              5 x5 - 3 x6 ≤ -176, -3 x1 + x2 - 3 x3 - 
              3 x4 - 5 x5 - 2 x6 ≤ -176, -3 x1 - 
              2 x2 + x3 - 5 x4 - 3 x5 - 
              3 x6 ≤ -176, -3 x1 - 2 x2 - 5 x3 + x4 - 
              3 x5 - 3 x6 ≤ -176, -3 x1 - 3 x2 + x3 - 
              5 x4 - 2 x5 - 3 x6 ≤ -176, -3 x1 - 
              3 x2 + x3 - 5 x4 - 3 x5 - 
              2 x6 ≤ -176, -3 x1 - 3 x2 - 5 x3 + x4 - 
              2 x5 - 3 x6 ≤ -176, -3 x1 - 3 x2 - 
              5 x3 + x4 - 3 x5 - 2 x6 ≤ -176, -3 x1 - 
              5 x2 - 2 x3 - 3 x4 + x5 - 
              3 x6 ≤ -176, -3 x1 - 5 x2 - 3 x3 - 
              2 x4 + x5 - 3 x6 ≤ -176, -3 x1 - 5 x2 - 
              3 x3 - 3 x4 + x5 - 2 x6 ≤ -176, -5 x1 - 
              2 x2 - 3 x3 - 3 x4 - 3 x5 + 
              x6 ≤ -176, -5 x1 - 3 x2 - 2 x3 - 3 x4 - 
              3 x5 + x6 ≤ -176, -5 x1 - 3 x2 - 3 x3 - 
              2 x4 - 3 x5 + x6 ≤ -176, -5 x1 - 3 x2 - 
              3 x3 - 3 x4 - 2 x5 + x6 ≤ -176, 
          2 x1 - x2 - 2 x3 - 2 x4 - 2 x5 - 4 x6 ≤ -83, 
          2 x1 - 2 x2 - x3 - 2 x4 - 2 x5 - 4 x6 ≤ -83, 
          2 x1 - 2 x2 - 2 x3 - x4 - 2 x5 - 4 x6 ≤ -83, 
          2 x1 - 2 x2 - 2 x3 - 2 x4 - x5 - 
              4 x6 ≤ -83, -x1 + 2 x2 - 2 x3 - 2 x4 - 
              4 x5 - 2 x6 ≤ -83, -x1 - 2 x2 + 2 x3 - 
              4 x4 - 2 x5 - 2 x6 ≤ -83, -x1 - 2 x2 - 
              4 x3 + 2 x4 - 2 x5 - 2 x6 ≤ -83, -x1 - 
              4 x2 - 2 x3 - 2 x4 + 2 x5 - 
              2 x6 ≤ -83, -2 x1 + 2 x2 - x3 - 2 x4 - 
              4 x5 - 2 x6 ≤ -83, -2 x1 + 2 x2 - 
              2 x3 - x4 - 4 x5 - 2 x6 ≤ -83, -2 x1 + 
              2 x2 - 2 x3 - 2 x4 - 4 x5 - 
              x6 ≤ -83, -2 x1 - x2 + 2 x3 - 4 x4 - 
              2 x5 - 2 x6 ≤ -83, -2 x1 - x2 - 4 x3 + 
              2 x4 - 2 x5 - 2 x6 ≤ -83, -2 x1 - 
              2 x2 + 2 x3 - 4 x4 - x5 - 
              2 x6 ≤ -83, -2 x1 - 2 x2 + 2 x3 - 
              4 x4 - 2 x5 - x6 ≤ -83, -2 x1 - 2 x2 - 
              4 x3 + 2 x4 - x5 - 2 x6 ≤ -83, -2 x1 - 
              2 x2 - 4 x3 + 2 x4 - 2 x5 - 
              x6 ≤ -83, -2 x1 - 4 x2 - x3 - 2 x4 + 
              2 x5 - 2 x6 ≤ -83, -2 x1 - 4 x2 - 
              2 x3 - x4 + 2 x5 - 2 x6 ≤ -83, -2 x1 - 
              4 x2 - 2 x3 - 2 x4 + 2 x5 - 
              x6 ≤ -83, -4 x1 - x2 - 2 x3 - 2 x4 - 
              2 x5 + 2 x6 ≤ -83, -4 x1 - 2 x2 - x3 - 
              2 x4 - 2 x5 + 2 x6 ≤ -83, -4 x1 - 
              2 x2 - 2 x3 - x4 - 2 x5 + 
              2 x6 ≤ -83, -4 x1 - 2 x2 - 2 x3 - 
              2 x4 - x5 + 2 x6 ≤ -83, 
          7 x1 + 4 x2 - 2 x4 + 4 x5 + 4 x6 ≤ 395, 
          7 x1 + 4 x2 - 2 x3 + 4 x5 + 4 x6 ≤ 395, 
          7 x1 + 4 x3 + 4 x4 - 2 x5 + 4 x6 ≤ 395, 
          7 x1 - 2 x2 + 4 x3 + 4 x4 + 4 x6 ≤ 395, 
          4 x1 + 7 x2 - 2 x4 + 4 x5 + 4 x6 ≤ 395, 
          4 x1 + 7 x2 - 2 x3 + 4 x5 + 4 x6 ≤ 395, 
          4 x1 + 4 x2 - 2 x4 + 7 x5 + 4 x6 ≤ 395, 
          4 x1 + 4 x2 - 2 x4 + 4 x5 + 7 x6 ≤ 395, 
          4 x1 + 4 x2 - 2 x3 + 7 x5 + 4 x6 ≤ 395, 
          4 x1 + 4 x2 - 2 x3 + 4 x5 + 7 x6 ≤ 395, 
          4 x1 + 7 x3 + 4 x4 - 2 x5 + 4 x6 ≤ 395, 
          4 x1 + 4 x3 + 7 x4 - 2 x5 + 4 x6 ≤ 395, 
          4 x1 + 4 x3 + 4 x4 - 2 x5 + 7 x6 ≤ 395, 
          4 x1 - 2 x2 + 7 x3 + 4 x4 + 4 x6 ≤ 395, 
          4 x1 - 2 x2 + 4 x3 + 7 x4 + 4 x6 ≤ 395, 
          4 x1 - 2 x2 + 4 x3 + 4 x4 + 7 x6 ≤ 395, 
          7 x2 + 4 x3 + 4 x4 + 4 x5 - 2 x6 ≤ 395, 
          4 x2 + 7 x3 + 4 x4 + 4 x5 - 2 x6 ≤ 395, 
          4 x2 + 4 x3 + 7 x4 + 4 x5 - 2 x6 ≤ 395, 
          4 x2 + 4 x3 + 4 x4 + 7 x5 - 2 x6 ≤ 
            395, -2 x1 + 7 x2 + 4 x3 + 4 x4 + 4 x5 ≤ 
            395, -2 x1 + 4 x2 + 7 x3 + 4 x4 + 4 x5 ≤ 
            395, -2 x1 + 4 x2 + 4 x3 + 7 x4 + 4 x5 ≤ 
            395, -2 x1 + 4 x2 + 4 x3 + 4 x4 + 7 x5 ≤ 395, 
          5 x1 + 3 x2 + 2 x3 + 2 x4 + 2 x5 ≤ 290, 
          5 x1 + 2 x2 + 3 x3 + 2 x4 + 2 x5 ≤ 290, 
          5 x1 + 2 x2 + 2 x3 + 3 x4 + 2 x5 ≤ 290, 
          5 x1 + 2 x2 + 2 x3 + 2 x4 + 3 x5 ≤ 290, 
          3 x1 + 5 x2 + 2 x3 + 2 x4 + 2 x6 ≤ 290, 
          3 x1 + 2 x2 + 5 x3 + 2 x5 + 2 x6 ≤ 290, 
          3 x1 + 2 x2 + 5 x4 + 2 x5 + 2 x6 ≤ 290, 
          3 x1 + 2 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 290, 
          2 x1 + 5 x2 + 3 x3 + 2 x4 + 2 x6 ≤ 290, 
          2 x1 + 5 x2 + 2 x3 + 3 x4 + 2 x6 ≤ 290, 
          2 x1 + 5 x2 + 2 x3 + 2 x4 + 3 x6 ≤ 290, 
          2 x1 + 3 x2 + 5 x3 + 2 x5 + 2 x6 ≤ 290, 
          2 x1 + 3 x2 + 5 x4 + 2 x5 + 2 x6 ≤ 290, 
          2 x1 + 2 x2 + 5 x3 + 3 x5 + 2 x6 ≤ 290, 
          2 x1 + 2 x2 + 5 x3 + 2 x5 + 3 x6 ≤ 290, 
          2 x1 + 2 x2 + 5 x4 + 3 x5 + 2 x6 ≤ 290, 
          2 x1 + 2 x2 + 5 x4 + 2 x5 + 3 x6 ≤ 290, 
          2 x1 + 3 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 290, 
          2 x1 + 2 x3 + 3 x4 + 5 x5 + 2 x6 ≤ 290, 
          2 x1 + 2 x3 + 2 x4 + 5 x5 + 3 x6 ≤ 290, 
          3 x2 + 2 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 290, 
          2 x2 + 3 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 290, 
          2 x2 + 2 x3 + 3 x4 + 2 x5 + 5 x6 ≤ 290, 
          2 x2 + 2 x3 + 2 x4 + 3 x5 + 5 x6 ≤ 290, 
          9 x1 + 6 x2 + 2 x3 + 6 x5 + 6 x6 ≤ 597, 
          9 x1 + 6 x2 + 2 x4 + 6 x5 + 6 x6 ≤ 597, 
          9 x1 + 2 x2 + 6 x3 + 6 x4 + 6 x6 ≤ 597, 
          9 x1 + 6 x3 + 6 x4 + 2 x5 + 6 x6 ≤ 597, 
          6 x1 + 9 x2 + 2 x3 + 6 x5 + 6 x6 ≤ 597, 
          6 x1 + 9 x2 + 2 x4 + 6 x5 + 6 x6 ≤ 597, 
          6 x1 + 6 x2 + 2 x3 + 9 x5 + 6 x6 ≤ 597, 
          6 x1 + 6 x2 + 2 x3 + 6 x5 + 9 x6 ≤ 597, 
          6 x1 + 6 x2 + 2 x4 + 9 x5 + 6 x6 ≤ 597, 
          6 x1 + 6 x2 + 2 x4 + 6 x5 + 9 x6 ≤ 597, 
          6 x1 + 2 x2 + 9 x3 + 6 x4 + 6 x6 ≤ 597, 
          6 x1 + 2 x2 + 6 x3 + 9 x4 + 6 x6 ≤ 597, 
          6 x1 + 2 x2 + 6 x3 + 6 x4 + 9 x6 ≤ 597, 
          6 x1 + 9 x3 + 6 x4 + 2 x5 + 6 x6 ≤ 597, 
          6 x1 + 6 x3 + 9 x4 + 2 x5 + 6 x6 ≤ 597, 
          6 x1 + 6 x3 + 6 x4 + 2 x5 + 9 x6 ≤ 597, 
          2 x1 + 9 x2 + 6 x3 + 6 x4 + 6 x5 ≤ 597, 
          2 x1 + 6 x2 + 9 x3 + 6 x4 + 6 x5 ≤ 597, 
          2 x1 + 6 x2 + 6 x3 + 9 x4 + 6 x5 ≤ 597, 
          2 x1 + 6 x2 + 6 x3 + 6 x4 + 9 x5 ≤ 597, 
          9 x2 + 6 x3 + 6 x4 + 6 x5 + 2 x6 ≤ 597, 
          6 x2 + 9 x3 + 6 x4 + 6 x5 + 2 x6 ≤ 597, 
          6 x2 + 6 x3 + 9 x4 + 6 x5 + 2 x6 ≤ 597, 
          6 x2 + 6 x3 + 6 x4 + 9 x5 + 2 x6 ≤ 597, 
          5 x1 + 2 x2 + 2 x3 + 2 x4 + 2 x6 ≤ 277, 
          5 x1 + 2 x2 + 2 x3 + 2 x5 + 2 x6 ≤ 277, 
          5 x1 + 2 x2 + 2 x4 + 2 x5 + 2 x6 ≤ 277, 
          5 x1 + 2 x3 + 2 x4 + 2 x5 + 2 x6 ≤ 277, 
          2 x1 + 5 x2 + 2 x3 + 2 x4 + 2 x5 ≤ 277, 
          2 x1 + 5 x2 + 2 x3 + 2 x5 + 2 x6 ≤ 277, 
          2 x1 + 5 x2 + 2 x4 + 2 x5 + 2 x6 ≤ 277, 
          2 x1 + 2 x2 + 5 x3 + 2 x4 + 2 x5 ≤ 277, 
          2 x1 + 2 x2 + 5 x3 + 2 x4 + 2 x6 ≤ 277, 
          2 x1 + 2 x2 + 2 x3 + 5 x4 + 2 x5 ≤ 277, 
          2 x1 + 2 x2 + 2 x3 + 5 x4 + 2 x6 ≤ 277, 
          2 x1 + 2 x2 + 2 x3 + 2 x4 + 5 x5 ≤ 277, 
          2 x1 + 2 x2 + 2 x3 + 2 x4 + 5 x6 ≤ 277, 
          2 x1 + 2 x2 + 2 x3 + 5 x5 + 2 x6 ≤ 277, 
          2 x1 + 2 x2 + 2 x3 + 2 x5 + 5 x6 ≤ 277, 
          2 x1 + 2 x2 + 2 x4 + 5 x5 + 2 x6 ≤ 277, 
          2 x1 + 2 x2 + 2 x4 + 2 x5 + 5 x6 ≤ 277, 
          2 x1 + 5 x3 + 2 x4 + 2 x5 + 2 x6 ≤ 277, 
          2 x1 + 2 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 277, 
          2 x1 + 2 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 277, 
          5 x2 + 2 x3 + 2 x4 + 2 x5 + 2 x6 ≤ 277, 
          2 x2 + 5 x3 + 2 x4 + 2 x5 + 2 x6 ≤ 277, 
          2 x2 + 2 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 277, 
          2 x2 + 2 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 277, 
          8 x1 + 5 x2 + 2 x3 + 2 x4 + 2 x6 ≤ 415, 
          8 x1 + 2 x2 + 5 x3 + 2 x5 + 2 x6 ≤ 415, 
          8 x1 + 2 x2 + 5 x4 + 2 x5 + 2 x6 ≤ 415, 
          8 x1 + 2 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 415, 
          5 x1 + 8 x2 + 2 x3 + 2 x4 + 2 x5 ≤ 415, 
          5 x1 + 2 x2 + 8 x3 + 2 x4 + 2 x5 ≤ 415, 
          5 x1 + 2 x2 + 2 x3 + 8 x4 + 2 x5 ≤ 415, 
          5 x1 + 2 x2 + 2 x3 + 2 x4 + 8 x5 ≤ 415, 
          2 x1 + 8 x2 + 5 x3 + 2 x5 + 2 x6 ≤ 415, 
          2 x1 + 8 x2 + 5 x4 + 2 x5 + 2 x6 ≤ 415, 
          2 x1 + 5 x2 + 8 x3 + 2 x4 + 2 x6 ≤ 415, 
          2 x1 + 5 x2 + 2 x3 + 8 x4 + 2 x6 ≤ 415, 
          2 x1 + 5 x2 + 2 x3 + 2 x4 + 8 x6 ≤ 415, 
          2 x1 + 2 x2 + 5 x3 + 8 x5 + 2 x6 ≤ 415, 
          2 x1 + 2 x2 + 5 x3 + 2 x5 + 8 x6 ≤ 415, 
          2 x1 + 2 x2 + 5 x4 + 8 x5 + 2 x6 ≤ 415, 
          2 x1 + 2 x2 + 5 x4 + 2 x5 + 8 x6 ≤ 415, 
          2 x1 + 8 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 415, 
          2 x1 + 2 x3 + 8 x4 + 5 x5 + 2 x6 ≤ 415, 
          2 x1 + 2 x3 + 2 x4 + 5 x5 + 8 x6 ≤ 415, 
          8 x2 + 2 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 415, 
          2 x2 + 8 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 415, 
          2 x2 + 2 x3 + 8 x4 + 2 x5 + 5 x6 ≤ 415, 
          2 x2 + 2 x3 + 2 x4 + 8 x5 + 5 x6 ≤ 415, 
          3 x1 + 2 x2 - 6 x3 ≤ 115, 
          3 x1 + 2 x4 - 6 x5 ≤ 115, 
          3 x1 - 6 x4 + 2 x5 ≤ 115, 
          3 x1 - 6 x2 + 2 x3 ≤ 115, 
          2 x1 + 3 x2 - 6 x3 ≤ 115, 
          2 x1 + 3 x4 - 6 x5 ≤ 115, 
          2 x1 - 6 x4 + 3 x5 ≤ 115, 
          2 x1 - 6 x2 + 3 x3 ≤ 115, 
          3 x2 + 2 x4 - 6 x6 ≤ 115, 
          3 x2 - 6 x4 + 2 x6 ≤ 115, 
          2 x2 + 3 x4 - 6 x6 ≤ 115, 
          2 x2 - 6 x4 + 3 x6 ≤ 115, 
          3 x3 + 2 x5 - 6 x6 ≤ 115, 
          3 x3 - 6 x5 + 2 x6 ≤ 115, 
          2 x3 + 3 x5 - 6 x6 ≤ 115, 
          2 x3 - 6 x5 + 3 x6 ≤ 
            115, -6 x3 + 3 x5 + 2 x6 ≤ 
            115, -6 x3 + 2 x5 + 3 x6 ≤ 
            115, -6 x2 + 3 x4 + 2 x6 ≤ 
            115, -6 x2 + 2 x4 + 3 x6 ≤ 
            115, -6 x1 + 3 x2 + 2 x3 ≤ 
            115, -6 x1 + 2 x2 + 3 x3 ≤ 
            115, -6 x1 + 3 x4 + 2 x5 ≤ 
            115, -6 x1 + 2 x4 + 3 x5 ≤ 115, 
          9 x1 + 6 x2 - 2 x3 ≤ 361, 
          9 x1 + 6 x4 - 2 x5 ≤ 361, 
          9 x1 - 2 x4 + 6 x5 ≤ 361, 
          9 x1 - 2 x2 + 6 x3 ≤ 361, 
          6 x1 + 9 x2 - 2 x3 ≤ 361, 
          6 x1 + 9 x4 - 2 x5 ≤ 361, 
          6 x1 - 2 x4 + 9 x5 ≤ 361, 
          6 x1 - 2 x2 + 9 x3 ≤ 361, 
          9 x2 + 6 x4 - 2 x6 ≤ 361, 
          9 x2 - 2 x4 + 6 x6 ≤ 361, 
          6 x2 + 9 x4 - 2 x6 ≤ 361, 
          6 x2 - 2 x4 + 9 x6 ≤ 361, 
          9 x3 + 6 x5 - 2 x6 ≤ 361, 
          9 x3 - 2 x5 + 6 x6 ≤ 361, 
          6 x3 + 9 x5 - 2 x6 ≤ 361, 
          6 x3 - 2 x5 + 9 x6 ≤ 
            361, -2 x3 + 9 x5 + 6 x6 ≤ 
            361, -2 x3 + 6 x5 + 9 x6 ≤ 
            361, -2 x2 + 9 x4 + 6 x6 ≤ 
            361, -2 x2 + 6 x4 + 9 x6 ≤ 
            361, -2 x1 + 9 x2 + 6 x3 ≤ 
            361, -2 x1 + 6 x2 + 9 x3 ≤ 
            361, -2 x1 + 9 x4 + 6 x5 ≤ 
            361, -2 x1 + 6 x4 + 9 x5 ≤ 
            361, -x3 - x4 - x6 ≤ -24, -x3 - x4 - 
              x5 ≤ -24, -x2 - x5 - 
              x6 ≤ -24, -x2 - x4 - 
              x5 ≤ -24, -x2 - x3 - 
              x5 ≤ -24, -x2 - x3 - 
              x4 ≤ -24, -x1 - x5 - 
