(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 191895, 3082]*) (*NotebookOutlinePosition[ 192571, 3106]*) (* CellTagsIndexPosition[ 192527, 3102]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Finiteness and upper bound computations for the four-vortex problem \ \>", "Title", FontSize->48], Cell[CellGroupData[{ Cell["Introduction", "Section", FontSize->24], Cell["\<\ This notebook contains computational algorithms and results which support the \ paper \"Finiteness of Stationary Configurations of the Four-Vortex 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. \ \>", "Text", FontSize->14] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Equilibria", FontSize->24]], "Section"], Cell[TextData[StyleBox["Section 2 of the paper is about the equilibria of the \ four-vortex problem. Here are some commands to set up the equations.", FontSize->16]], "Text"], Cell[BoxData[{ \(VortexIVBar[i_, n_]\ := \ Plus @@ \((Table[G[j]/\((z[i] - z[j])\), {j, 1, i - 1}]~Join~ Table[G[j]/\((z[i] - z[j])\), {j, i + 1, n}])\)\[IndentingNewLine]\[IndentingNewLine]\), "\ \[IndentingNewLine]", \(Denoms[i_, n_]\ := \ Times @@ \((Table[\((z[i] - z[j])\), {j, i + 1, n}]~Join~ Table[\((z[i] - z[j])\), {j, 1, i - 1}])\)\[IndentingNewLine]\[IndentingNewLine]\), "\ \[IndentingNewLine]", \(VortexEquilibriaEqs[ n_]\ := \ \(Table[Denoms[i, n]*VortexIVBar[i, n], {i, 1, n}] // Factor\) // Numerator\[IndentingNewLine]\), "\[IndentingNewLine]", \(VortexEquilibriaEqs0[ n_]\ := \ \(Table[ Denoms[i, n]*VortexIVBar[i, n], {i, 3, n}] /. {z[n - 1] \[Rule] 1, z[n] \[Rule] 0} // Factor\) // Numerator\[IndentingNewLine]\[IndentingNewLine]\), "\ \[IndentingNewLine]", \(\)}], "Input"], Cell[TextData[StyleBox["Here are the two normalized equations using the \ notation of the paper.", FontSize->16]], "Text"], Cell[BoxData[ \({F3, F4} = \ VortexEquilibriaEqs0[4]\)], "Input"], Cell[TextData[StyleBox["The resultant with respect to z2. The coefficients \ are simplified using the equation L=0", FontSize->16]], "Text"], Cell[BoxData[{ \(rz1\ = \ \ Resultant[F3, F4, z[2]] // Factor\[IndentingNewLine]\), "\[IndentingNewLine]", \(clrz1\ = \ CoefficientList[rz1, z[1]] // Factor\), "\[IndentingNewLine]", \(\(L = G[1] G[2] + G[1] G[3] + G[1] G[4] + G[2] G[3] + G[2] G[4] + G[3] G[4];\)\), "\[IndentingNewLine]", \(\(clrz1[\([2]\)]\ = \ clrz1[\([2]\)] + L // Factor;\)\), "\[IndentingNewLine]", \(\(clrz1[\([3]\)]\ = \ clrz1[\([3]\)] - L // Factor;\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(rz1 = \ clrz1 . {1, z[1], z[1]^2}\)}], "Input"], Cell[BoxData[{ \({a, b, c}\ = \ clrz1/\((\(-G[1]\))\) // Factor\[IndentingNewLine]\), "\[IndentingNewLine]", \(disc\ = b^2 - 4*a*c // Expand\), "\[IndentingNewLine]", \(disc\ = \ disc + 4 L // Factor\[IndentingNewLine]\), "\[IndentingNewLine]", \(z1sol\ = \ \((\(-b\) + I*Sqrt[3]*G[2])\)/\((2*a)\)\)}], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Rigidly Translating Solutions", "Section", FontSize->24], Cell["\<\ These calculations reproduce the computer-assisted parts of section 3, which \ shows that there at most 6 rigidly translating solutions of the four-vortex \ problem. \ \>", "Text", FontSize->14], Cell[BoxData[ \(VarNames[n_] := Flatten[Table[{z[j] \[Rule] ToExpression[StringJoin["\", ToString[j]]], G[j] \[Rule] ToExpression[StringJoin["\", ToString[j]]]}, {j, 1, n}]]; G[i_, n_] := \((Sum[ If[j \[NotEqual] i, G[j] Product[ If[k \[NotEqual] j && k \[NotEqual] i, z[i] - z[k], 1], {k, 1, n}] Product[ If[k \[NotEqual] i && k \[NotEqual] n, z[n] - z[k], 1], {k, 1, n}], 0], {j, 1, n}]\[IndentingNewLine]\t + \ Sum[If[j \[NotEqual] n, G[j] Product[ If[k \[NotEqual] i && k \[NotEqual] n, z[i] - z[k], 1], {k, 1, n}] Product[ If[k \[NotEqual] j && k \[NotEqual] n, z[n] - z[k], 1], {k, 1, n}], 0], {j, 1, n}])\) /. VarNames[n]\)], "Input", FontSize->14], Cell[TextData[StyleBox["Here are the euqations called G2 and G3 in the \ paper.", FontSize->16]], "Text"], Cell[BoxData[ \(RigidTranslateSystem = Factor[{G[2, 4], G[3, 4]} /. {z4 \[Rule] 0, z3 \[Rule] 1}]\)], "Input", FontSize->14], Cell[TextData[StyleBox["After dividing out a trivial factor, the resultant \ with respect to z2 gives a degree 6 polynomial in z1.", FontSize->16]], "Text"], Cell[BoxData[{ \(Factor[ Resultant[RigidTranslateSystem[\([1]\)], RigidTranslateSystem[\([2]\)], z2]]\), "\[IndentingNewLine]", \(\(p6 = Factor[Resultant[RigidTranslateSystem[\([1]\)], RigidTranslateSystem[\([2]\)], z2]]/\((\((\(-1\) + z1)\)\ z1\^3\ )\);\)\)}], "Input", FontSize->14], Cell[TextData[StyleBox["The next computation shows that the polynomial p6 \ cannot vanish identically for any relevant values of the vorticities.", FontSize->16]], "Text"], Cell[BoxData[{ \(RigidTranslateCoefficientIdeal = Flatten[{G1 + G2 + G3 + G4, G1*G2*G3*G4 - 1, Table[Coefficient[p6, z1, i], {i, 0, 6}]}]\[IndentingNewLine]\), "\[IndentingNewLine]", \(GroebnerBasis[ RigidTranslateCoefficientIdeal, {G1, G2, G3, G4}]\)}], "Input", FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell["Collinear Relative Equilibria", "Section", FontSize->24], Cell["\<\ The following calculations illustrate the computations in section 4, which \ show that there are at most 12 collinear relative equilibria in the \ four-vortex problem. Here are the equations. \ \>", "Text", FontSize->14], Cell[BoxData[{ StyleBox[ RowBox[{\(H[i_, n_] := G[i, n] + \[Lambda]\ \((z[i] - z[n])\) Product[ If[k \[NotEqual] i && k \[NotEqual] n, z[i] - z[k], 1], {k, 1, n}]\ Product[ If[k \[NotEqual] n, z[n] - z[k], 1], {k, 1, n}] /. VarNames[n]\), "\[IndentingNewLine]"}], FontSize->12], "\[IndentingNewLine]", StyleBox[\(CollinearEqs = {H[1, 4], H[2, 4], H[3, 4]} /. {z4 \[Rule] 0, z3 \[Rule] 1}\), FontSize->12]}], "Input", FontSize->14], Cell[TextData[{ StyleBox["Next we eliminate", FontSize->16], StyleBox[" l ", FontFamily->"Symbol", FontSize->16], StyleBox["and divide out some trivial factors.", FontSize->16] }], "Text"], Cell[BoxData[{ \(CollinearEqsResultants = Flatten[Table[ Factor[Resultant[CollinearEqs[\([i]\)], CollinearEqs[\([j]\)], \[Lambda]]], {i, 1, 2}, {j, i + 1, 3}]]\[IndentingNewLine]\), "\[IndentingNewLine]", \({K2, K3} = Numerator[ Factor[{CollinearEqsResultants[\([2]\)], CollinearEqsResultants[\([3]\)]}/\((\((\(-1\) + z2)\)\ \((\(-1\) + z1)\)\ z1\ z2\ )\)]]\)}], "Input"], Cell[TextData[StyleBox["A resultant leads to a twelfth degree polynomial for \ z1.", FontSize->16]], "Text"], Cell[BoxData[ \(P12 = Factor[Resultant[K2, K3, z2]]/\((\((\(-1\) + z1)\)\^5\ z1\^5\ )\)\)], "Input"], Cell[TextData[StyleBox["Verification that P12 does not vanish identically.", FontSize->16]], "Text"], Cell[BoxData[{ \(\(P12CoefficientTable = Table[Factor[Coefficient[P12, z1, i]], {i, 0, 12}];\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(Factor[ GroebnerBasis[ Union[{G1\ G2\ G3\ G4\ - 1}, P12CoefficientTable], {G1, G2, G3, G4}, MonomialOrder \[Rule] DegreeReverseLexicographic]]\)}], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["\<\ Strictly Planar Relative Equilibria with nonzero total circulation\ \>", "Section", FontSize->24], Cell["This section contains our calculations used in section 5.", "Text", FontSize->16], Cell[TextData[StyleBox["Evaluate the small data cell below to define vertex \ and inequality lists for the final Minkowski sum polytope:", FontSize->16]], "Text"], Cell[BoxData[{ \(\(\(v1t9bH = {{0, 6, 12, 18, 14, 10}, {0, 6, 12, 18, 14, 14}, {0, 6, 12, 18, 16, 10}, {0, 6, 12, 18, 16, 14}, {0, 6, 14, 18, 14, 8}, {0, 6, 14, 18, 16, 8}, {0, 6, 14, 18, 16, 12}, {0, 6, 16, 18, 10, 10}, {0, 6, 16, 18, 10, 14}, {0, 6, 16, 18, 12, 14}, {0, 6, 18, 18, 10, 8}, {0, 6, 18, 18, 10, 12}, {0, 6, 18, 18, 12, 8}, {0, 6, 18, 18, 12, 12}, {0, 8, 10, 16, 18, 10}, {0, 8, 10, 16, 18, 14}, {0, 8, 10, 18, 14, 10}, {0, 8, 10, 18, 14, 14}, {0, 8, 12, 18, 16, 14}, {0, 8, 12, 20, 12, 8}, {0, 8, 12, 20, 12, 12}, {0, 8, 12, 20, 14, 8}, {0, 8, 12, 20, 14, 12}, {0, 8, 16, 18, 8, 10}, {0, 8, 16, 18, 8, 14}, {0, 8, 16, 18, 12, 14}, {0, 8, 16, 20, 8, 8}, {0, 8, 16, 20, 8, 12}, {0, 8, 16, 20, 10, 8}, {0, 8, 16, 20, 10, 12}, {0, 8, 18, 16, 8, 10}, {0, 8, 18, 16, 8, 14}, {0, 8, 18, 16, 10, 14}, {0, 8, 20, 16, 8, 8}, {0, 8, 20, 16, 8, 12}, {0, 8, 20, 16, 10, 8}, {0, 8, 20, 16, 10, 12}, {0, 10, 8, 14, 18, 10}, {0, 10, 8, 14, 18, 14}, {0, 10, 8, 18, 16, 10}, {0, 10, 8, 18, 16, 14}, {0, 10, 10, 14, 20, 8}, {0, 10, 10, 14, 20, 12}, {0, 10, 10, 16, 18, 14}, {0, 10, 10, 18, 16, 14}, {0, 10, 10, 20, 14, 8}, {0, 10, 10, 20, 14, 12}, {0, 10, 16, 18, 8, 14}, {0, 10, 16, 18, 10, 14}, {0, 10, 16, 20, 8, 8}, {0, 10, 16, 20, 8, 12}, {0, 10, 18, 16, 6, 10}, {0, 10, 18, 16, 6, 14}, {0, 10, 18, 16, 10, 14}, {0, 10, 18, 18, 6, 8}, {0, 10, 18, 18, 6, 