              x6 ≤ -24, -x1 - x4 - 
              x6 ≤ -24, -x1 - x3 - 
              x6 ≤ -24, -x1 - x3 - 
              x4 ≤ -24, -x1 - x2 - 
              x6 ≤ -24, -x1 - x2 - 
              x5 ≤ -24, -2 x2 - 3 x3 - 2 x4 - 3 x5 - 
              5 x6 ≤ -182, -3 x2 - 2 x3 - 3 x4 - 
              2 x5 - 5 x6 ≤ -182, -2 x1 - 3 x3 - 
              2 x4 - 5 x5 - 3 x6 ≤ -182, -2 x1 - 
              2 x2 - 5 x3 - 3 x5 - 
              3 x6 ≤ -182, -2 x1 - 3 x2 - 5 x4 - 
              2 x5 - 3 x6 ≤ -182, -2 x1 - 5 x2 - 
              2 x3 - 3 x4 - 3 x6 ≤ -182, -3 x1 - 
              2 x3 - 3 x4 - 5 x5 - 
              2 x6 ≤ -182, -3 x1 - 2 x2 - 5 x4 - 
              3 x5 - 2 x6 ≤ -182, -3 x1 - 3 x2 - 
              5 x3 - 2 x5 - 2 x6 ≤ -182, -3 x1 - 
              5 x2 - 3 x3 - 2 x4 - 
              2 x6 ≤ -182, -5 x1 - 2 x2 - 2 x3 - 
              3 x4 - 3 x5 ≤ -182, -5 x1 - 3 x2 - 
              3 x3 - 2 x4 - 2 x5 ≤ -182, -3 x2 - 
              4 x3 - 4 x4 - 3 x5 - 
              6 x6 ≤ -248, -4 x2 - 3 x3 - 3 x4 - 
              4 x5 - 6 x6 ≤ -248, -3 x1 - 4 x3 - 
              4 x4 - 6 x5 - 3 x6 ≤ -248, -3 x1 - 
              4 x2 - 6 x4 - 4 x5 - 
              3 x6 ≤ -248, -3 x1 - 4 x2 - 6 x3 - 
              4 x5 - 3 x6 ≤ -248, -3 x1 - 6 x2 - 
              4 x3 - 4 x4 - 3 x6 ≤ -248, -4 x1 - 
              3 x3 - 3 x4 - 6 x5 - 
              4 x6 ≤ -248, -4 x1 - 3 x2 - 6 x4 - 
              3 x5 - 4 x6 ≤ -248, -4 x1 - 3 x2 - 
              6 x3 - 3 x5 - 4 x6 ≤ -248, -4 x1 - 
              6 x2 - 3 x3 - 3 x4 - 
              4 x6 ≤ -248, -6 x1 - 3 x2 - 4 x3 - 
              4 x4 - 3 x5 ≤ -248, -6 x1 - 4 x2 - 
              3 x3 - 3 x4 - 4 x5 ≤ -248, 
          4 x1 + x2 + x4 - 2 x6 ≤ 130, 
          4 x1 + x3 + x5 - 2 x6 ≤ 130, 
          x1 + 4 x2 + x4 - 2 x5 ≤ 130, 
          x1 + x2 - 2 x3 + 4 x4 ≤ 130, 
          x1 + 4 x3 - 2 x4 + x5 ≤ 130, 
          x1 - 2 x2 + x3 + 4 x5 ≤ 130, 
          4 x2 + x3 - 2 x5 + x6 ≤ 130, 
          x2 + 4 x3 - 2 x4 + x6 ≤ 
            130, -2 x3 + 4 x4 + x5 + x6 ≤ 
            130, -2 x2 + x4 + 4 x5 + x6 ≤ 
            130, -2 x1 + x2 + x3 + 4 x6 ≤ 
            130, -2 x1 + x4 + x5 + 4 x6 ≤ 
            130, -3 x3 - 3 x4 - x5 - x6 ≤ -71, -x2 - 
              3 x3 - 3 x4 - x6 ≤ -71, -3 x2 - x4 - 
              3 x5 - x6 ≤ -71, -3 x2 - x3 - 3 x5 - 
              x6 ≤ -71, -x1 - 3 x3 - 3 x4 - 
              x5 ≤ -71, -x1 - x2 - 3 x3 - 
              3 x4 ≤ -71, -x1 - 3 x2 - x4 - 
              3 x5 ≤ -71, -x1 - 3 x2 - x3 - 
              3 x5 ≤ -71, -3 x1 - x4 - x5 - 
              3 x6 ≤ -71, -3 x1 - x3 - x5 - 
              3 x6 ≤ -71, -3 x1 - x2 - x4 - 
              3 x6 ≤ -71, -3 x1 - x2 - x3 - 
              3 x6 ≤ -71, -3 x3 - x4 - x5 - 
              x6 ≤ -47, -x2 - x3 - 3 x5 - 
              x6 ≤ -47, -x2 - x3 - 3 x4 - 
              x6 ≤ -47, -3 x2 - x4 - x5 - 
              x6 ≤ -47, -x1 - x3 - x5 - 
              3 x6 ≤ -47, -x1 - x3 - 3 x4 - 
              x5 ≤ -47, -x1 - x2 - x4 - 
              3 x6 ≤ -47, -x1 - x2 - x4 - 
              3 x5 ≤ -47, -x1 - x2 - 3 x3 - 
              x4 ≤ -47, -x1 - 3 x2 - x3 - 
              x5 ≤ -47, -3 x1 - x4 - x5 - 
              x6 ≤ -47, -3 x1 - x2 - x3 - 
              x6 ≤ -47, 
          x1 - 2 x2 - 8 x3 - 8 x4 - 2 x5 - 4 x6 ≤ -215, 
          x1 - 8 x2 - 2 x3 - 2 x4 - 8 x5 - 
              4 x6 ≤ -215, -2 x1 + x2 - 8 x3 - 8 x4 - 
              4 x5 - 2 x6 ≤ -215, -2 x1 - 4 x2 - 
              8 x3 - 8 x4 + x5 - 2 x6 ≤ -215, -2 x1 - 
              8 x2 + x3 - 4 x4 - 8 x5 - 
              2 x6 ≤ -215, -2 x1 - 8 x2 - 4 x3 + x4 - 
              8 x5 - 2 x6 ≤ -215, -4 x1 - 2 x2 - 
              8 x3 - 8 x4 - 2 x5 + x6 ≤ -215, -4 x1 - 
              8 x2 - 2 x3 - 2 x4 - 8 x5 + 
              x6 ≤ -215, -8 x1 + x2 - 2 x3 - 2 x4 - 
              4 x5 - 8 x6 ≤ -215, -8 x1 - 2 x2 + x3 - 
              4 x4 - 2 x5 - 8 x6 ≤ -215, -8 x1 - 
              2 x2 - 4 x3 + x4 - 2 x5 - 
              8 x6 ≤ -215, -8 x1 - 4 x2 - 2 x3 - 
              2 x4 + x5 - 8 x6 ≤ -215, 
          9 x1 + 6 x2 + 4 x5 + 6 x6 ≤ 535, 
          9 x1 + 4 x2 + 6 x5 + 6 x6 ≤ 535, 
          9 x1 + 6 x3 + 4 x4 + 6 x6 ≤ 535, 
          9 x1 + 4 x3 + 6 x4 + 6 x6 ≤ 535, 
          6 x1 + 9 x2 + 6 x5 + 4 x6 ≤ 535, 
          6 x1 + 6 x2 + 9 x5 + 4 x6 ≤ 535, 
          6 x1 + 6 x2 + 4 x5 + 9 x6 ≤ 535, 
          6 x1 + 4 x2 + 6 x5 + 9 x6 ≤ 535, 
          6 x1 + 9 x3 + 6 x4 + 4 x6 ≤ 535, 
          6 x1 + 6 x3 + 9 x4 + 4 x6 ≤ 535, 
          6 x1 + 6 x3 + 4 x4 + 9 x6 ≤ 535, 
          6 x1 + 4 x3 + 6 x4 + 9 x6 ≤ 535, 
          4 x1 + 9 x2 + 6 x5 + 6 x6 ≤ 535, 
          4 x1 + 6 x2 + 9 x5 + 6 x6 ≤ 535, 
          4 x1 + 9 x3 + 6 x4 + 6 x6 ≤ 535, 
          4 x1 + 6 x3 + 9 x4 + 6 x6 ≤ 535, 
          9 x2 + 6 x3 + 4 x4 + 6 x5 ≤ 535, 
          9 x2 + 4 x3 + 6 x4 + 6 x5 ≤ 535, 
          6 x2 + 9 x3 + 6 x4 + 4 x5 ≤ 535, 
          6 x2 + 6 x3 + 9 x4 + 4 x5 ≤ 535, 
          6 x2 + 6 x3 + 4 x4 + 9 x5 ≤ 535, 
          6 x2 + 4 x3 + 6 x4 + 9 x5 ≤ 535, 
          4 x2 + 9 x3 + 6 x4 + 6 x5 ≤ 535, 
          4 x2 + 6 x3 + 9 x4 + 6 x5 ≤ 535, 
          x1 + x2 - 2 x6 ≤ 44, x1 + x2 - 2 x5 ≤ 44, 
          x1 + x3 - 2 x6 ≤ 44, x1 + x3 - 2 x4 ≤ 44, 
          x1 + x4 - 2 x6 ≤ 44, x1 + x5 - 2 x6 ≤ 44, 
          x1 - 2 x3 + x4 ≤ 44, x1 - 2 x2 + x5 ≤ 44, 
          x2 + x3 - 2 x5 ≤ 44, x2 + x3 - 2 x4 ≤ 44, 
          x2 + x4 - 2 x5 ≤ 44, x2 - 2 x5 + x6 ≤ 44, 
          x2 - 2 x3 + x4 ≤ 44, x3 - 2 x4 + x5 ≤ 44, 
          x3 - 2 x4 + x6 ≤ 44, -2 x3 + x4 + x5 ≤ 
            44, -2 x3 + x4 + x6 ≤ 
            44, -2 x2 + x3 + x5 ≤ 
            44, -2 x2 + x4 + x5 ≤ 
            44, -2 x2 + x5 + x6 ≤ 
            44, -2 x1 + x2 + x6 ≤ 
            44, -2 x1 + x3 + x6 ≤ 
            44, -2 x1 + x4 + x6 ≤ 
            44, -2 x1 + x5 + x6 ≤ 44, 
          3 x1 + 3 x2 - 2 x6 ≤ 136, 
          3 x1 + 3 x2 - 2 x5 ≤ 136, 
          3 x1 + 3 x3 - 2 x6 ≤ 136, 
          3 x1 + 3 x3 - 2 x4 ≤ 136, 
          3 x1 + 3 x4 - 2 x6 ≤ 136, 
          3 x1 + 3 x5 - 2 x6 ≤ 136, 
          3 x1 - 2 x3 + 3 x4 ≤ 136, 
          3 x1 - 2 x2 + 3 x5 ≤ 136, 
          3 x2 + 3 x3 - 2 x5 ≤ 136, 
          3 x2 + 3 x3 - 2 x4 ≤ 136, 
          3 x2 + 3 x4 - 2 x5 ≤ 136, 
          3 x2 - 2 x5 + 3 x6 ≤ 136, 
          3 x2 - 2 x3 + 3 x4 ≤ 136, 
          3 x3 - 2 x4 + 3 x5 ≤ 136, 
          3 x3 - 2 x4 + 3 x6 ≤ 
            136, -2 x3 + 3 x4 + 3 x5 ≤ 
            136, -2 x3 + 3 x4 + 3 x6 ≤ 
            136, -2 x2 + 3 x3 + 3 x5 ≤ 
            136, -2 x2 + 3 x4 + 3 x5 ≤ 
            136, -2 x2 + 3 x5 + 3 x6 ≤ 
            136, -2 x1 + 3 x2 + 3 x6 ≤ 
            136, -2 x1 + 3 x3 + 3 x6 ≤ 
            136, -2 x1 + 3 x4 + 3 x6 ≤ 
            136, -2 x1 + 3 x5 + 3 x6 ≤ 136, 
          3 x1 - 2 x5 - 2 x6 ≤ 47, 
          3 x1 - 2 x4 - 2 x6 ≤ 47, 
          3 x1 - 2 x3 - 2 x6 ≤ 47, 
          3 x1 - 2 x2 - 2 x6 ≤ 47, 
          3 x2 - 2 x5 - 2 x6 ≤ 47, 
          3 x2 - 2 x4 - 2 x5 ≤ 47, 
          3 x2 - 2 x3 - 2 x5 ≤ 47, 
          3 x3 - 2 x4 - 2 x6 ≤ 47, 
          3 x3 - 2 x4 - 2 x5 ≤ 
            47, -2 x3 + 3 x4 - 2 x6 ≤ 
            47, -2 x3 + 3 x4 - 2 x5 ≤ 
            47, -2 x2 + 3 x3 - 2 x4 ≤ 
            47, -2 x2 + 3 x5 - 2 x6 ≤ 
            47, -2 x2 - 2 x4 + 3 x5 ≤ 
            47, -2 x2 - 2 x3 + 3 x4 ≤ 
            47, -2 x2 - 2 x3 + 3 x5 ≤ 
            47, -2 x1 + 3 x2 - 2 x5 ≤ 
            47, -2 x1 + 3 x3 - 2 x4 ≤ 
            47, -2 x1 - 2 x5 + 3 x6 ≤ 
            47, -2 x1 - 2 x4 + 3 x6 ≤ 
            47, -2 x1 - 2 x3 + 3 x4 ≤ 
            47, -2 x1 - 2 x3 + 3 x6 ≤ 
            47, -2 x1 - 2 x2 + 3 x5 ≤ 
            47, -2 x1 - 2 x2 + 3 x6 ≤ 47, 
          11 x1 + 2 x2 + 2 x4 - 4 x6 ≤ 335, 
          11 x1 + 2 x3 + 2 x5 - 4 x6 ≤ 335, 
          2 x1 + 11 x2 + 2 x4 - 4 x5 ≤ 335, 
          2 x1 + 2 x2 - 4 x3 + 11 x4 ≤ 335, 
          2 x1 + 11 x3 - 4 x4 + 2 x5 ≤ 335, 
          2 x1 - 4 x2 + 2 x3 + 11 x5 ≤ 335, 
          11 x2 + 2 x3 - 4 x5 + 2 x6 ≤ 335, 
          2 x2 + 11 x3 - 4 x4 + 2 x6 ≤ 
            335, -4 x3 + 11 x4 + 2 x5 + 2 x6 ≤ 
            335, -4 x2 + 2 x4 + 11 x5 + 2 x6 ≤ 
            335, -4 x1 + 2 x2 + 2 x3 + 11 x6 ≤ 
            335, -4 x1 + 2 x4 + 2 x5 + 11 x6 ≤ 335, 
          3 x1 - 2 x3 - 6 x4 - 6 x5 - 6 x6 ≤ -161, 
          3 x1 - 2 x2 - 6 x4 - 6 x5 - 6 x6 ≤ -161, 
          3 x1 - 6 x2 - 6 x3 - 2 x5 - 6 x6 ≤ -161, 
          3 x1 - 6 x2 - 6 x3 - 2 x4 - 6 x6 ≤ -161, 
          3 x2 - 2 x3 - 6 x4 - 6 x5 - 
              6 x6 ≤ -161, -2 x2 + 3 x3 - 6 x4 - 
              6 x5 - 6 x6 ≤ -161, -6 x2 - 6 x3 + 
              3 x4 - 2 x5 - 6 x6 ≤ -161, -6 x2 - 
              6 x3 - 2 x4 + 3 x5 - 
              6 x6 ≤ -161, -2 x1 + 3 x2 - 6 x4 - 
              6 x5 - 6 x6 ≤ -161, -2 x1 + 3 x3 - 
              6 x4 - 6 x5 - 6 x6 ≤ -161, -2 x1 - 
              6 x2 - 6 x3 + 3 x4 - 
              6 x6 ≤ -161, -2 x1 - 6 x2 - 6 x3 + 
              3 x5 - 6 x6 ≤ -161, -6 x1 + 3 x2 - 
              6 x3 - 6 x5 - 2 x6 ≤ -161, -6 x1 + 
              3 x2 - 6 x3 - 2 x4 - 
              6 x5 ≤ -161, -6 x1 - 6 x3 + 3 x4 - 
              6 x5 - 2 x6 ≤ -161, -6 x1 - 6 x3 - 
              2 x4 - 6 x5 + 3 x6 ≤ -161, -6 x1 - 
              2 x2 - 6 x3 + 3 x4 - 
              6 x5 ≤ -161, -6 x1 - 2 x2 - 6 x3 - 
              6 x5 + 3 x6 ≤ -161, -6 x1 - 6 x2 + 
              3 x3 - 6 x4 - 2 x6 ≤ -161, -6 x1 - 
              6 x2 + 3 x3 - 6 x4 - 
              2 x5 ≤ -161, -6 x1 - 6 x2 - 6 x4 + 
              3 x5 - 2 x6 ≤ -161, -6 x1 - 6 x2 - 
              6 x4 - 2 x5 + 3 x6 ≤ -161, -6 x1 - 
              6 x2 - 2 x3 - 6 x4 + 
              3 x5 ≤ -161, -6 x1 - 6 x2 - 2 x3 - 
              6 x4 + 3 x6 ≤ -161, 
          9 x1 + 6 x2 - 2 x4 + 6 x5 + 6 x6 ≤ 555, 
          9 x1 + 6 x2 - 2 x3 + 6 x5 + 6 x6 ≤ 555, 
          9 x1 + 6 x3 + 6 x4 - 2 x5 + 6 x6 ≤ 555, 
          9 x1 - 2 x2 + 6 x3 + 6 x4 + 6 x6 ≤ 555, 
          6 x1 + 9 x2 - 2 x4 + 6 x5 + 6 x6 ≤ 555, 
          6 x1 + 9 x2 - 2 x3 + 6 x5 + 6 x6 ≤ 555, 
          6 x1 + 6 x2 - 2 x4 + 9 x5 + 6 x6 ≤ 555, 
          6 x1 + 6 x2 - 2 x4 + 6 x5 + 9 x6 ≤ 555, 
          6 x1 + 6 x2 - 2 x3 + 9 x5 + 6 x6 ≤ 555, 
          6 x1 + 6 x2 - 2 x3 + 6 x5 + 9 x6 ≤ 555, 
          6 x1 + 9 x3 + 6 x4 - 2 x5 + 6 x6 ≤ 555, 
          6 x1 + 6 x3 + 9 x4 - 2 x5 + 6 x6 ≤ 555, 
          6 x1 + 6 x3 + 6 x4 - 2 x5 + 9 x6 ≤ 555, 
          6 x1 - 2 x2 + 9 x3 + 6 x4 + 6 x6 ≤ 555, 
          6 x1 - 2 x2 + 6 x3 + 9 x4 + 6 x6 ≤ 555, 
          6 x1 - 2 x2 + 6 x3 + 6 x4 + 9 x6 ≤ 555, 
          9 x2 + 6 x3 + 6 x4 + 6 x5 - 2 x6 ≤ 555, 
          6 x2 + 9 x3 + 6 x4 + 6 x5 - 2 x6 ≤ 555, 
          6 x2 + 6 x3 + 9 x4 + 6 x5 - 2 x6 ≤ 555, 
          6 x2 + 6 x3 + 6 x4 + 9 x5 - 2 x6 ≤ 
            555, -2 x1 + 9 x2 + 6 x3 + 6 x4 + 6 x5 ≤ 
            555, -2 x1 + 6 x2 + 9 x3 + 6 x4 + 6 x5 ≤ 
            555, -2 x1 + 6 x2 + 6 x3 + 9 x4 + 6 x5 ≤ 
            555, -2 x1 + 6 x2 + 6 x3 + 6 x4 + 9 x5 ≤ 555, 
          15 x1 + 10 x2 + 6 x3 + 6 x5 + 6 x6 ≤ 895, 
          15 x1 + 6 x2 + 10 x3 + 6 x4 + 6 x6 ≤ 895, 
          15 x1 + 6 x2 + 6 x4 + 10 x5 + 6 x6 ≤ 895, 
          15 x1 + 6 x3 + 10 x4 + 6 x5 + 6 x6 ≤ 895, 
          10 x1 + 15 x2 + 6 x3 + 6 x5 + 6 x6 ≤ 895, 
          10 x1 + 6 x2 + 15 x3 + 6 x4 + 6 x6 ≤ 895, 
          10 x1 + 6 x2 + 6 x4 + 15 x5 + 6 x6 ≤ 895, 
          10 x1 + 6 x3 + 15 x4 + 6 x5 + 6 x6 ≤ 895, 
          6 x1 + 15 x2 + 10 x3 + 6 x4 + 6 x5 ≤ 895, 
          6 x1 + 15 x2 + 6 x4 + 6 x5 + 10 x6 ≤ 895, 
          6 x1 + 10 x2 + 15 x3 + 6 x4 + 6 x5 ≤ 895, 
          6 x1 + 10 x2 + 6 x4 + 6 x5 + 15 x6 ≤ 895, 
          6 x1 + 6 x2 + 6 x3 + 15 x4 + 10 x5 ≤ 895, 
          6 x1 + 6 x2 + 6 x3 + 15 x4 + 10 x6 ≤ 895, 
          6 x1 + 6 x2 + 6 x3 + 10 x4 + 15 x5 ≤ 895, 
          6 x1 + 6 x2 + 6 x3 + 10 x4 + 15 x6 ≤ 895, 
          6 x1 + 6 x2 + 6 x3 + 15 x5 + 10 x6 ≤ 895, 
          6 x1 + 6 x2 + 6 x3 + 10 x5 + 15 x6 ≤ 895, 
          6 x1 + 15 x3 + 6 x4 + 6 x5 + 10 x6 ≤ 895, 
          6 x1 + 10 x3 + 6 x4 + 6 x5 + 15 x6 ≤ 895, 
          15 x2 + 6 x3 + 10 x4 + 6 x5 + 6 x6 ≤ 895, 
          10 x2 + 6 x3 + 15 x4 + 6 x5 + 6 x6 ≤ 895, 
          6 x2 + 15 x3 + 6 x4 + 10 x5 + 6 x6 ≤ 895, 
          6 x2 + 10 x3 + 6 x4 + 15 x5 + 6 x6 ≤ 895, 
          x1 + x2 - 2 x3 ≤ 46, x1 + x4 - 2 x5 ≤ 46, 
          x1 - 2 x4 + x5 ≤ 46, x1 - 2 x2 + x3 ≤ 46, 
          x2 + x4 - 2 x6 ≤ 46, x2 - 2 x4 + x6 ≤ 46, 
          x3 + x5 - 2 x6 ≤ 46, 
          x3 - 2 x5 + x6 ≤ 46, -2 x3 + x5 + x6 ≤ 
            46, -2 x2 + x4 + x6 ≤ 
            46, -2 x1 + x2 + x3 ≤ 
            46, -2 x1 + x4 + x5 ≤ 46, 
          6 x1 + 3 x2 + 2 x3 + 2 x4 + 2 x5 ≤ 313, 
          6 x1 + 2 x2 + 3 x3 + 2 x4 + 2 x5 ≤ 313, 
          6 x1 + 2 x2 + 2 x3 + 3 x4 + 2 x5 ≤ 313, 
          6 x1 + 2 x2 + 2 x3 + 2 x4 + 3 x5 ≤ 313, 
          3 x1 + 6 x2 + 2 x3 + 2 x4 + 2 x6 ≤ 313, 
          3 x1 + 2 x2 + 6 x3 + 2 x5 + 2 x6 ≤ 313, 
          3 x1 + 2 x2 + 6 x4 + 2 x5 + 2 x6 ≤ 313, 
          3 x1 + 2 x3 + 2 x4 + 6 x5 + 2 x6 ≤ 313, 
          2 x1 + 6 x2 + 3 x3 + 2 x4 + 2 x6 ≤ 313, 
          2 x1 + 6 x2 + 2 x3 + 3 x4 + 2 x6 ≤ 313, 
          2 x1 + 6 x2 + 2 x3 + 2 x4 + 3 x6 ≤ 313, 
          2 x1 + 3 x2 + 6 x3 + 2 x5 + 2 x6 ≤ 313, 
          2 x1 + 3 x2 + 6 x4 + 2 x5 + 2 x6 ≤ 313, 
          2 x1 + 2 x2 + 6 x3 + 3 x5 + 2 x6 ≤ 313, 
          2 x1 + 2 x2 + 6 x3 + 2 x5 + 3 x6 ≤ 313, 
          2 x1 + 2 x2 + 6 x4 + 3 x5 + 2 x6 ≤ 313, 
          2 x1 + 2 x2 + 6 x4 + 2 x5 + 3 x6 ≤ 313, 
          2 x1 + 3 x3 + 2 x4 + 6 x5 + 2 x6 ≤ 313, 
          2 x1 + 2 x3 + 3 x4 + 6 x5 + 2 x6 ≤ 313, 
          2 x1 + 2 x3 + 2 x4 + 6 x5 + 3 x6 ≤ 313, 
          3 x2 + 2 x3 + 2 x4 + 2 x5 + 6 x6 ≤ 313, 
          2 x2 + 3 x3 + 2 x4 + 2 x5 + 6 x6 ≤ 313, 
          2 x2 + 2 x3 + 3 x4 + 2 x5 + 6 x6 ≤ 313, 
          2 x2 + 2 x3 + 2 x4 + 3 x5 + 6 x6 ≤ 313, 
          25 x1 + 10 x2 + 4 x3 + 10 x4 + 4 x5 + 4 x6 ≤ 1221, 
          25 x1 + 4 x2 + 10 x3 + 4 x4 + 10 x5 + 4 x6 ≤ 1221, 
          10 x1 + 25 x2 + 4 x3 + 10 x4 + 4 x5 + 4 x6 ≤ 1221, 
          10 x1 + 10 x2 + 4 x3 + 25 x4 + 4 x5 + 4 x6 ≤ 1221, 
          10 x1 + 4 x2 + 25 x3 + 4 x4 + 10 x5 + 4 x6 ≤ 1221, 
          10 x1 + 4 x2 + 10 x3 + 4 x4 + 25 x5 + 4 x6 ≤ 1221, 
          4 x1 + 25 x2 + 10 x3 + 4 x4 + 4 x5 + 10 x6 ≤ 1221, 
          4 x1 + 10 x2 + 25 x3 + 4 x4 + 4 x5 + 10 x6 ≤ 1221, 
          4 x1 + 10 x2 + 10 x3 + 4 x4 + 4 x5 + 25 x6 ≤ 1221, 
          4 x1 + 4 x2 + 4 x3 + 25 x4 + 10 x5 + 10 x6 ≤ 1221, 
          4 x1 + 4 x2 + 4 x3 + 10 x4 + 25 x5 + 10 x6 ≤ 1221, 
          4 x1 + 4 x2 + 4 x3 + 10 x4 + 10 x5 + 25 x6 ≤ 1221, 
          5 x1 + 2 x2 + 2 x3 + 2 x4 ≤ 245, 
          5 x1 + 2 x2 + 2 x3 + 2 x5 ≤ 245, 
          5 x1 + 2 x2 + 2 x4 + 2 x5 ≤ 245, 
          5 x1 + 2 x3 + 2 x4 + 2 x5 ≤ 245, 
          2 x1 + 5 x2 + 2 x3 + 2 x4 ≤ 245, 
          2 x1 + 5 x2 + 2 x3 + 2 x6 ≤ 245, 
          2 x1 + 5 x2 + 2 x4 + 2 x6 ≤ 245, 
          2 x1 + 2 x2 + 5 x3 + 2 x5 ≤ 245, 
          2 x1 + 2 x2 + 5 x3 + 2 x6 ≤ 245, 
          2 x1 + 2 x2 + 5 x4 + 2 x5 ≤ 245, 
          2 x1 + 2 x2 + 5 x4 + 2 x6 ≤ 245, 
          2 x1 + 5 x3 + 2 x5 + 2 x6 ≤ 245, 
          2 x1 + 2 x3 + 2 x4 + 5 x5 ≤ 245, 
          2 x1 + 2 x3 + 5 x5 + 2 x6 ≤ 245, 
          2 x1 + 5 x4 + 2 x5 + 2 x6 ≤ 245, 
          2 x1 + 2 x4 + 5 x5 + 2 x6 ≤ 245, 
          5 x2 + 2 x3 + 2 x4 + 2 x6 ≤ 245, 
          2 x2 + 5 x3 + 2 x5 + 2 x6 ≤ 245, 
          2 x2 + 2 x3 + 2 x4 + 5 x6 ≤ 245, 
          2 x2 + 2 x3 + 2 x5 + 5 x6 ≤ 245, 
          2 x2 + 5 x4 + 2 x5 + 2 x6 ≤ 245, 
          2 x2 + 2 x4 + 2 x5 + 5 x6 ≤ 245, 
          2 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 245, 
          2 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 
            245, -x2 - x3 - x4 - x5 - 
              2 x6 ≤ -75, -x1 - x3 - x4 - 2 x5 - 
              x6 ≤ -75, -x1 - x2 - 2 x4 - x5 - 
              x6 ≤ -75, -x1 - x2 - 2 x3 - x5 - 
              x6 ≤ -75, -x1 - 2 x2 - x3 - x4 - 
              x6 ≤ -75, -2 x1 - x2 - x3 - x4 - 
              x5 ≤ -75, 
          3 x1 - x3 - x5 - 3 x6 ≤ 31, 
          3 x1 - x2 - x4 - 3 x6 ≤ 31, 
          3 x2 - x3 - 3 x5 - x6 ≤ 
            31, -3 x3 + 3 x4 - x5 - x6 ≤ 
            31, -x2 + 3 x3 - 3 x4 - x6 ≤ 
            31, -3 x2 - x4 + 3 x5 - x6 ≤ 
            31, -x1 + 3 x2 - x4 - 3 x5 ≤ 
            31, -x1 + 3 x3 - 3 x4 - x5 ≤ 
            31, -x1 - x2 - 3 x3 + 3 x4 ≤ 
            31, -x1 - 3 x2 - x3 + 3 x5 ≤ 
            31, -3 x1 - x4 - x5 + 3 x6 ≤ 
            31, -3 x1 - x2 - x3 + 3 x6 ≤ 31, 
          3 x1 - 2 x3 - 6 x4 - 8 x5 - 8 x6 ≤ -207, 
          3 x1 - 2 x2 - 8 x4 - 6 x5 - 8 x6 ≤ -207, 
          3 x1 - 6 x2 - 8 x3 - 2 x5 - 8 x6 ≤ -207, 
          3 x1 - 8 x2 - 6 x3 - 2 x4 - 8 x6 ≤ -207, 
          3 x2 - 2 x3 - 6 x4 - 8 x5 - 
              8 x6 ≤ -207, -2 x2 + 3 x3 - 8 x4 - 
              6 x5 - 8 x6 ≤ -207, -6 x2 - 8 x3 + 
              3 x4 - 2 x5 - 8 x6 ≤ -207, -8 x2 - 
              6 x3 - 2 x4 + 3 x5 - 
              8 x6 ≤ -207, -2 x1 + 3 x2 - 8 x4 - 
              8 x5 - 6 x6 ≤ -207, -2 x1 + 3 x3 - 
              8 x4 - 8 x5 - 6 x6 ≤ -207, -2 x1 - 
              8 x2 - 8 x3 + 3 x4 - 
              6 x6 ≤ -207, -2 x1 - 8 x2 - 8 x3 + 
              3 x5 - 6 x6 ≤ -207, -6 x1 + 3 x2 - 
              8 x3 - 8 x5 - 2 x6 ≤ -207, -6 x1 - 
              8 x3 + 3 x4 - 8 x5 - 
              2 x6 ≤ -207, -6 x1 - 8 x2 + 3 x3 - 
              8 x4 - 2 x6 ≤ -207, -6 x1 - 8 x2 - 
              8 x4 + 3 x5 - 2 x6 ≤ -207, -8 x1 + 
              3 x2 - 6 x3 - 2 x4 - 
              8 x5 ≤ -207, -8 x1 - 6 x3 - 2 x4 - 
              8 x5 + 3 x6 ≤ -207, -8 x1 - 2 x2 - 
              8 x3 + 3 x4 - 6 x5 ≤ -207, -8 x1 - 
              2 x2 - 8 x3 - 6 x5 + 
              3 x6 ≤ -207, -8 x1 - 6 x2 + 3 x3 - 
              8 x4 - 2 x5 ≤ -207, -8 x1 - 6 x2 - 
              8 x4 - 2 x5 + 3 x6 ≤ -207, -8 x1 - 
              8 x2 - 2 x3 - 6 x4 + 
              3 x5 ≤ -207, -8 x1 - 8 x2 - 2 x3 - 
              6 x4 + 3 x6 ≤ -207, 
          9 x1 + 2 x2 - 4 x6 ≤ 245, 
          9 x1 + 2 x3 - 4 x6 ≤ 245, 
          9 x1 + 2 x4 - 4 x6 ≤ 245, 
          9 x1 + 2 x5 - 4 x6 ≤ 245, 
          2 x1 + 9 x2 - 4 x5 ≤ 245, 
          2 x1 + 9 x3 - 4 x4 ≤ 245, 
          2 x1 - 4 x3 + 9 x4 ≤ 245, 
          2 x1 - 4 x2 + 9 x5 ≤ 245, 
          9 x2 + 2 x3 - 4 x5 ≤ 245, 
          9 x2 + 2 x4 - 4 x5 ≤ 245, 
          9 x2 - 4 x5 + 2 x6 ≤ 245, 
          2 x2 + 9 x3 - 4 x4 ≤ 245, 
          2 x2 - 4 x3 + 9 x4 ≤ 245, 
          9 x3 - 4 x4 + 2 x5 ≤ 245, 
          9 x3 - 4 x4 + 2 x6 ≤ 
            245, -4 x3 + 9 x4 + 2 x5 ≤ 
            245, -4 x3 + 9 x4 + 2 x6 ≤ 
            245, -4 x2 + 2 x3 + 9 x5 ≤ 
            245, -4 x2 + 2 x4 + 9 x5 ≤ 
            245, -4 x2 + 9 x5 + 2 x6 ≤ 
            245, -4 x1 + 2 x2 + 9 x6 ≤ 
            245, -4 x1 + 2 x3 + 9 x6 ≤ 
            245, -4 x1 + 2 x4 + 9 x6 ≤ 
            245, -4 x1 + 2 x5 + 9 x6 ≤ 245, 
          x1 - 2 x3 - 2 x4 ≤ 1, 
          x1 - 2 x2 - 2 x5 ≤ 1, 
          x2 - 2 x3 - 2 x4 ≤ 
            1, -2 x3 - 2 x4 + x5 ≤ 
            1, -2 x3 - 2 x4 + x6 ≤ 
            1, -2 x2 + x3 - 2 x5 ≤ 
            1, -2 x2 + x4 - 2 x5 ≤ 
            1, -2 x2 - 2 x5 + x6 ≤ 
            1, -2 x1 + x2 - 2 x6 ≤ 
            1, -2 x1 + x3 - 2 x6 ≤ 
            1, -2 x1 + x4 - 2 x6 ≤ 
            1, -2 x1 + x5 - 2 x6 ≤ 1, 
          9 x1 - 2 x3 - 2 x5 - 6 x6 ≤ 137, 
          9 x1 - 2 x2 - 2 x4 - 6 x6 ≤ 137, 
          9 x2 - 2 x3 - 6 x5 - 2 x6 ≤ 
            137, -6 x3 + 9 x4 - 2 x5 - 2 x6 ≤ 
            137, -2 x2 + 9 x3 - 6 x4 - 2 x6 ≤ 
            137, -6 x2 - 2 x4 + 9 x5 - 2 x6 ≤ 
            137, -2 x1 + 9 x2 - 2 x4 - 6 x5 ≤ 
            137, -2 x1 + 9 x3 - 6 x4 - 2 x5 ≤ 
            137, -2 x1 - 2 x2 - 6 x3 + 9 x4 ≤ 
            137, -2 x1 - 6 x2 - 2 x3 + 9 x5 ≤ 
            137, -6 x1 - 2 x4 - 2 x5 + 9 x6 ≤ 
            137, -6 x1 - 2 x2 - 2 x3 + 9 x6 ≤ 137, 
          4 x1 + x2 + x5 - 2 x6 ≤ 130, 
          4 x1 + x3 + x4 - 2 x6 ≤ 130, 
          x1 + 4 x2 - 2 x5 + x6 ≤ 130, 
          x1 + 4 x3 - 2 x4 + x6 ≤ 130, 
          x1 - 2 x3 + 4 x4 + x6 ≤ 130, 
          x1 - 2 x2 + 4 x5 + x6 ≤ 130, 
          4 x2 + x3 + x4 - 2 x5 ≤ 130, 
          x2 + 4 x3 - 2 x4 + x5 ≤ 130, 
          x2 - 2 x3 + 4 x4 + x5 ≤ 
            130, -2 x2 + x3 + x4 + 4 x5 ≤ 
            130, -2 x1 + x2 + x5 + 4 x6 ≤ 
            130, -2 x1 + x3 + x4 + 4 x6 ≤ 130, 
          3 x1 + x2 - 2 x6 ≤ 86, 
          3 x1 + x3 - 2 x6 ≤ 86, 
          3 x1 + x4 - 2 x6 ≤ 86, 
          3 x1 + x5 - 2 x6 ≤ 86, 
          x1 + 3 x2 - 2 x5 ≤ 86, 
          x1 + 3 x3 - 2 x4 ≤ 86, 
          x1 - 2 x3 + 3 x4 ≤ 86, 
          x1 - 2 x2 + 3 x5 ≤ 86, 
          3 x2 + x3 - 2 x5 ≤ 86, 
          3 x2 + x4 - 2 x5 ≤ 86, 
          3 x2 - 2 x5 + x6 ≤ 86, 
          x2 + 3 x3 - 2 x4 ≤ 86, 
          x2 - 2 x3 + 3 x4 ≤ 86, 
          3 x3 - 2 x4 + x5 ≤ 86, 
          3 x3 - 2 x4 + x6 ≤ 
            86, -2 x3 + 3 x4 + x5 ≤ 
            86, -2 x3 + 3 x4 + x6 ≤ 
            86, -2 x2 + x3 + 3 x5 ≤ 
            86, -2 x2 + x4 + 3 x5 ≤ 
            86, -2 x2 + 3 x5 + x6 ≤ 
            86, -2 x1 + x2 + 3 x6 ≤ 
            86, -2 x1 + x3 + 3 x6 ≤ 
            86, -2 x1 + x4 + 3 x6 ≤ 
            86, -2 x1 + x5 + 3 x6 ≤ 86, 
          5 x1 + 2 x2 + 2 x6 ≤ 219, 
          5 x1 + 2 x3 + 2 x6 ≤ 219, 
          5 x1 + 2 x4 + 2 x6 ≤ 219, 
          5 x1 + 2 x5 + 2 x6 ≤ 219, 
          2 x1 + 5 x2 + 2 x5 ≤ 219, 
          2 x1 + 2 x2 + 5 x5 ≤ 219, 
          2 x1 + 2 x2 + 5 x6 ≤ 219, 
          2 x1 + 5 x3 + 2 x4 ≤ 219, 
          2 x1 + 2 x3 + 5 x4 ≤ 219, 
          2 x1 + 2 x3 + 5 x6 ≤ 219, 
          2 x1 + 2 x4 + 5 x6 ≤ 219, 
          2 x1 + 2 x5 + 5 x6 ≤ 219, 
          5 x2 + 2 x3 + 2 x5 ≤ 219, 
          5 x2 + 2 x4 + 2 x5 ≤ 219, 
          5 x2 + 2 x5 + 2 x6 ≤ 219, 
          2 x2 + 5 x3 + 2 x4 ≤ 219, 
          2 x2 + 2 x3 + 5 x4 ≤ 219, 
          2 x2 + 2 x3 + 5 x5 ≤ 219, 
          2 x2 + 2 x4 + 5 x5 ≤ 219, 
          2 x2 + 5 x5 + 2 x6 ≤ 219, 
          5 x3 + 2 x4 + 2 x5 ≤ 219, 
          5 x3 + 2 x4 + 2 x6 ≤ 219, 
          2 x3 + 5 x4 + 2 x5 ≤ 219, 
          2 x3 + 5 x4 + 2 x6 ≤ 219, 
          11 x1 + 2 x2 + 2 x5 - 4 x6 ≤ 335, 
          11 x1 + 2 x3 + 2 x4 - 4 x6 ≤ 335, 
          2 x1 + 11 x2 - 4 x5 + 2 x6 ≤ 335, 
          2 x1 + 11 x3 - 4 x4 + 2 x6 ≤ 335, 
          2 x1 - 4 x3 + 11 x4 + 2 x6 ≤ 335, 
          2 x1 - 4 x2 + 11 x5 + 2 x6 ≤ 335, 
          11 x2 + 2 x3 + 2 x4 - 4 x5 ≤ 335, 
          2 x2 + 11 x3 - 4 x4 + 2 x5 ≤ 335, 
          2 x2 - 4 x3 + 11 x4 + 2 x5 ≤ 
            335, -4 x2 + 2 x3 + 2 x4 + 11 x5 ≤ 
            335, -4 x1 + 2 x2 + 2 x5 + 11 x6 ≤ 
            335, -4 x1 + 2 x3 + 2 x4 + 11 x6 ≤ 
            335, -9 x3 - 11 x4 - 3 x5 - 
              3 x6 ≤ -225, -3 x2 - 11 x3 - 9 x4 - 
              3 x6 ≤ -225, -9 x2 - 3 x4 - 11 x5 - 
              3 x6 ≤ -225, -11 x2 - 3 x3 - 9 x5 - 
              3 x6 ≤ -225, -3 x1 - 11 x3 - 9 x4 - 
              3 x5 ≤ -225, -3 x1 - 3 x2 - 9 x3 - 
              11 x4 ≤ -225, -3 x1 - 9 x2 - 3 x3 - 
              11 x5 ≤ -225, -3 x1 - 11 x2 - 3 x4 - 
              9 x5 ≤ -225, -9 x1 - 3 x4 - 3 x5 - 
              11 x6 ≤ -225, -9 x1 - 3 x2 - 3 x3 - 
              11 x6 ≤ -225, -11 x1 - 3 x3 - 3 x5 - 
              9 x6 ≤ -225, -11 x1 - 3 x2 - 3 x4 - 
              9 x6 ≤ -225, -3 x3 - 3 x4 - 
              x6 ≤ -52, -3 x3 - 3 x4 - 
              x5 ≤ -52, -x2 - 3 x3 - 
              3 x4 ≤ -52, -3 x2 - 3 x5 - 
              x6 ≤ -52, -3 x2 - x4 - 
              3 x5 ≤ -52, -3 x2 - x3 - 
              3 x5 ≤ -52, -x1 - 3 x3 - 
              3 x4 ≤ -52, -x1 - 3 x2 - 
              3 x5 ≤ -52, -3 x1 - x5 - 
              3 x6 ≤ -52, -3 x1 - x4 - 
              3 x6 ≤ -52, -3 x1 - x3 - 
              3 x6 ≤ -52, -3 x1 - x2 - 
              3 x6 ≤ -52, 
          19 x1 + 10 x2 + 4 x3 + 4 x4 + 10 x5 + 4 x6 ≤ 1047, 
          19 x1 + 4 x2 + 10 x3 + 10 x4 + 4 x5 + 4 x6 ≤ 1047, 
          10 x1 + 19 x2 + 4 x3 + 4 x4 + 4 x5 + 10 x6 ≤ 1047, 
          10 x1 + 4 x2 + 19 x3 + 4 x4 + 4 x5 + 10 x6 ≤ 1047, 
          10 x1 + 4 x2 + 4 x3 + 19 x4 + 4 x5 + 10 x6 ≤ 1047, 
          10 x1 + 4 x2 + 4 x3 + 4 x4 + 19 x5 + 10 x6 ≤ 1047, 
          4 x1 + 19 x2 + 10 x3 + 10 x4 + 4 x5 + 4 x6 ≤ 1047, 
          4 x1 + 10 x2 + 19 x3 + 4 x4 + 10 x5 + 4 x6 ≤ 1047, 
          4 x1 + 10 x2 + 4 x3 + 19 x4 + 10 x5 + 4 x6 ≤ 1047, 
          4 x1 + 10 x2 + 4 x3 + 4 x4 + 10 x5 + 19 x6 ≤ 1047, 
          4 x1 + 4 x2 + 10 x3 + 10 x4 + 19 x5 + 4 x6 ≤ 1047, 
          4 x1 + 4 x2 + 10 x3 + 10 x4 + 4 x5 + 19 x6 ≤ 1047, 
          x1 - 2 x2 - 3 x3 - 2 x4 - 3 x5 - 5 x6 ≤ -161, 
          x1 - 3 x2 - 2 x3 - 3 x4 - 2 x5 - 
              5 x6 ≤ -161, -2 x1 + x2 - 3 x3 - 2 x4 - 
              5 x5 - 3 x6 ≤ -161, -2 x1 - 2 x2 - 
              5 x3 + x4 - 3 x5 - 3 x6 ≤ -161, -2 x1 - 
              3 x2 + x3 - 5 x4 - 2 x5 - 
              3 x6 ≤ -161, -2 x1 - 5 x2 - 2 x3 - 
              3 x4 + x5 - 3 x6 ≤ -161, -3 x1 + x2 - 
              2 x3 - 3 x4 - 5 x5 - 
              2 x6 ≤ -161, -3 x1 - 2 x2 + x3 - 5 x4 - 
              3 x5 - 2 x6 ≤ -161, -3 x1 - 3 x2 - 
              5 x3 + x4 - 2 x5 - 2 x6 ≤ -161, -3 x1 - 
              5 x2 - 3 x3 - 2 x4 + x5 - 
              2 x6 ≤ -161, -5 x1 - 2 x2 - 2 x3 - 
              3 x4 - 3 x5 + x6 ≤ -161, -5 x1 - 3 x2 - 
              3 x3 - 2 x4 - 2 x5 + x6 ≤ -161, 
          5 x1 + 5 x2 + 2 x3 + 2 x4 + 2 x5 + 2 x6 ≤ 360, 
          5 x1 + 2 x2 + 5 x3 + 2 x4 + 2 x5 + 2 x6 ≤ 360, 
          5 x1 + 2 x2 + 2 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 360, 
          5 x1 + 2 x2 + 2 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 360, 
          2 x1 + 5 x2 + 5 x3 + 2 x4 + 2 x5 + 2 x6 ≤ 360, 
          2 x1 + 5 x2 + 2 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 360, 
          2 x1 + 5 x2 + 2 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 360, 
          2 x1 + 2 x2 + 5 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 360, 
          2 x1 + 2 x2 + 5 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 360, 
          2 x1 + 2 x2 + 2 x3 + 5 x4 + 5 x5 + 2 x6 ≤ 360, 
          2 x1 + 2 x2 + 2 x3 + 5 x4 + 2 x5 + 5 x6 ≤ 360, 
          2 x1 + 2 x2 + 2 x3 + 2 x4 + 5 x5 + 5 x6 ≤ 360, 
          x1 - 2 x3 - 2 x4 + x6 ≤ 22, 
          x1 - 2 x2 - 2 x5 + x6 ≤ 22, 
          x2 - 2 x3 - 2 x4 + x5 ≤ 
            22, -2 x2 + x3 + x4 - 2 x5 ≤ 
            22, -2 x1 + x2 + x5 - 2 x6 ≤ 
            22, -2 x1 + x3 + x4 - 2 x6 ≤ 22, 
          5 x1 + 2 x2 + 2 x4 + 2 x6 ≤ 251, 
          5 x1 + 2 x3 + 2 x5 + 2 x6 ≤ 251, 
          2 x1 + 5 x2 + 2 x4 + 2 x5 ≤ 251, 
          2 x1 + 2 x2 + 2 x3 + 5 x4 ≤ 251, 
          2 x1 + 2 x2 + 2 x3 + 5 x5 ≤ 251, 
          2 x1 + 2 x2 + 2 x3 + 5 x6 ≤ 251, 
          2 x1 + 5 x3 + 2 x4 + 2 x5 ≤ 251, 
          2 x1 + 2 x4 + 2 x5 + 5 x6 ≤ 251, 
          5 x2 + 2 x3 + 2 x5 + 2 x6 ≤ 251, 
          2 x2 + 5 x3 + 2 x4 + 2 x6 ≤ 251, 
          2 x2 + 2 x4 + 5 x5 + 2 x6 ≤ 251, 
          2 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 251, 
          5 x1 + 2 x2 + 2 x5 ≤ 213, 
          5 x1 + 2 x3 + 2 x4 ≤ 213, 
          2 x1 + 5 x2 + 2 x6 ≤ 213, 
          2 x1 + 5 x3 + 2 x6 ≤ 213, 
          2 x1 + 5 x4 + 2 x6 ≤ 213, 
          2 x1 + 5 x5 + 2 x6 ≤ 213, 
          5 x2 + 2 x3 + 2 x4 ≤ 213, 
          2 x2 + 5 x3 + 2 x5 ≤ 213, 
          2 x2 + 5 x4 + 2 x5 ≤ 213, 
          2 x2 + 2 x5 + 5 x6 ≤ 213, 
          2 x3 + 2 x4 + 5 x5 ≤ 213, 
          2 x3 + 2 x4 + 5 x6 ≤ 213, 
          5 x1 - 4 x2 - 6 x3 - 4 x4 - 6 x5 - 
              10 x6 ≤ -247, 
          5 x1 - 6 x2 - 4 x3 - 6 x4 - 4 x5 - 
              10 x6 ≤ -247, -4 x1 + 5 x2 - 6 x3 - 
              4 x4 - 10 x5 - 6 x6 ≤ -247, -4 x1 - 
              4 x2 - 10 x3 + 5 x4 - 6 x5 - 
              6 x6 ≤ -247, -4 x1 - 6 x2 + 5 x3 - 
              10 x4 - 4 x5 - 6 x6 ≤ -247, -4 x1 - 
              10 x2 - 4 x3 - 6 x4 + 5 x5 - 
              6 x6 ≤ -247, -6 x1 + 5 x2 - 4 x3 - 
              6 x4 - 10 x5 - 4 x6 ≤ -247, -6 x1 - 
              4 x2 + 5 x3 - 10 x4 - 6 x5 - 
              4 x6 ≤ -247, -6 x1 - 6 x2 - 10 x3 + 
              5 x4 - 4 x5 - 4 x6 ≤ -247, -6 x1 - 
              10 x2 - 6 x3 - 4 x4 + 5 x5 - 
              4 x6 ≤ -247, -10 x1 - 4 x2 - 4 x3 - 
              6 x4 - 6 x5 + 5 x6 ≤ -247, -10 x1 - 
              6 x2 - 6 x3 - 4 x4 - 4 x5 + 5 x6 ≤ -247, 
          9 x1 + 9 x2 - 2 x4 + 6 x5 + 6 x6 ≤ 612, 
          9 x1 + 6 x2 - 2 x3 + 9 x5 + 6 x6 ≤ 612, 
          9 x1 + 9 x3 + 6 x4 - 2 x5 + 6 x6 ≤ 612, 
          9 x1 - 2 x2 + 6 x3 + 9 x4 + 6 x6 ≤ 612, 
          6 x1 + 9 x2 - 2 x3 + 6 x5 + 9 x6 ≤ 612, 
          6 x1 + 6 x2 - 2 x4 + 9 x5 + 9 x6 ≤ 612, 
          6 x1 + 6 x3 + 9 x4 - 2 x5 + 9 x6 ≤ 612, 
          6 x1 - 2 x2 + 9 x3 + 6 x4 + 9 x6 ≤ 612, 
          9 x2 + 9 x3 + 6 x4 + 6 x5 - 2 x6 ≤ 612, 
          6 x2 + 6 x3 + 9 x4 + 9 x5 - 2 x6 ≤ 
            612, -2 x1 + 9 x2 + 6 x3 + 9 x4 + 6 x5 ≤ 
            612, -2 x1 + 6 x2 + 9 x3 + 6 x4 + 9 x5 ≤ 612, 
          4 x1 + x2 - 2 x6 ≤ 109, 
          4 x1 + x3 - 2 x6 ≤ 109, 
          4 x1 + x4 - 2 x6 ≤ 109, 
          4 x1 + x5 - 2 x6 ≤ 109, 
          x1 + 4 x2 - 2 x5 ≤ 109, 
          x1 + 4 x3 - 2 x4 ≤ 109, 
          x1 - 2 x3 + 4 x4 ≤ 109, 
          x1 - 2 x2 + 4 x5 ≤ 109, 
          4 x2 + x3 - 2 x5 ≤ 109, 
          4 x2 + x4 - 2 x5 ≤ 109, 
          4 x2 - 2 x5 + x6 ≤ 109, 
          x2 + 4 x3 - 2 x4 ≤ 109, 
          x2 - 2 x3 + 4 x4 ≤ 109, 
          4 x3 - 2 x4 + x5 ≤ 109, 
          4 x3 - 2 x4 + x6 ≤ 
            109, -2 x3 + 4 x4 + x5 ≤ 
            109, -2 x3 + 4 x4 + x6 ≤ 
            109, -2 x2 + x3 + 4 x5 ≤ 
            109, -2 x2 + x4 + 4 x5 ≤ 
            109, -2 x2 + 4 x5 + x6 ≤ 
            109, -2 x1 + x2 + 4 x6 ≤ 
            109, -2 x1 + x3 + 4 x6 ≤ 
            109, -2 x1 + x4 + 4 x6 ≤ 
            109, -2 x1 + x5 + 4 x6 ≤ 109, 
          5 x1 + 5 x2 + 2 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 423, 
          5 x1 + 2 x2 + 5 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 423, 
          2 x1 + 5 x2 + 5 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 423, 
          2 x1 + 2 x2 + 2 x3 + 5 x4 + 5 x5 + 5 x6 ≤ 423, 
          5 x1 + 5 x2 + 2 x3 + 2 x5 + 2 x6 ≤ 330, 
          5 x1 + 2 x2 + 5 x3 + 2 x4 + 2 x6 ≤ 330, 
          5 x1 + 2 x2 + 2 x4 + 5 x5 + 2 x6 ≤ 330, 
          5 x1 + 2 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 330, 
          2 x1 + 5 x2 + 5 x3 + 2 x4 + 2 x5 ≤ 330, 
          2 x1 + 5 x2 + 2 x4 + 2 x5 + 5 x6 ≤ 330, 
          2 x1 + 2 x2 + 2 x3 + 5 x4 + 5 x5 ≤ 330, 
          2 x1 + 2 x2 + 2 x3 + 5 x4 + 5 x6 ≤ 330, 
          2 x1 + 2 x2 + 2 x3 + 5 x5 + 5 x6 ≤ 330, 
          2 x1 + 5 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 330, 
          5 x2 + 2 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 330, 
          2 x2 + 5 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 330, 
          8 x1 + 5 x2 + 2 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 486, 
          8 x1 + 2 x2 + 5 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 486, 
          5 x1 + 8 x2 + 2 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 486, 
          5 x1 + 2 x2 + 8 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 486, 
          5 x1 + 2 x2 + 2 x3 + 8 x4 + 2 x5 + 5 x6 ≤ 486, 
          5 x1 + 2 x2 + 2 x3 + 2 x4 + 8 x5 + 5 x6 ≤ 486, 
          2 x1 + 8 x2 + 5 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 486, 
          2 x1 + 5 x2 + 8 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 486, 
          2 x1 + 5 x2 + 2 x3 + 8 x4 + 5 x5 + 2 x6 ≤ 486, 
          2 x1 + 5 x2 + 2 x3 + 2 x4 + 5 x5 + 8 x6 ≤ 486, 
          2 x1 + 2 x2 + 5 x3 + 5 x4 + 8 x5 + 2 x6 ≤ 486, 
          2 x1 + 2 x2 + 5 x3 + 5 x4 + 2 x5 + 8 x6 ≤ 486, 
          9 x1 + 6 x2 + 6 x5 + 4 x6 ≤ 529, 
          9 x1 + 6 x3 + 6 x4 + 4 x6 ≤ 529, 
          6 x1 + 9 x2 + 4 x5 + 6 x6 ≤ 529, 
          6 x1 + 4 x2 + 9 x5 + 6 x6 ≤ 529, 
          6 x1 + 9 x3 + 4 x4 + 6 x6 ≤ 529, 
          6 x1 + 4 x3 + 9 x4 + 6 x6 ≤ 529, 
          4 x1 + 6 x2 + 6 x5 + 9 x6 ≤ 529, 
          4 x1 + 6 x3 + 6 x4 + 9 x6 ≤ 529, 
          9 x2 + 6 x3 + 6 x4 + 4 x5 ≤ 529, 
          6 x2 + 9 x3 + 4 x4 + 6 x5 ≤ 529, 
          6 x2 + 4 x3 + 9 x4 + 6 x5 ≤ 529, 
          4 x2 + 6 x3 + 6 x4 + 9 x5 ≤ 
            529, -x3 - x4 ≤ -12, -x2 - 
              x5 ≤ -12, -x1 - 
              x6 ≤ -12, -x3 - x4 - x5 - 
              x6 ≤ -45, -x2 - x4 - x5 - 
              x6 ≤ -45, -x2 - x3 - x5 - 
              x6 ≤ -45, -x2 - x3 - x4 - 
              x6 ≤ -45, -x1 - x4 - x5 - 
              x6 ≤ -45, -x1 - x3 - x5 - 
              x6 ≤ -45, -x1 - x3 - x4 - 
              x5 ≤ -45, -x1 - x2 - x4 - 
              x6 ≤ -45, -x1 - x2 - x4 - 
              x5 ≤ -45, -x1 - x2 - x3 - 
              x6 ≤ -45, -x1 - x2 - x3 - 
              x5 ≤ -45, -x1 - x2 - x3 - 
              x4 ≤ -45, 
          3 x1 + 3 x2 + 2 x5 + 2 x6 ≤ 208, 
          3 x1 + 2 x2 + 3 x5 + 2 x6 ≤ 208, 
          3 x1 + 3 x3 + 2 x4 + 2 x6 ≤ 208, 
          3 x1 + 2 x3 + 3 x4 + 2 x6 ≤ 208, 
          2 x1 + 3 x2 + 2 x5 + 3 x6 ≤ 208, 
          2 x1 + 2 x2 + 3 x5 + 3 x6 ≤ 208, 
          2 x1 + 3 x3 + 2 x4 + 3 x6 ≤ 208, 
          2 x1 + 2 x3 + 3 x4 + 3 x6 ≤ 208, 
          3 x2 + 3 x3 + 2 x4 + 2 x5 ≤ 208, 
          3 x2 + 2 x3 + 3 x4 + 2 x5 ≤ 208, 
          2 x2 + 3 x3 + 2 x4 + 3 x5 ≤ 208, 
          2 x2 + 2 x3 + 3 x4 + 3 x5 ≤ 208, 
          5 x1 + 2 x2 - 4 x4 - 4 x5 - 4 x6 ≤ 25, 
          5 x1 + 2 x3 - 4 x4 - 4 x5 - 4 x6 ≤ 25, 
          5 x1 - 4 x2 - 4 x3 + 2 x4 - 4 x6 ≤ 25, 
          5 x1 - 4 x2 - 4 x3 + 2 x5 - 4 x6 ≤ 25, 
          2 x1 + 5 x2 - 4 x4 - 4 x5 - 4 x6 ≤ 25, 
          2 x1 + 5 x3 - 4 x4 - 4 x5 - 4 x6 ≤ 25, 
          2 x1 - 4 x2 - 4 x3 + 5 x4 - 4 x6 ≤ 25, 
          2 x1 - 4 x2 - 4 x3 + 5 x5 - 4 x6 ≤ 25, 
          5 x2 + 2 x3 - 4 x4 - 4 x5 - 4 x6 ≤ 25, 
          2 x2 + 5 x3 - 4 x4 - 4 x5 - 4 x6 ≤ 
            25, -4 x2 - 4 x3 + 5 x4 + 2 x5 - 4 x6 ≤ 
            25, -4 x2 - 4 x3 + 2 x4 + 5 x5 - 4 x6 ≤ 
            25, -4 x1 + 5 x2 - 4 x3 + 2 x4 - 4 x5 ≤ 
            25, -4 x1 + 5 x2 - 4 x3 - 4 x5 + 2 x6 ≤ 
            25, -4 x1 + 2 x2 - 4 x3 + 5 x4 - 4 x5 ≤ 
            25, -4 x1 + 2 x2 - 4 x3 - 4 x5 + 5 x6 ≤ 
            25, -4 x1 - 4 x3 + 5 x4 - 4 x5 + 2 x6 ≤ 
            25, -4 x1 - 4 x3 + 2 x4 - 4 x5 + 5 x6 ≤ 
            25, -4 x1 - 4 x2 + 5 x3 - 4 x4 + 2 x5 ≤ 
            25, -4 x1 - 4 x2 + 5 x3 - 4 x4 + 2 x6 ≤ 
            25, -4 x1 - 4 x2 + 2 x3 - 4 x4 + 5 x5 ≤ 
            25, -4 x1 - 4 x2 + 2 x3 - 4 x4 + 5 x6 ≤ 
            25, -4 x1 - 4 x2 - 4 x4 + 5 x5 + 2 x6 ≤ 
            25, -4 x1 - 4 x2 - 4 x4 + 2 x5 + 5 x6 ≤ 25, 
          9 x1 + 6 x2 + 4 x3 ≤ 421, 
          9 x1 + 4 x2 + 6 x3 ≤ 421, 
          9 x1 + 6 x4 + 4 x5 ≤ 421, 
          9 x1 + 4 x4 + 6 x5 ≤ 421, 
          6 x1 + 9 x2 + 4 x3 ≤ 421, 
          6 x1 + 4 x2 + 9 x3 ≤ 421, 
          6 x1 + 9 x4 + 4 x5 ≤ 421, 
          6 x1 + 4 x4 + 9 x5 ≤ 421, 
          4 x1 + 9 x2 + 6 x3 ≤ 421, 
          4 x1 + 6 x2 + 9 x3 ≤ 421, 
          4 x1 + 9 x4 + 6 x5 ≤ 421, 
          4 x1 + 6 x4 + 9 x5 ≤ 421, 
          9 x2 + 6 x4 + 4 x6 ≤ 421, 
          9 x2 + 4 x4 + 6 x6 ≤ 421, 
          6 x2 + 9 x4 + 4 x6 ≤ 421, 
          6 x2 + 4 x4 + 9 x6 ≤ 421, 
          4 x2 + 9 x4 + 6 x6 ≤ 421, 
          4 x2 + 6 x4 + 9 x6 ≤ 421, 
          9 x3 + 6 x5 + 4 x6 ≤ 421, 
          9 x3 + 4 x5 + 6 x6 ≤ 421, 
          6 x3 + 9 x5 + 4 x6 ≤ 421, 
          6 x3 + 4 x5 + 9 x6 ≤ 421, 
          4 x3 + 9 x5 + 6 x6 ≤ 421, 
          4 x3 + 6 x5 + 9 x6 ≤ 421, 
          5 x1 + 2 x2 + 2 x3 + 2 x4 + 2 x5 + 2 x6 ≤ 297, 
          2 x1 + 5 x2 + 2 x3 + 2 x4 + 2 x5 + 2 x6 ≤ 297, 
          2 x1 + 2 x2 + 5 x3 + 2 x4 + 2 x5 + 2 x6 ≤ 297, 
          2 x1 + 2 x2 + 2 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 297, 
          2 x1 + 2 x2 + 2 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 297, 
          2 x1 + 2 x2 + 2 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 297, 
          3 x1 - 2 x3 - 2 x5 ≤ 53, 
          3 x1 - 2 x2 - 2 x4 ≤ 53, 
          3 x2 - 2 x3 - 2 x6 ≤ 53, 
          3 x4 - 2 x5 - 2 x6 ≤ 
            53, -2 x4 + 3 x5 - 2 x6 ≤ 
            53, -2 x4 - 2 x5 + 3 x6 ≤ 
            53, -2 x2 + 3 x3 - 2 x6 ≤ 
            53, -2 x2 - 2 x3 + 3 x6 ≤ 
            53, -2 x1 + 3 x2 - 2 x4 ≤ 
            53, -2 x1 + 3 x3 - 2 x5 ≤ 
            53, -2 x1 - 2 x3 + 3 x5 ≤ 
            53, -2 x1 - 2 x2 + 3 x4 ≤ 53, 
          x1 + x2 + x5 ≤ 69, x1 + x2 + x6 ≤ 69, 
          x1 + x3 + x4 ≤ 69, x1 + x3 + x6 ≤ 69, 
          x1 + x4 + x6 ≤ 69, x1 + x5 + x6 ≤ 69, 
          x2 + x3 + x4 ≤ 69, x2 + x3 + x5 ≤ 69, 
          x2 + x4 + x5 ≤ 69, x2 + x5 + x6 ≤ 69, 
          x3 + x4 + x5 ≤ 69, x3 + x4 + x6 ≤ 69, 
          3 x1 + 2 x2 ≤ 123, 3 x1 + 2 x3 ≤ 123, 
          3 x1 + 2 x4 ≤ 123, 3 x1 + 2 x5 ≤ 123, 
          2 x1 + 3 x2 ≤ 123, 2 x1 + 3 x3 ≤ 123, 
          2 x1 + 3 x4 ≤ 123, 2 x1 + 3 x5 ≤ 123, 
          3 x2 + 2 x3 ≤ 123, 3 x2 + 2 x4 ≤ 123, 
          3 x2 + 2 x6 ≤ 123, 2 x2 + 3 x3 ≤ 123, 
          2 x2 + 3 x4 ≤ 123, 2 x2 + 3 x6 ≤ 123, 
          3 x3 + 2 x5 ≤ 123, 3 x3 + 2 x6 ≤ 123, 
          2 x3 + 3 x5 ≤ 123, 2 x3 + 3 x6 ≤ 123, 
          3 x4 + 2 x5 ≤ 123, 3 x4 + 2 x6 ≤ 123, 
          2 x4 + 3 x5 ≤ 123, 2 x4 + 3 x6 ≤ 123, 
          3 x5 + 2 x6 ≤ 123, 2 x5 + 3 x6 ≤ 123, 
          5 x1 + 2 x2 + 2 x4 ≤ 213, 
          5 x1 + 2 x3 + 2 x5 ≤ 213, 
          2 x1 + 5 x2 + 2 x4 ≤ 213, 
          2 x1 + 2 x2 + 5 x4 ≤ 213, 
          2 x1 + 5 x3 + 2 x5 ≤ 213, 
          2 x1 + 2 x3 + 5 x5 ≤ 213, 
          5 x2 + 2 x3 + 2 x6 ≤ 213, 
          2 x2 + 5 x3 + 2 x6 ≤ 213, 
          2 x2 + 2 x3 + 5 x6 ≤ 213, 
          5 x4 + 2 x5 + 2 x6 ≤ 213, 
          2 x4 + 5 x5 + 2 x6 ≤ 213, 
          2 x4 + 2 x5 + 5 x6 ≤ 213, 
          5 x1 + 2 x2 + 2 x3 + 2 x4 + 2 x5 ≤ 267, 
          2 x1 + 5 x2 + 2 x3 + 2 x4 + 2 x6 ≤ 267, 
          2 x1 + 2 x2 + 5 x3 + 2 x5 + 2 x6 ≤ 267, 
          2 x1 + 2 x2 + 5 x4 + 2 x5 + 2 x6 ≤ 267, 
          2 x1 + 2 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 267, 
          2 x2 + 2 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 
            267, -x6 ≤ 0, -x5 ≤ 
            0, -x4 ≤ 0, -x3 ≤ 
            0, -x2 ≤ 0, -x1 ≤ 0, 
          x1 - 2 x2 - 2 x3 - 2 x4 - 2 x5 - 
              4 x6 ≤ -129, -2 x1 + x2 - 2 x3 - 2 x4 - 
              4 x5 - 2 x6 ≤ -129, -2 x1 - 2 x2 + x3 - 
              4 x4 - 2 x5 - 2 x6 ≤ -129, -2 x1 - 
              2 x2 - 4 x3 + x4 - 2 x5 - 
              2 x6 ≤ -129, -2 x1 - 4 x2 - 2 x3 - 
              2 x4 + x5 - 2 x6 ≤ -129, -4 x1 - 2 x2 - 
              2 x3 - 2 x4 - 2 x5 + x6 ≤ -129, 
          x1 + x2 + x4 ≤ 69, x1 + x3 + x5 ≤ 69, 
          x2 + x3 + x6 ≤ 69, x4 + x5 + x6 ≤ 69, 
          3 x1 + 3 x2 + 3 x5 + 2 x6 ≤ 227, 
          3 x1 + 3 x2 + 2 x5 + 3 x6 ≤ 227, 
          3 x1 + 2 x2 + 3 x5 + 3 x6 ≤ 227, 
          3 x1 + 3 x3 + 3 x4 + 2 x6 ≤ 227, 
          3 x1 + 3 x3 + 2 x4 + 3 x6 ≤ 227, 
          3 x1 + 2 x3 + 3 x4 + 3 x6 ≤ 227, 
          2 x1 + 3 x2 + 3 x5 + 3 x6 ≤ 227, 
          2 x1 + 3 x3 + 3 x4 + 3 x6 ≤ 227, 
          3 x2 + 3 x3 + 3 x4 + 2 x5 ≤ 227, 
          3 x2 + 3 x3 + 2 x4 + 3 x5 ≤ 227, 
          3 x2 + 2 x3 + 3 x4 + 3 x5 ≤ 227, 
          2 x2 + 3 x3 + 3 x4 + 3 x5 ≤ 227, 
          3 x1 + 2 x2 + 2 x5 + 2 x6 ≤ 187, 
          3 x1 + 2 x3 + 2 x4 + 2 x6 ≤ 187, 
          2 x1 + 3 x2 + 2 x5 + 2 x6 ≤ 187, 
          2 x1 + 2 x2 + 3 x5 + 2 x6 ≤ 187, 
          2 x1 + 2 x2 + 2 x5 + 3 x6 ≤ 187, 
          2 x1 + 3 x3 + 2 x4 + 2 x6 ≤ 187, 
          2 x1 + 2 x3 + 3 x4 + 2 x6 ≤ 187, 
          2 x1 + 2 x3 + 2 x4 + 3 x6 ≤ 187, 
          3 x2 + 2 x3 + 2 x4 + 2 x5 ≤ 187, 
          2 x2 + 3 x3 + 2 x4 + 2 x5 ≤ 187, 
          2 x2 + 2 x3 + 3 x4 + 2 x5 ≤ 187, 
          2 x2 + 2 x3 + 2 x4 + 3 x5 ≤ 
            187, -x3 - 3 x4 - 3 x5 - 
              3 x6 ≤ -121, -x2 - 3 x4 - 3 x5 - 
              3 x6 ≤ -121, -3 x2 - 3 x3 - x5 - 
              3 x6 ≤ -121, -3 x2 - 3 x3 - x4 - 
              3 x6 ≤ -121, -x1 - 3 x4 - 3 x5 - 
              3 x6 ≤ -121, -x1 - 3 x2 - 3 x3 - 
              3 x6 ≤ -121, -3 x1 - 3 x3 - 3 x5 - 
              x6 ≤ -121, -3 x1 - 3 x3 - x4 - 
              3 x5 ≤ -121, -3 x1 - x2 - 3 x3 - 
              3 x5 ≤ -121, -3 x1 - 3 x2 - 3 x4 - 
              x6 ≤ -121, -3 x1 - 3 x2 - 3 x4 - 
              x5 ≤ -121, -3 x1 - 3 x2 - x3 - 
              3 x4 ≤ -121, 
          3 x1 + 2 x2 + 2 x3 ≤ 151, 
          3 x1 + 2 x4 + 2 x5 ≤ 151, 
          2 x1 + 3 x2 + 2 x3 ≤ 151, 
          2 x1 + 2 x2 + 3 x3 ≤ 151, 
          2 x1 + 3 x4 + 2 x5 ≤ 151, 
          2 x1 + 2 x4 + 3 x5 ≤ 151, 
          3 x2 + 2 x4 + 2 x6 ≤ 151, 
          2 x2 + 3 x4 + 2 x6 ≤ 151, 
          2 x2 + 2 x4 + 3 x6 ≤ 151, 
          3 x3 + 2 x5 + 2 x6 ≤ 151, 
          2 x3 + 3 x5 + 2 x6 ≤ 151, 
          2 x3 + 2 x5 + 3 x6 ≤ 151, 
          3 x1 - 2 x3 - 2 x5 - 2 x6 ≤ 15, 
          3 x1 - 2 x2 - 2 x4 - 2 x6 ≤ 15, 
          3 x2 - 2 x3 - 2 x5 - 2 x6 ≤ 
            15, -2 x3 + 3 x4 - 2 x5 - 2 x6 ≤ 
            15, -2 x2 + 3 x3 - 2 x4 - 2 x6 ≤ 
            15, -2 x2 - 2 x4 + 3 x5 - 2 x6 ≤ 
            15, -2 x1 + 3 x2 - 2 x4 - 2 x5 ≤ 
            15, -2 x1 + 3 x3 - 2 x4 - 2 x5 ≤ 
            15, -2 x1 - 2 x4 - 2 x5 + 3 x6 ≤ 
            15, -2 x1 - 2 x2 - 2 x3 + 3 x4 ≤ 
            15, -2 x1 - 2 x2 - 2 x3 + 3 x5 ≤ 
            15, -2 x1 - 2 x2 - 2 x3 + 3 x6 ≤ 15, 
          3 x1 - 2 x6 ≤ 63, 3 x2 - 2 x5 ≤ 63, 
          3 x3 - 2 x4 ≤ 63, -2 x3 + 3 x4 ≤ 
            63, -2 x2 + 3 x5 ≤ 
            63, -2 x1 + 3 x6 ≤ 63, 
          3 x1 + 2 x2 + 2 x5 + 3 x6 ≤ 208, 
          3 x1 + 2 x3 + 2 x4 + 3 x6 ≤ 208, 
          2 x1 + 3 x2 + 3 x5 + 2 x6 ≤ 208, 
          2 x1 + 3 x3 + 3 x4 + 2 x6 ≤ 208, 
          3 x2 + 2 x3 + 2 x4 + 3 x5 ≤ 208, 
          2 x2 + 3 x3 + 3 x4 + 2 x5 ≤ 208, 
          5 x1 + 2 x2 + 2 x3 + 2 x4 + 2 x5 + 5 x6 ≤ 360, 
          2 x1 + 5 x2 + 2 x3 + 2 x4 + 5 x5 + 2 x6 ≤ 360, 
          2 x1 + 2 x2 + 5 x3 + 5 x4 + 2 x5 + 2 x6 ≤ 360, 
          x1 - 2 x4 - 2 x5 - 2 x6 ≤ -47, 
          x1 - 2 x2 - 2 x3 - 2 x6 ≤ -47, 
          x2 - 2 x4 - 2 x5 - 2 x6 ≤ -47, 
          x3 - 2 x4 - 2 x5 - 2 x6 ≤ -47, -2 x2 - 
              2 x3 + x4 - 2 x6 ≤ -47, -2 x2 - 2 x3 + 
              x5 - 2 x6 ≤ -47, -2 x1 + x2 - 2 x3 - 
              2 x5 ≤ -47, -2 x1 - 2 x3 + x4 - 
              2 x5 ≤ -47, -2 x1 - 2 x3 - 2 x5 + 
              x6 ≤ -47, -2 x1 - 2 x2 + x3 - 
              2 x4 ≤ -47, -2 x1 - 2 x2 - 2 x4 + 
              x5 ≤ -47, -2 x1 - 2 x2 - 2 x4 + 
              x6 ≤ -47, x1 ≤ 29, 
          x2 ≤ 29, x3 ≤ 29, x4 ≤ 29, 
          x5 ≤ 29, 
          x6 ≤ 
            29, -x3 - x5 - x6 ≤ -30, -x2 - x4 - 
              x6 ≤ -30, -x1 - x4 - 
              x5 ≤ -30, -x1 - x2 - 
              x3 ≤ -30, x1 + x6 ≤ 50, 
          x2 + x5 ≤ 50, x3 + x4 ≤ 50, 
          x1 + x2 - 2 x4 - 2 x5 - 2 x6 ≤ -28, 
          x1 + x3 - 2 x4 - 2 x5 - 2 x6 ≤ -28, 
          x1 - 2 x2 - 2 x3 + x4 - 2 x6 ≤ -28, 
          x1 - 2 x2 - 2 x3 + x5 - 2 x6 ≤ -28, 
          x2 + x3 - 2 x4 - 2 x5 - 2 x6 ≤ -28, -2 x2 - 
              2 x3 + x4 + x5 - 2 x6 ≤ -28, -2 x1 + x2 - 
              2 x3 + x4 - 2 x5 ≤ -28, -2 x1 + x2 - 
              2 x3 - 2 x5 + x6 ≤ -28, -2 x1 - 2 x3 + 
              x4 - 2 x5 + x6 ≤ -28, -2 x1 - 2 x2 + x3 - 
              2 x4 + x5 ≤ -28, -2 x1 - 2 x2 + x3 - 
              2 x4 + x6 ≤ -28, -2 x1 - 2 x2 - 2 x4 + 
              x5 + x6 ≤ -28, 
          x1 + x2 + x5 + x6 ≤ 81, 
          x1 + x3 + x4 + x6 ≤ 81, 
          x2 + x3 + x4 + x5 ≤ 81, x1 + x2 ≤ 48, 
          x1 + x3 ≤ 48, x1 + x4 ≤ 48, 
          x1 + x5 ≤ 48, x2 + x3 ≤ 48, 
          x2 + x4 ≤ 48, x2 + x6 ≤ 48, 
          x3 + x5 ≤ 48, x3 + x6 ≤ 48, 
          x4 + x5 ≤ 48, x4 + x6 ≤ 48, 
          x5 + x6 ≤ 48, 3 x1 + 3 x2 + 2 x3 ≤ 170, 
          3 x1 + 2 x2 + 3 x3 ≤ 170, 
          3 x1 + 3 x4 + 2 x5 ≤ 170, 
          3 x1 + 2 x4 + 3 x5 ≤ 170, 
          2 x1 + 3 x2 + 3 x3 ≤ 170, 
          2 x1 + 3 x4 + 3 x5 ≤ 170, 
          3 x2 + 3 x4 + 2 x6 ≤ 170, 
          3 x2 + 2 x4 + 3 x6 ≤ 170, 
          2 x2 + 3 x4 + 3 x6 ≤ 170, 
          3 x3 + 3 x5 + 2 x6 ≤ 170, 
          3 x3 + 2 x5 + 3 x6 ≤ 170, 
          2 x3 + 3 x5 + 3 x6 ≤ 170, 
          x1 + x2 + x3 ≤ 63, x1 + x4 + x5 ≤ 63, 
          x2 + x4 + x6 ≤ 63, 
          x3 + x5 + x6 ≤ 
            63, -x4 - x5 - x6 ≤ -36, -x2 - x3 - 
              x6 ≤ -36, -x1 - x3 - 
              x5 ≤ -36, -x1 - x2 - 
              x4 ≤ -36, -x1 - x2 - x3 - x4 - x5 - 
              x6 ≤ -90};

Length[acdzconv]
Length[acdzineq]

Reduced Systems

In this section we compute the reduced systems corresponding to the 
Minkowski sum polytope P of the nine Albouy-Chenciner-Dziobek equations.  
After eliminating the trivial ones, we analyze the rest using Groenber bases.

Nontrivial facets

The inequalities produced by Porta involve variables x1, ..., x6.  
First we define some utility functions for substituting six values for these 
variables and for reading off the left and right sides of the inequality.  
The left side will be a linear form in the xi and the right side is a 
constant.  The inequalities are all of the form   lhs <= rhs

Subst[v_]  :=  {x1 -> v[[1]],  x2 -> v[[2]],  
          x3 -> v[[3]], x4 -> v[[4]], 
          x5 -> v[[5]], 
          x6 -> v[[6]]};
lhs[LessEqual[a_, b_]]  :=  a
rhs[LessEqual[a_, b_]]  :=  b

A very important step is to test each of the facet inequalities to see if  the corresponding reduced system is trivial.   The reduced system  corresponding to a certain vector  α is obtained as follows.  For each polynomial of the system we want to  select all the terms whose exponent vectors k  which minimize the linear form   α1 k1 + ... + α6 k6 .   The corresponding vectors k lie on a face of the Newton polytope defined by the supporting hyperplane   α1 k1 + ... + α6 k6 >= min  where min is the minimum value of the form.  It is clear that  finding these terms is a task which can be done using the exponent lists  rather than the equations themselves.

Note that the Porta inequalities defining the facets are expressed as   lhs <= const so must look for the maximum values of the left hand sides on  each list of exponents and then select those exponents which attain this  maximum value.  The first two functions below carry out these steps.  Then  the corresponding reduced polynomial will consist of a single term if there  is just one exponent vector which achieve the maximum value.  The third  function below checks this and returns a 1 if the given reduced polynomial is  nontrivial.  Finally, the fourth function tests a list of polynomials and  returns True if and only if all of the resulting reduced polynomials do not  reduce to a single term.

FindMax[linform_, vertlist_]  :=  
      Max[ Map[linform /. Subst[#] &, 
          vertlist]]


    GetMaximalExponents[ineq_, 
        vertlist_] := 
With[{linform = lhs[ineq], 
          maxval  =  FindMax[lhs[ineq], vertlist]},  
        Select[vertlist, ((linform /. Subst[#])  == 
                maxval) &]]


  (*returns 1 if the inequality determines a reduced polynomial with more than one term *) 

    Nontrivial[ineq_, vertlist_] :=  
      If[Length[GetMaximalExponents[ineq, vertlist]] > 1, 1, 
        0]

 (* 
      returns 1 if ineq is nontrivial all of the reduced polynomials whose exponents are in vllist (list of exponent lists) *) 

    AllNontrivial[ineq_, vllist_]  := 
If[
        Min[Map[Nontrivial[ineq, #] &, vllist]] > 0, True, 
        False]

We use this function to test each of the 2980 facets for 
nontriviality.  Fortunately, only 53 of them survive the test.

nontrivialfacets  =  
        Select[acdzineq, 
          AllNontrivial[#, explist9] &];
Length[%]

Before displaying the answer we read off the normal vectors α (putting in a minus sign to reverse the inequalities) and use these  vectors to sort them into a convenient order.  Finally we display the answer  as a table.  The inequalities are still in Porta form however.  The  inequalities displayed in Table 1 in the paper have all been reversed and the  variables xi replaced by ki.

GetAlpha[
        LessEqual[a_, b_]] :=  -Coefficient[
          a, {x1, x2, x3, x4, x5, x6}]

    
nontrivialfacets  =  
        Sort[nontrivialfacets, ({1, 1, 1, 1, 1, 1} . 
                  GetAlpha[#1] > {1, 1, 1, 1, 1, 1} . 
                  GetAlpha[#2]) &];

    
{{Table[i, {i, 1, 27}], Take[nontrivialfacets, 27]} // Transpose // 
        MatrixForm, 
{Table[i, {i, 28, 53}], 
            Drop[nontrivialfacets, 27]} // Transpose // 
        MatrixForm}

Nontrivial lower-dimensional faces and permutation symmetry

We also need to find all the lower-dimensional faces of P which 
lead to nontrivial reduced systems.  Every face of P is determined by some 
supporting hyperplane which, in turn, is represented by some linear 
inequality.  If two or more facets of P are incident, then their intersection 
is a face and one can find an inequality for that face by simply adding the 
corresponding inequalities for the facets.  Finally, we can test this face 
for nontriviality using the functions defined in the last subsection.

To begin we define functions for determining whether or not a 
collection of facets are incident.  We just find a list of the vertices of 
the polytope in each facet and see if the lists have a nonempty intersection. 
 The first function below takes an inequality and a vertex list and finds all 
the vertices on the list which satisfy the corresponding equality.

FindFacet[ineq_, vlist_] := 
      Select[vlist, ((lhs[ineq] /. Subst[#]) === 
              rhs[ineq]) &]

We specify a potential face by a set of facets.  We have a list of 
53 nontrivial facets and we can specify any one of them by its position on 
this list (its index).  Then a set of facets is given by a list of such 
indices (always in order).  For example, the index list {1, 22, 36} would 
represent the face determined by intersecting the facets corresponding to 
inequalities 1, 22, and 36 in our list.  The next function takes such an 
index list,  an inequality list and a list of vertices defining a polytope 
and determines if the facets from the list are really incident in the 
polytope.

FacetsIncident[indlist_, ineqlist_, vlist_]  :=  
      With[{f = 
            Map[FindFacet[#, vlist] &, 
              Part[ineqlist, indlist]]}, 
If[
          Length[Intersection @@ f] > 0, True, False]]

Once we have some incident facets, we can test to see if the 
resulting face is nontrivial.  We just create an inequality defining that 
face by adding the inequalities from the facets  and use this inequality in 
the function AllNontrivial defined in the last subsection.

AddLEInequalities[indlist_, ineqlist_] := 
      Module[{ins, rights,  lefts}, 
ins  =  
          Part[ineqlist, indlist]; 
rights  =  
          Map[rhs, ins]; 
lefts  =  
          Map[lhs, ins]; 
LessEqual[Plus @@ lefts, 
          Plus @@ rights]]

    
NontrivialFace[indlist_, ineqlist_, explist_]  :=  
      With[{in = 
            AddLEInequalities[indlist, 
              ineqlist]}, 
AllNontrivial[in, 
          explist]]

Before applying this to our list of 53 nontrival facets we 
introduce some functions to describe the action of the permutation group S4. 
This group,  called sigma4 below, is just represented by a list of all 24 
possible permutations of {1 ,2, 3, 4}.



The group acts on the subscripts of the mi and the rij variables and 
therefore induces an action on the Minkowski sum polytope P.  If two faces of 
P are symmetric in this way, then it suffices to check the reduced system of 
one of them.  First we will describe the action of S4 on our list of 
inequalities.  To do this we replace the variables x1, ..., x6 by new 
variables k[i,j] which reflect their roles as exponents of the variables rij.

sigma4  =  Permutations[{1, 2, 3, 4}]

    
k[i_, i_] := 0
\(\(\(k[i_, j_] := k[j, i] /; j < i\)\(
\)
    \)\)
kvars  =  {k[1, 2], k[1, 3], k[1, 4], k[2, 3], k[2, 4], 
          k[3, 4]};

    
kineqs  =  
        nontrivialfacets /. {x1 -> k[1, 2], x2 -> k[1, 3], 
            x3 -> k[1, 4], x4 -> k[2, 3], x5 -> k[2, 4], 
            x6 -> k[3, 4]};

Next we define the action of a permuation on a variable, k[i,j].  
The corresponding action on a inequality is obtained by simply acting on all 
the variables in the inequality.  The first two functions below implement 
this.  Once we have permuted the variables in an inequality, it will be equal 
to one of the other inequalities on our list.  The third function below looks 
up the index of the permuted inequality in the list.  So we know have an 
action of S4 on the numbers 1 -- 53.  Finally, the fourth function below 
extends this action to index lists, consisting of several number from 1 -- 
53.  This implements the action of the symmetry on the faces of P.

\(\(\(Permute[perm_, k[i_, j_]] := \ 
      k[perm[\([i]\)], perm[\([j]\)]]\)\(
\)
    \)\)
\(\(\(Permute[perm_, LessEqual[a_, b_]] := \ 
      With[{coeffs = \ Coefficient[a, kvars]}, 
LessEqual[
          coeffs . Map[Permute[perm, #] &, kvars], b]]\)\(
\)
    \)\)
PermutedIndex[perm_, ineqlist_, ind_]  :=  
      With[{pineq  =  
            Permute[perm, 
              ineqlist[[ind]]]}, 
Position[ineqlist, 
            pineq][[1, 1]]
]

    
PermutedIndexList[perm_, ineqlist_, indlist_]  :=  
      Sort[Map[PermutedIndex[perm, ineqlist, #] &, 
          indlist]]

The first function below finds the orbit of a face (represented by an index 
list) under the group action, i.e, all the symmetrical faces; the Union 
command puts the orbit in lexicographic order.  Then the second function 
below reads off the minimal representative for the orbit with respect to 
lexicographic order.

IndexListOrbit[pgroup_, ineqlist_, indlist_] :=  
      Union[Map[PermutedIndexList[#, ineqlist, indlist] &, 
          pgroup]]

    
MinimalOrbitRep[pgroup_, ineqlist_, indlist_] :=  
      First[IndexListOrbit[pgroup, ineqlist, indlist]]

To facilitate a recursive approach to finding the nontrivial faces 
we begin by defining a function which finds subfaces of a given face.  If the 
given face is represented by a list of k indices (i.e., it is an intersection 
of k nontrivial facets) we want to construct a list of subfaces, each defined 
by a list of k+1 indices.  We will always represent faces by ordered index 
lists, so that when we extend a list, we only need to consider values for the 
k+1 st index which are greater than the k-th given index.

ExtendIndexList[ineqlist_, {}]  :=  
      Table[{i}, {i, 1, Length[ineqlist]}]
ExtendIndexList[ineqlist_, indlist_]  :=  
      Table[indlist~Join~{i}, {i, Last[indlist] + 1, 
          Length[ineqlist]}]

The next two functions put all of this group theory to work.  Given a face, 
represented by an index list of size k, we want to make a list of all 
possible extensions to lists of size k+1, in such a way that the list of 
possible extensions contains just the minimal representative from each 
symmetry group orbit.  In other words, its a list of all possible extensions 
up to symmetry.  Then we do the same for a list of faces and combine the 
results.



The first functions below works as follows. As explained in section 4.2 of 
the paper, we only need to extend each k-tuple {i1, ..., ik} by appending 
(k+1)-st indices i(k+1) > ik.  Then we compute minimal repesentative of the 
orbit and append it to a running list of representatives.  Taking the Union 
at the end eliminates duplications and puts the list in lexicographical 
order.



The second function below just applies this procedure to each element of a 
list of faces and Union's the results.  So we are in a positions to 
inductively construct all the nontrivial faces.

ExtendedMinimalOrbitReps[pgroup_, ineqlist_, indlist_]  :=  
      Module[{i, ext, minrep, oreps = {}}, 
ext  =  
          ExtendIndexList[ineqlist, indlist]; 
For[i = 1, 
          i ≤ Length[ext], i++, 
minrep = 
            MinimalOrbitRep[pgroup, ineqlist, 
              ext[[i]]]; 
AppendTo[oreps, 
            minrep];
]; 
oreps // 
          Union]

    
ExtendedMinimalOrbitRepsList[pgroup_, ineqlist_, 
        indlistlist_]  :=  
Map[
            ExtendedMinimalOrbitReps[pgroup, ineqlist, #] &, indlistlist] // 
          Flatten[#, 1] & // Union

We begin with the empty list of faces and we construct all the nontrivial 
facets up to symmetry.  First we construct a list of minimal orbit 
representatives for the facets

faces1   =  
      ExtendedMinimalOrbitRepsList[sigma4, kineqs, {{}}]

At the next step we first find minimal orbit reps for the extensions of the 
minimal reps for the facets.  This will be a list of pairs of indices.  We 
then eliminate all the pairs for which the two facets are not incident and 
those for which the resulting reduced systems is trivial.

faces2   =  
      ExtendedMinimalOrbitRepsList[sigma4, kineqs, 
        faces1]
faces2  =  
      Select[faces2, (NontrivialFace[#, nontrivialfacets, explist9]  && 
              FacetsIncident[#, nontrivialfacets, acdzconv]) &]

Now we use the same method to inductively construct minimal 
representatives for all of the nontriival faces.

faces3   =  
        ExtendedMinimalOrbitRepsList[sigma4, kineqs, 
          faces2];
faces3  =  
      Select[faces3, (NontrivialFace[#, nontrivialfacets, explist9]  && 
              FacetsIncident[#, nontrivialfacets, 
                acdzconv]) &]

    
faces4   =  
        ExtendedMinimalOrbitRepsList[sigma4, kineqs, 
          faces3];
faces4  =  
      Select[faces4, (NontrivialFace[#, nontrivialfacets, explist9]  && 
              FacetsIncident[#, nontrivialfacets, 
                acdzconv]) &]

    
faces5  =  
        ExtendedMinimalOrbitRepsList[sigma4, kineqs, 
          faces4];
faces5  =  
      Select[faces5, (NontrivialFace[#, nontrivialfacets, explist9]  && 
              FacetsIncident[#, nontrivialfacets, acdzconv]) &]

Finally we eliminate any faces which have only normals with indices 
1 -- 21 because we are only considering faces with (inward) normal vectors in 
the half-space (-1,-1,-1,-1,-1,-1,-1).(a1, ... , a6 ) >= 0.  The normals in 
the list of inequalities above have to be reversed, so the inequalities 1 -- 
21 are in the wrong half-space.  We are left with the following list of faces 
to check.

nontrivialfacereps  = {{22}, {25}, {29}, {33}, {36}, {48}, {2, 
          25}, {2, 36}, {14, 25}, {14, 36}, {18, 29}, {22, 48}, {25, 
          36}, {33, 48}, {2, 14, 25}, {2, 14, 36}, {2, 25, 36}, {14, 25, 
          36}, {2, 14, 25, 36}}

Analyzing the reduced systems

Here is the list of faces to be analyzed from the last 
subsection.

nontrivialfacereps

By definition, the reduced polynomial corresponding to a certain 
inequality of the form lhs >= rhs consists of those terms for which the 
exponent vector minimizes the linear form lhs.  Since all of our inequalities 
are reversed, we take the maximal terms instead.  To get the reduced system 
we just reduce each polynomial.



To find the reduced system corresponding to a face defined by a list of 
indices of inequalites we add the inequalities to obtain a single defining 
inequality for the face.

ReducePoly[p_, ineq_]  := 
      Module[{q, linform, maxval, explist, 
          vars}, 
vars  =  {r12, r13, r14, r23, r24, 
            r34}; 
q = 
          Expand[p]; 
linform  =  
          lhs[ineq]; 
explist  =  
          GetAllExponents[q, vars]; 
maxval  =  
          FindMax[linform, explist]; 
Select[
          q, ((linform /. Subst[GetExponents[#, vars]]) == 
                maxval) &]
]

    
\(\(\(ReducedSystem[LessEqual[lhs_, rhs_], eqlist_]\  := \ 
      Map[ReducePoly[#, LessEqual[lhs, rhs]] &, eqlist]\)\(
\)
    \)\)
ReducedSystem[indlist_, ineqlist_, eqlist_]  :=  
      ReducedSystem[AddLEInequalities[indlist, ineqlist], eqlist]

Here are some utility functions to eliminate factors of variables 
(in our case, the rij) from the equations of the reduced systems

\(\(\(RemoveFactor[poly_, var_]\  := 
      Module[{i, pow, p}, 
p\  = \ 
          Expand[poly]; 
pow = \ 
          Min[Table[
              Exponent[p[\([i]\)], var], {i, 1, 
                Length[p]}]]; 
If[
          pow > 0 && pow < Infinity, \((poly/var^pow)\) // Factor, 
          poly]]\)\(
\)
    \)\)
CleanUp[poly_, vars_]  :=  
Fold[RemoveFactor, 
        poly, vars ]

Now we begin to analyze all the reduced systems on our list of 
nontrivial faces.  To eliminate the quasi-homogeneity of the reduced systems 
we add in a normalization condition.

nzeq  =  r12*r13*r14*r23*r24*r34 - 1

We will start from the end of the list of nontrivial faces, the 
face determined by intersections facets 2, 14, 25, 36.  The method is to find 
and clean up the reduced system, append the normalization conditions and then 
use the GroebnerBasis command to eliminate the variables rij and find 
polynomial constraints on the masses.

red  =  
      ReducedSystem[{2, 14, 25, 36}, nontrivialfacets, acdzeqs] // 
        Factor
red  = Map[CleanUp[#, vars4bp] &, red]
GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // 
      Factor

The result shows that the reduced system corresponding to this face 
can have solutions in the algebraic torus only if m1+m2+m3 = 0.  Many of the 
other reduced systems produce similar results.   Here are the computations 
for the various triples of indices in the list of nontrivial faces.

red  =  
        ReducedSystem[{2, 14, 25}, nontrivialfacets, acdzeqs] // 
          Factor;
red  = Map[CleanUp[#, vars4bp] &, red]
GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // 
      Factor

    
red  =  
        ReducedSystem[{2, 14, 36}, nontrivialfacets, acdzeqs] // 
          Factor;
red  = Map[CleanUp[#, vars4bp] &, red]
GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // 
      Factor

    
red  =  
        ReducedSystem[{2, 25, 36}, nontrivialfacets, acdzeqs] // 
          Factor;
red  = Map[CleanUp[#, vars4bp] &, red]
GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // 
      Factor

    
red  =  
        ReducedSystem[{14, 25, 36}, nontrivialfacets, acdzeqs] // 
          Factor;
red  = Map[CleanUp[#, vars4bp] &, red]
GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // 
      Factor

Here are the computations for the pairs of indices in nontrivial 
face list.  In each case we obtain some mass polynomials of the form   mi, mi 
+ mj, mi + mj + mk, or m1+m2+m3+m4.

red  =  
        ReducedSystem[{2, 25}, nontrivialfacets, acdzeqs] // 
          Factor;
red  = Map[CleanUp[#, vars4bp] &, red]
GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // 
      Factor

    
red  =  
        ReducedSystem[{2, 36}, nontrivialfacets, acdzeqs] // 
          Factor;
red  = Map[CleanUp[#, vars4bp] &, red]
GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // 
      Factor

    
red  =  
        ReducedSystem[{14, 25}, nontrivialfacets, acdzeqs] // 
          Factor;
red  = Map[CleanUp[#, vars4bp] &, red]
GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // 
      Factor

    
red  =  
        ReducedSystem[{14, 36}, nontrivialfacets, acdzeqs] // 
          Factor;
red  = Map[CleanUp[#, vars4bp] &, red]
GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // 
      Factor

    
red  =  
        ReducedSystem[{18, 29}, nontrivialfacets, acdzeqs] // 
          Factor;
red  = Map[CleanUp[#, vars4bp] &, red]
GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // 
      Factor

    
red  =  
        ReducedSystem[{22, 48}, nontrivialfacets, acdzeqs] // 
          Factor;
red  = Map[CleanUp[#, vars4bp] &, red]
GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // 
      Factor

    
red  =  
        ReducedSystem[{25, 36}, nontrivialfacets, acdzeqs] // 
          Factor;
red  = Map[CleanUp[#, vars4bp] &, red]
GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // 
      Factor

    
red  =  
        ReducedSystem[{33, 48}, nontrivialfacets, acdzeqs] // 
          Factor;
red  = Map[CleanUp[#, vars4bp] &, red]
GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // 
      Factor

Now for the facets.  The results for all of the facets except 22 
,33 involve simple sums of masses.  We leave out 48 until the next cell 
because the Groebner basis computation is time consuming.

red  =  
        ReducedSystem[{25}, nontrivialfacets, acdzeqs] // 
          Factor;
red  = Map[CleanUp[#, vars4bp] &, red]
GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // 
      Factor

    
red  =  
        ReducedSystem[{29}, nontrivialfacets, acdzeqs] // Factor;
red  = Map[CleanUp[#, vars4bp] &, red]
GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // 
      Factor

    
red  =  
        ReducedSystem[{36}, nontrivialfacets, acdzeqs] // Factor;
red  = Map[CleanUp[#, vars4bp] &, red]
GroebnerBasis[red~Join~{nzeq}, {m1, m2, m3, m4}, vars4bp] // 
      Factor

Facet 48 leads to a similar condition but the Groebner basis 
computation is faster using Macaulay 2.  (All of the previous computations 
were checked with Macaulay 2.)  The Macaulay computation was done using the 
ring

R = QQ[r12,r13,r14,r23,r24,r34,m1,m2,m3,m4,MonomialOrder=>Eliminate 6]

We simply record the equations and the resulting Groebner basis here.

red  =  
        ReducedSystem[{48}, nontrivialfacets, acdzeqs] // Factor;
red  = Map[CleanUp[#, vars4bp] &, red];
red48  =  red~Join~{nzeq}
gb48 = {m3 + m4,  m1 + m2 + m3 + m4}

Facets 22 and 33 were also analyzed with Macaulay 2.  We give the 
equations and the Groebner bases here.  Here is facet 22. The mass polynomial 
is quadratic and it can vanish for some positive values of the masses.  This 
means that for those masses, the reduced system with the normalization 
condition may be solved.

red  =  
        ReducedSystem[{22}, nontrivialfacets, acdzeqs] // Factor;
red  = Map[CleanUp[#, vars4bp] &, red];
red22  =  red~Join~{nzeq}
gb22 = {m2 m3 - m1 m4}

Here is facet 33

red  =  
        ReducedSystem[{33}, nontrivialfacets, acdzeqs] // Factor;
red  = Map[CleanUp[#, vars4bp] &, red];
red33  =  red~Join~{nzeq}
\(gbnewton33 = {m1^8  m3^11 - m1^7  m2*m3^11 + m1^6  m2^2  m3^11 + 
            2  m1^5  m2^3  m3^11 - 2  m1^4  m2^4  m3^11 + 
            2  m1^3  m2^5  m3^11 + m1^2  m2^6  m3^11 - m1*m2^7  m3^11 + 
            m2^8  m3^11 + 2  m1^8  m3^10  m4 - 2  m1^7  m2*m3^10  m4 + 
            2  m1^6  m2^2  m3^10  m4 + 4  m1^5  m2^3  m3^10  m4 - 
            4  m1^4  m2^4  m3^10  m4 + 4  m1^3  m2^5  m3^10  m4 + 
            2  m1^2  m2^6  m3^10  m4 - 2  m1*m2^7  m3^10  m4 + 
            2  m2^8  m3^10  m4 + m1^8  m3^9  m4^2 - m1^7  m2*m3^9  m4^2 + 
            m1^6  m2^2  m3^9  m4^2 + 2  m1^5  m2^3  m3^9  m4^2 - 
            2  m1^4  m2^4  m3^9  m4^2 + 2  m1^3  m2^5  m3^9  m4^2 + 
            m1^2  m2^6  m3^9  m4^2 - m1*m2^7  m3^9  m4^2 + m2^8  m3^9  m4^2 + 
            3  m1^8  m3^8  m4^3 - 3  m1^7  m2*m3^8  m4^3 + 
            3  m1^6  m2^2  m3^8  m4^3 - 10  m1^5  m2^3  m3^8  m4^3 + 
            10  m1^4  m2^4  m3^8  m4^3 - 10  m1^3  m2^5  m3^8  m4^3 + 
            3  m1^2  m2^6  m3^8  m4^3 - 3  m1*m2^7  m3^8  m4^3 + 
            3  m2^8  m3^8  m4^3 + 6  m1^8  m3^7  m4^4 - 
            6  m1^7  m2*m3^7  m4^4 + 6  m1^6  m2^2  m3^7  m4^4 - 
            20  m1^5  m2^3  m3^7  m4^4 + 20  m1^4  m2^4  m3^7  m4^4 - 
            20  m1^3  m2^5  m3^7  m4^4 + 6  m1^2  m2^6  m3^7  m4^4 - 
            6  m1*m2^7  m3^7  m4^4 + 6  m2^8  m3^7  m4^4 + 
            3  m1^8  m3^6  m4^5 - 3  m1^7  m2*m3^6  m4^5 + 
            3  m1^6  m2^2  m3^6  m4^5 - 10  m1^5  m2^3  m3^6  m4^5 + 
            10  m1^4  m2^4  m3^6  m4^5 - 10  m1^3  m2^5  m3^6  m4^5 + 
            3  m1^2  m2^6  m3^6  m4^5 - 3  m1*m2^7  m3^6  m4^5 + 
            3  m2^8  m3^6  m4^5 + 3  m1^8  m3^5  m4^6 - 
            3  m1^7  m2*m3^5  m4^6 + 3  m1^6  m2^2  m3^5  m4^6 - 
            10  m1^5  m2^3  m3^5  m4^6 + 10  m1^4  m2^4  m3^5  m4^6 - 
            10  m1^3  m2^5  m3^5  m4^6 + 3  m1^2  m2^6  m3^5  m4^6 - 
            3  m1*m2^7  m3^5  m4^6 + 3  m2^8  m3^5  m4^6 + 
            6  m1^8  m3^4  m4^7 - 6  m1^7  m2*m3^4  m4^7 + 
            6  m1^6  m2^2  m3^4  m4^7 - 20  m1^5  m2^3  m3^4  m4^7 + 
            20  m1^4  m2^4  m3^4  m4^7 - 20  m1^3  m2^5  m3^4  m4^7 + 
            6  m1^2  m2^6  m3^4  m4^7 - 6  m1*m2^7  m3^4  m4^7 + 
            6  m2^8  m3^4  m4^7 + 3  m1^8  m3^3  m4^8 - 
            3  m1^7  m2*m3^3  m4^8 + 3  m1^6  m2^2  m3^3  m4^8 - 
            10  m1^5  m2^3  m3^3  m4^8 + 10  m1^4  m2^4  m3^3  m4^8 - 
            10  m1^3  m2^5  m3^3  m4^8 + 3  m1^2  m2^6  m3^3  m4^8 - 
            3  m1*m2^7  m3^3  m4^8 + 3  m2^8  m3^3  m4^8 + m1^8  m3^2  m4^9 - 
            m1^7  m2*m3^2  m4^9 + m1^6  m2^2  m3^2  m4^9 + 
            2  m1^5  m2^3  m3^2  m4^9 - 2  m1^4  m2^4  m3^2  m4^9 + 
            2  m1^3  m2^5  m3^2  m4^9 + m1^2  m2^6  m3^2  m4^9 - 
            m1*m2^7  m3^2  m4^9 + m2^8  m3^2  m4^9 + 2  m1^8  m3*m4^10 - 
            2  m1^7  m2*m3*m4^10 + 2  m1^6  m2^2  m3*m4^10 + 
            4  m1^5  m2^3  m3*m4^10 - 4  m1^4  m2^4  m3*m4^10 + 
            4  m1^3  m2^5  m3*m4^10 + 2  m1^2  m2^6  m3*m4^10 - 
            2  m1*m2^7  m3*m4^10 + 2  m2^8  m3*m4^10 + m1^8  m4^11 - 
            m1^7  m2*m4^11 + m1^6  m2^2  m4^11 + 2  m1^5  m2^3  m4^11 - 
            2  m1^4  m2^4  m4^11 + 2  m1^3  m2^5  m4^11 + m1^2  m2^6  m4^11 - 
            m1*m2^7  m4^11 + m2^8  m4^11, 

          m1^9  m3^10 + 3  m1^6  m2^3  m3^10 + 3  m1^3  m2^6  m3^10 + 
            m2^9  m3^10 + m1^9  m3^9  m4 + 3  m1^6  m2^3  m3^9  m4 + 
            3  m1^3  m2^6  m3^9  m4 + m2^9  m3^9  m4 + 3  m1^9  m3^7  m4^3 - 
            7  m1^6  m2^3  m3^7  m4^3 - 7  m1^3  m2^6  m3^7  m4^3 + 
            3  m2^9  m3^7  m4^3 + 3  m1^9  m3^6  m4^4 - 
            7  m1^6  m2^3  m3^6  m4^4 - 7  m1^3  m2^6  m3^6  m4^4 + 
            3  m2^9  m3^6  m4^4 + 3  m1^9  m3^4  m4^6 - 
            7  m1^6  m2^3  m3^4  m4^6 - 7  m1^3  m2^6  m3^4  m4^6 + 
            3  m2^9  m3^4  m4^6 + 3  m1^9  m3^3  m4^7 - 
            7  m1^6  m2^3  m3^3  m4^7 - 7  m1^3  m2^6  m3^3  m4^7 + 
            3  m2^9  m3^3  m4^7 + m1^9  m3*m4^9 + 3  m1^6  m2^3  m3*m4^9 + 
            3  m1^3  m2^6  m3*m4^9 + m2^9  m3*m4^9 + m1^9  m4^10 + 
            3  m1^6  m2^3  m4^10 + 3  m1^3  m2^6  m4^10 + m2^9  m4^10, 

          m1^10  m3^9 + m1^9  m2*m3^9 + 3  m1^7  m2^3  m3^9 + 
            3  m1^6  m2^4  m3^9 + 3  m1^4  m2^6  m3^9 + 3  m1^3  m2^7  m3^9 + 
            m1*m2^9  m3^9 + m2^10  m3^9 + 3  m1^10  m3^6  m4^3 + 
            3  m1^9  m2*m3^6  m4^3 - 7  m1^7  m2^3  m3^6  m4^3 - 
            7  m1^6  m2^4  m3^6  m4^3 - 7  m1^4  m2^6  m3^6  m4^3 - 
            7  m1^3  m2^7  m3^6  m4^3 + 3  m1*m2^9  m3^6  m4^3 + 
            3  m2^10  m3^6  m4^3 + 3  m1^10  m3^3  m4^6 + 
            3  m1^9  m2*m3^3  m4^6 - 7  m1^7  m2^3  m3^3  m4^6 - 
            7  m1^6  m2^4  m3^3  m4^6 - 7  m1^4  m2^6  m3^3  m4^6 - 
            7  m1^3  m2^7  m3^3  m4^6 + 3  m1*m2^9  m3^3  m4^6 + 
            3  m2^10  m3^3  m4^6 + m1^10  m4^9 + m1^9  m2*m4^9 + 
            3  m1^7  m2^3  m4^9 + 3  m1^6  m2^4  m4^9 + 3  m1^4  m2^6  m4^9 + 
            3  m1^3  m2^7  m4^9 + m1*m2^9  m4^9 + m2^10  m4^9, 

          m1^11  m3^8 + 2  m1^10  m2*m3^8 + m1^9  m2^2  m3^8 + 
            3  m1^8  m2^3  m3^8 + 6  m1^7  m2^4  m3^8 + 3  m1^6  m2^5  m3^8 + 
            3  m1^5  m2^6  m3^8 + 6  m1^4  m2^7  m3^8 + 3  m1^3  m2^8  m3^8 + 
            m1^2  m2^9  m3^8 + 2  m1*m2^10  m3^8 + m2^11  m3^8 - 
            m1^11  m3^7  m4 - 2  m1^10  m2*m3^7  m4 - m1^9  m2^2  m3^7  m4 - 
            3  m1^8  m2^3  m3^7  m4 - 6  m1^7  m2^4  m3^7  m4 - 
            3  m1^6  m2^5  m3^7  m4 - 3  m1^5  m2^6  m3^7  m4 - 
            6  m1^4  m2^7  m3^7  m4 - 3  m1^3  m2^8  m3^7  m4 - 
            m1^2  m2^9  m3^7  m4 - 2  m1*m2^10  m3^7  m4 - m2^11  m3^7  m4 + 
            m1^11  m3^6  m4^2 + 2  m1^10  m2*m3^6  m4^2 + 
            m1^9  m2^2  m3^6  m4^2 + 3  m1^8  m2^3  m3^6  m4^2 + 
            6  m1^7  m2^4  m3^6  m4^2 + 3  m1^6  m2^5  m3^6  m4^2 + 
            3  m1^5  m2^6  m3^6  m4^2 + 6  m1^4  m2^7  m3^6  m4^2 + 
            3  m1^3  m2^8  m3^6  m4^2 + m1^2  m2^9  m3^6  m4^2 + 
            2  m1*m2^10  m3^6  m4^2 + m2^11  m3^6  m4^2 + 
            2  m1^11  m3^5  m4^3 + 4  m1^10  m2*m3^5  m4^3 + 
            2  m1^9  m2^2  m3^5  m4^3 - 10  m1^8  m2^3  m3^5  m4^3 - 
            20  m1^7  m2^4  m3^5  m4^3 - 10  m1^6  m2^5  m3^5  m4^3 - 
            10  m1^5  m2^6  m3^5  m4^3 - 20  m1^4  m2^7  m3^5  m4^3 - 
            10  m1^3  m2^8  m3^5  m4^3 + 2  m1^2  m2^9  m3^5  m4^3 + 
            4  m1*m2^10  m3^5  m4^3 + 2  m2^11  m3^5  m4^3 - 
            2  m1^11  m3^4  m4^4 - 4  m1^10  m2*m3^4  m4^4 - 
            2  m1^9  m2^2  m3^4  m4^4 + 10  m1^8  m2^3  m3^4  m4^4 + 
            20  m1^7  m2^4  m3^4  m4^4 + 10  m1^6  m2^5  m3^4  m4^4 + 
            10  m1^5  m2^6  m3^4  m4^4 + 20  m1^4  m2^7  m3^4  m4^4 + 
            10  m1^3  m2^8  m3^4  m4^4 - 2  m1^2  m2^9  m3^4  m4^4 - 
            4  m1*m2^10  m3^4  m4^4 - 2  m2^11  m3^4  m4^4 + 
            2  m1^11  m3^3  m4^5 + 4  m1^10  m2*m3^3  m4^5 + 
            2  m1^9  m2^2  m3^3  m4^5 - 10  m1^8  m2^3  m3^3  m4^5 - 
            20  m1^7  m2^4  m3^3  m4^5 - 10  m1^6  m2^5  m3^3  m4^5 - 
            10  m1^5  m2^6  m3^3  m4^5 - 20  m1^4  m2^7  m3^3  m4^5 - 
            10  m1^3  m2^8  m3^3  m4^5 + 2  m1^2  m2^9  m3^3  m4^5 + 
            4  m1*m2^10  m3^3  m4^5 + 2  m2^11  m3^3  m4^5 + 
            m1^11  m3^2  m4^6 + 2  m1^10  m2*m3^2  m4^6 + 
            m1^9  m2^2  m3^2  m4^6 + 3  m1^8  m2^3  m3^2  m4^6 + 
            6  m1^7  m2^4  m3^2  m4^6 + 3  m1^6  m2^5  m3^2  m4^6 + 
            3  m1^5  m2^6  m3^2  m4^6 + 6  m1^4  m2^7  m3^2  m4^6 + 
            3  m1^3  m2^8  m3^2  m4^6 + m1^2  m2^9  m3^2  m4^6 + 
            2  m1*m2^10  m3^2  m4^6 + m2^11  m3^2  m4^6 - m1^11  m3*m4^7 - 
            2  m1^10  m2*m3*m4^7 - m1^9  m2^2  m3*m4^7 - 
            3  m1^8  m2^3  m3*m4^7 - 6  m1^7  m2^4  m3*m4^7 - 
            3  m1^6  m2^5  m3*m4^7 - 3  m1^5  m2^6  m3*m4^7 - 
            6  m1^4  m2^7  m3*m4^7 - 3  m1^3  m2^8  m3*m4^7 - 
            m1^2  m2^9  m3*m4^7 - 2  m1*m2^10  m3*m4^7 - m2^11  m3*m4^7 + 
            m1^11  m4^8 + 2  m1^10  m2*m4^8 + m1^9  m2^2  m4^8 + 
            3  m1^8  m2^3  m4^8 + 6  m1^7  m2^4  m4^8 + 3  m1^6  m2^5  m4^8 + 
            3  m1^5  m2^6  m4^8 + 6  m1^4  m2^7  m4^8 + 3  m1^3  m2^8  m4^8 + 
            m1^2  m2^9  m4^8 + 2  m1*m2^10  m4^8 + m2^11  m4^8} // 
        Factor\)

(m3 + m4)^2*(m3^3 + m4^3) // Factor

The Groebner basis gb33 contains 4 mass polynomials but they are 
all multiples of the polynomial Q below.  All 4 of these polynomials are 
divisors of the mass polynomial

(m1 + m2)^2(m3 + m4)^2 (m1^3+m2^3) (m3^3+m4^3)  Q 

Therefore this mass polynomial is in the ideal generated by the reduced 
system as claimed in the paper.



The following cell displays Q and shows that it can be written in the form of 
equation (19) in the paper.

Q = ((m1^6) (m3^6) + 2 (m1^3) (m2^3) (m3^6) + (m2^6) (m3^6) + 
            2 (m1^6) (m3^3) (m4^3) - 12 (m1^3) (m2^3) (m3^3) (m4^3) + 
            2 (m2^6) (m3^3) (m4^3) + (m1^6) (m4^6) + 2 (m1^3) (m2^3) (m4^6) + 
            (m2^6) (m4^6));
Qeq19  =  (m1^3 - m2^3)^2 (m3^3 - m4^3)^2 + 
        4 (m1^3 - m2^3)^2*m3^3*m4^3 + 
        4 (m3^3 - m4^3)^2*m1^3*m2^3
Q - Qeq19 // Expand

This polynomial also has positive roots, so the facets 22 and 33 
will be analyzed further in the next section.

Exceptional Cases

In this section we will show that there do not exist Puiseux series 
solutions of orders which are positive multiples of the normal vectors  a22 = 
( 0, 0, -1, -1, 0 , 0) or  a33 = (0,  -1,  -1, -1, -1,  0 )

Facet 22

If m1 m4 - m2 m3 is not zero, the reduced equations for this facet 
have no solutions in the algebraic torus. So there can be no Puiseux series 
solution in this case.  We may assume without loss of generality that m4 =  
1; therefore we begin with the full system so equations with mass 
substitutions  m4 = 1 and m1 m4 = m2 m3

eqs22  =  acdzeqs /. {m4 -> 1, m1 -> m2*m3}

Make a change of variables corresponding to the normal vector 
alpha22=(0,0,-1,-1,0,0).  After this substitution, we will be looking for 
series solutions for all variables starting with the power t^0, except r14 
will be gone (without loss of generality, we can look for a Puiseux solution 
with r14 = 1/t)

sub0  =  {r14 -> 1/t, 
        r23 -> r23/t}
eqs221 = eqs22 /. sub0 // Factor // Numerator

Here are the lowest order terms in t.  The order 0 terms are 
equivalent to the reduced system red22.  There are no terms at order 1.  We 
truncate the equations above order 3 since the other terms will not be 
relevant.

F0  =  eqs221 /. t -> 0 // Factor

    F1  =  Coefficient[eqs221, t] // Factor

    F2  =  Coefficient[eqs221, t^2] // Factor

    F3  =  Coefficient[eqs221, t^3] // Factor

    F  =  F0  +  t*F1  +  t^2*F2  +  t^3*F3;

Solve the reduced system for the leading order terms of a Puiseux 
solution. We begin by "cleaning up"  the equautions (eliminating factors of 
the indicated variables).

allvars  =  {r12, r13, r14, r23, r24, r34, m1, m2, m3, 
          m4};
F00 =  Map[CleanUp[#, allvars] &, F0]

The first two equations are uniquely solveable for r13^3 and r12^3. 
 We make these substitutions.

F001  =  
      Map[CleanUp[#, allvars] &, 
          F00 /. {r13^3 -> -m3*r23^2*r24^3, 
              r12^3 -> -m2*r23^2*r34^3}] // 
        Factor

Equations 5 and 6 now force us to take r23 = 1, -1 , i or -i.  
First we show that the cases r23 = 1, -1 are impossible for positive masses  
In each case we can find a solution only if  m2 + m3 = 0.

F001 /. r23 -> 1 // Factor
% /. {r34^3 -> 1/(1 - m2), r24^3 -> 1/(1 - m3)} // 
        Factor // Numerator
F001 /. r23 -> -1 // Factor
% /. {r34^3 -> 1/(1 - m2), r24^3 -> 1/(1 - m3)} // 
        Factor // Numerator

On the other hand, the cases r23 = i and r23 = -i are 
possible.

F001 /. r23 -> I // Factor
% /. {r34^3 -> 1/(1 + m2), r24^3 -> 1/(1 + m3)} // 
        Factor // Numerator
F001 /. r23 -> -I // Factor
% /. {r34^3 -> 1/(1 + m2), r24^3 -> 1/(1 + m3)} // 
        Factor // Numerator

Here is a substitution valid for all relevant solutions of the 
reduced system.

sub1 = {r12^3 -> m2/(1 + m2), r34^3 -> 1/(1 + m2), 
        r13^3 -> m3/(1 + m3), r24^3 -> 1/(1 + m3), 
        r23^2 -> -1, r23^3 -> -r23, r23^4 -> 1, 
        r12^5 -> m2*r12^2/(1 + m2), 
        r34^5 -> r34^2/(1 + m2), 
        r13^5 -> m3*r13^2/(1 + m3), 
        r24^5 -> r24^2/(1 + m3)}
F00 /. sub1 // Factor

We want to show that the solution of the reduced system does not 
really determine a continuum of solutions by showing that the Puiseux series 
solutions cannot be continued to higher order terms.  To do this we have to 
do some rescalings and substitutions.  We have a system 

F(x,t) = F0(x) + t^2 F2(x) + t^3 F3(x) + ...

where x =( r12 ,r13, r23 ,r24, r34 )  and  r14 = 1/t .  We also have a 
solution x0 of F0(x0) = 0 (the reduced equations).  We use the implicit 
function theorem to see that any Puiseux solution x = x0 + o(t) must be a 
power series in t.  It suffices to show that the 9 x 5 matrix DF0(x0) has 
rank 5.   We single out a 5 x 5 submatrix and take its determinant, making 
the substition corresponding to the solutions of the reduced system.

grad[f_]  :=  {D[f, r12], D[f, r13], D[f, r23], D[f, r24], 
        D[f, r34]}
DF0  =  
        Map[grad, F0] /. sub1 // Factor;
DF0 // MatrixForm
(Det[DF0[[{1, 2, 4, 5, 7}]]] /. sub1 // Factor // 
          Numerator) /. sub1

Since r23 is not 1 or -1 and since the masses are positive, this 
determinant is nonzero.

Knowing that our Puiseux solution is a power series and that the first order 
term in our equation is F1=0, we are justified in setting x = x0 + t^2 u+ t^3 
v + ... .  We will derive the (linear) equations for u and v

Ft  =  
        F /. {r12 -> r12 + t^2*u12 + t^3*v12, 
            r13 -> r13 + t^2*u13 + t^3*v13, 
            r23 -> r23 + t^2*u23 + t^3*v23, 
            r24 -> r24 + t^2*u24 + t^3*v24, 
            r34 -> 
              r34 + t^2*u34 + t^3*v34};
Ft0  =  (Ft /. t -> 0 // Factor) /. sub1 // 
        Factor
Ft1  =  
      Coefficient[Ft, t] /. sub1 // Factor
Ft2  =  
      Coefficient[Ft, t^2] /. sub1 // Factor
Ft3  =  Coefficient[Ft, t^3] /. sub1 // Factor

Look at the t^2 terms which are linear in the new variable uij.  
Solve five of the equations to find the uij.  It turns out (for some reason) 
that the resulting solution works for all nine equations.

Ft2  =  Numerator[Ft2]
Ft2five  =  
        Ft2[[{1, 2, 4, 5, 7}]];
usol  =  Solve[
              Ft2five == {0, 0, 0, 0, 0}, {u12, u13, u23, u24, 
                u34}][[1]] /. sub1 // 
        FullSimplify

    
(Ft2 /. usol // Factor) /. sub1 // Simplify

Now make a substitution to go on to the next order.  This gives 
linear equations for the vij.  We find the augmented matrix of this system of 
nine equations and five unknowns.

Ft3u  = Ft3 /. usol // Factor // 
          Numerator;
augv[f_]  :=  {Coefficient[f, v12], Coefficient[f, v13], 
        Coefficient[f, v23], Coefficient[f, v24], Coefficient[f, v34], 
        f /. {v12 -> 0, v13 -> 0, v23 -> 0, v24 -> 0, 
            v34 -> 0}}
Ft3umatrix  =  
        Map[augv, Ft3u] /. sub1 // Factor;
Ft3umatrix // MatrixForm

The resulting augmented matrix has rank six which shows that the 
system is inconsistent.

(Det[Ft3umatrix[[{1, 2, 3, 4, 5, 7}]]] /. sub1 // Factor // 
          Numerator);
% /. sub1 // Factor

Facet 33

If the mass polynomials for the reduced equations do not vanish 
then we are done.  Since we are assuming positive masses, the only way for 
these polynomials to vanish is to have Q = 0 and this implies that m1= m2 and 
m3= m4.   So without loss of generality, we may begin with the equations and 
the mass substitutions   m1=m2 and m3 = m4 = 1.

eqs33  =  
      acdzeqs /. {m4 -> 1, m3 -> 1, m2 -> m1}

Make a change of variables corresponding to the normal vector 
alpha33=(0,-1,-1,-1,-1,0).  After this substitution, we will be looking for 
series solutions for all variables starting with the power t^0, except r13 
will be gone (without loss of generality, we can look for a Puiseux solution 
with r13 = 1/t)

sub0  =  {r13 -> 1/t, r14 -> r14/t, r23 -> r23/t, 
        r24 -> r24/t}
eqs331 = eqs33 /. sub0 // Factor // Numerator

Here are the lowest order terms in t.  The order 0 terms are 
equivalent to the reduced system red33.

F0  =  eqs331 /. t -> 0 // Factor
F1  =  Coefficient[eqs331, t] // Factor
F2  =  Coefficient[eqs331, t^2] // Factor
F3  =  Coefficient[eqs331, t^3] // Factor
F  =  F0  +  t*F1  +  t^2*F2  +  t^3*F3;

Solve the reduced system.

Solve the reduced system for the leading order terms of a Puiseux 
solution. We begin by "cleaning up"  the equautions (eliminating factors of 
the indicated variables).

allvars  =  {r12, r13, r14, r23, r24, r34, m1, m2, m3, 
          m4};
F00 =  Map[CleanUp[#, allvars] &, F0]

Equations 1 and 5  are uniquely solveable for r12^3 and r34^3.  We 
make these substitutions.

F001  =  
      Map[CleanUp[#, allvars] &, 
          F00 /. {r34^3 -> 1/(1 + m1), 
              r12^3 -> m1/(1 + m1)}] // Factor

The second equation gives us r23^2 = -2 - r14^2, after which we are 
forced to choose r24=1 or -1. First consider r24 = 1 (which means r23^2 = - 
3).  The result forces us to a contradictary value of r23 -- thus r24 = 1 is 
impossible

F002  =  
      Map[CleanUp[#, allvars] &, 
          F001 /. {r23^2 -> -2 - r14^2, 
              r23^3 -> r23*(-2 - r14^2)}] // 
        Factor
Map[CleanUp[#, allvars] &, F002 /. {r24 -> 1}] // 
      Factor
Map[CleanUp[#, allvars] &, % /. {r14 -> I}] // Factor

Now we try r24 = -1.  We are forced to pick  r14 = -r23 = i  or r14 
= -r23 = - i

Map[CleanUp[#, allvars] &, F002 /. {r24 -> -1}] // 
      Factor
Map[CleanUp[#, allvars] &, % /. {r14 -> I}] // 
      Factor
Map[CleanUp[#, allvars] &, % /. {r23 -> -I}] // 
      Factor

    
Map[CleanUp[#, allvars] &, F002 /. {r24 -> -1}] // 
      Factor
Map[CleanUp[#, allvars] &, % /. {r14 -> -I}] // 
      Factor
Map[CleanUp[#, allvars] &, % /. {r23 -> I}] // Factor

Here is the solution of the reduced system with r14 = -I and r23= 
I.  The other case is similar.

sub1 = {r34^3 -> 1/(1 + m1), 
        r12^3 -> m1/(1 + m1), r14 -> -I, r23 -> I, 
        r24 -> -1}

    
F00 /. sub1 // Factor

We want to show that the solution of the reduced system does not 
really determine a continuum of solutions by showing that the Puiseux series 
solutions cannot be continued to higher order terms.  To do this we have to 
do some rescalings and substitutions.  We have a system 

F(x,t) = F0(x) + t^2 F2(x) + t^3 F3(x) + ...

where x =( r12 ,r14, r23 ,r24, r34 )  and  r13 = 1/t .  We also have a 
solution x0 of F0(x0) = 0 (the reduced equations).  We use the implicit 
function theorem to see that any Puiseux solution x = x0 + o(t) must be a 
power series in t.  It suffices to show that the 9 x 5 matrix DF0(x0) has 
rank 5.   We single out a 5 x 5 submatrix and take its determinant, making 
the substition corresponding to the solutions of the reduced system.

grad[f_]  :=  {D[f, r12], D[f, r14], D[f, r23], D[f, r24], 
        D[f, r34]}
DF0  =  
        Map[grad, F0] /. sub1 // Factor;
DF0 // MatrixForm
(Det[DF0[[{1, 2, 5, 6, 9}]]] /. sub1 // Factor // 
          Numerator) /. sub1

For some reason, it turns out that F1 vanishes at x0

F1 /. sub1 // Factor

Ft  =  
        F /. {r12 -> r12 + t^2*u12 + t^3*v12, 
            r13 -> r13 + t^2*u13 + t^3*v13, 
            r23 -> r23 + t^2*u23 + t^3*v23, 
            r24 -> r24 + t^2*u24 + t^3*v24, 
            r34 -> 
              r34 + t^2*u34 + t^3*v34};
Ft0  =  (Ft /. t -> 0 // Factor) /. sub1 // 
        Factor
Ft1  =  
      Coefficient[Ft, t] /. sub1 // Factor
Ft2  =  
      Coefficient[Ft, t^2] /. sub1 // Factor
Ft3  =  Coefficient[Ft, t^3] /. sub1 // Factor

Knowing this, we are justified in setting x = x0 + t^2 u+ t^3 v + 
... .  We will derive the equations for u and v

Ft  =  
        F /. {r12 -> r12 + t^2*u12 + t^3*v12, 
            r14 -> r14 + t^2*u14 + t^3*v14, 
            r23 -> r23 + t^2*u23 + t^3*v23, 
            r24 -> r24 + t^2*u24 + t^3*v24, 
            r34 -> 
              r34 + t^2*u34 + t^3*v34};
Ft0  =  (Ft /. t -> 0 // Factor) /. sub1 // 
        Factor
Ft1  =  
      Coefficient[Ft, t] /. sub1 // Factor
Ft2  =  
      Coefficient[Ft, t^2] /. sub1 // Factor
Ft3  =  Coefficient[Ft, t^3] /. sub1 // Factor

Ft2  =  Numerator[Ft2]
Ft2five  =  
        Ft2[[{1, 2, 5, 6, 9}]];
usol  =  Solve[
              Ft2five == {0, 0, 0, 0, 0}, {u12, u14, u23, u24, 
                u34}][[1]] /. sub1 // 
        FullSimplify

    
(Ft2 /. usol // Factor) /. sub1 // Simplify

Now make a substitution to go on to the next order.  This gives 
linear equations for the vij.  We find the augmented matrix of this system of 
nine equations and five unknowns.

Ft3u  = Ft3 /. usol // Factor // 
          Numerator;
augv[f_]  :=  {Coefficient[f, v12], Coefficient[f, v14], 
        Coefficient[f, v23], Coefficient[f, v24], Coefficient[f, v34], 
        f /. {v12 -> 0, v14 -> 0, v23 -> 0, v24 -> 0, 
            v34 -> 0}}
Ft3umatrix  =  
        Map[augv, Ft3u] /. sub1 // Factor;
Ft3umatrix // MatrixForm

The resulting augmented matrix has rank six which shows that the 
system is inconsistent.

(Det[Ft3umatrix[[{1, 2, 3, 5, 6, 9}]]] /. sub1 // Factor // 
          Numerator);
% /. sub1 // Factor