12}, {0, 10, 20, 16, 8, 8}, {0, 10, 20, 16, 8, 12}, {0, 12, 6, 14, 18, 10}, {0, 12, 6, 14, 18, 14}, {0, 12, 6, 16, 18, 10}, {0, 12, 6, 16, 18, 14}, {0, 12, 8, 12, 20, 8}, {0, 12, 8, 12, 20, 12}, {0, 12, 8, 14, 20, 8}, {0, 12, 8, 14, 20, 12}, {0, 12, 8, 16, 18, 14}, {0, 12, 18, 16, 6, 14}, {0, 12, 18, 16, 8, 14}, {0, 12, 18, 18, 6, 8}, {0, 12, 18, 18, 6, 12}, {0, 12, 20, 12, 8, 8}, {0, 12, 20, 12, 8, 12}, {0, 14, 6, 14, 18, 8}, {0, 14, 6, 16, 18, 8}, {0, 14, 6, 16, 18, 12}, {0, 14, 18, 10, 8, 10}, {0, 14, 18, 10, 8, 14}, {0, 14, 18, 12, 6, 10}, {0, 14, 18, 12, 6, 14}, {0, 14, 18, 14, 6, 8}, {0, 14, 20, 10, 10, 8}, {0, 14, 20, 10, 10, 12}, {0, 14, 20, 12, 8, 8}, {0, 14, 20, 12, 8, 12}, {0, 16, 6, 10, 18, 10}, {0, 16, 6, 10, 18, 14}, {0, 16, 6, 12, 18, 14}, {0, 16, 8, 8, 18, 10}, {0, 16, 8, 8, 18, 14}, {0, 16, 8, 8, 20, 8}, {0, 16, 8, 8, 20, 12}, {0, 16, 8, 10, 20, 8}, {0, 16, 8, 10, 20, 12}, {0, 16, 8, 12, 18, 14}, {0, 16, 10, 8, 18, 14}, {0, 16, 10, 8, 20, 8}, {0, 16, 10, 8, 20, 12}, {0, 16, 10, 10, 18, 14}, {0, 16, 18, 8, 10, 10}, {0, 16, 18, 8, 10, 14}, {0, 16, 18, 10, 10, 14}, {0, 16, 18, 12, 6, 10}, {0, 16, 18, 12, 6, 14}, {0, 16, 18, 12, 8, 14}, {0, 16, 18, 14, 6, 8}, {0, 16, 18, 14, 6, 12}, {0, 18, 6, 10, 18, 8}, {0, 18, 6, 10, 18, 12}, {0, 18, 6, 12, 18, 8}, {0, 18, 6, 12, 18, 12}, {0, 18, 8, 8, 16, 10}, {0, 18, 8, 8, 16, 14}, {0, 18, 8, 10, 16, 14}, {0, 18, 10, 6, 16, 10}, {0, 18, 10, 6, 16, 14}, {0, 18, 10, 6, 18, 8}, {0, 18, 10, 6, 18, 12}, {0, 18, 10, 10, 16, 14}, {0, 18, 12, 6, 16, 14}, {0, 18, 12, 6, 18, 8}, {0, 18, 12, 6, 18, 12}, {0, 18, 12, 8, 16, 14}, {0, 18, 14, 6, 12, 10}, {0, 18, 14, 6, 12, 14}, {0, 18, 14, 6, 14, 8}, {0, 18, 14, 8, 10, 10}, {0, 18, 14, 8, 10, 14}, {0, 18, 16, 6, 12, 10}, {0, 18, 16, 6, 12, 14}, {0, 18, 16, 6, 14, 8}, {0, 18, 16, 6, 14, 12}, {0, 18, 16, 8, 12, 14}, {0, 18, 16, 10, 8, 10}, {0, 18, 16, 10, 8, 14}, {0, 18, 16, 10, 10, 14}, {0, 20, 8, 8, 16, 8}, {0, 20, 8, 8, 16, 12}, {0, 20, 8, 10, 16, 8}, {0, 20, 8, 10, 16, 12}, {0, 20, 10, 8, 16, 8}, {0, 20, 10, 8, 16, 12}, {0, 20, 12, 8, 12, 8}, {0, 20, 12, 8, 12, 12}, {0, 20, 14, 8, 12, 8}, {0, 20, 14, 8, 12, 12}, {0, 20, 14, 10, 10, 8}, {0, 20, 14, 10, 10, 12}, {6, 0, 12, 18, 10, 14}, {6, 0, 12, 18, 10, 16}, {6, 0, 12, 18, 14, 14}, {6, 0, 12, 18, 14, 16}, {6, 0, 14, 18, 8, 14}, {6, 0, 14, 18, 8, 16}, {6, 0, 14, 18, 12, 16}, {6, 0, 16, 18, 10, 10}, {6, 0, 16, 18, 14, 10}, {6, 0, 16, 18, 14, 12}, {6, 0, 18, 18, 8, 10}, {6, 0, 18, 18, 8, 12}, {6, 0, 18, 18, 12, 10}, {6, 0, 18, 18, 12, 12}, {6, 6, 12, 18, 14, 16}, {6, 6, 12, 18, 16, 14}, {6, 6, 12, 22, 10, 12}, {6, 6, 12, 22, 12, 10}, {6, 6, 16, 14, 8, 18}, {6, 6, 16, 14, 18, 8}, {6, 6, 16, 18, 12, 14}, {6, 6, 16, 18, 14, 12}, {6, 6, 16, 20, 10, 12}, {6, 6, 16, 20, 12, 10}, {6, 6, 20, 14, 8, 14}, {6, 6, 20, 14, 14, 8}, {6, 6, 20, 16, 10, 12}, {6, 6, 20, 16, 12, 10}, {6, 8, 8, 10, 22, 12}, {6, 8, 8, 12, 22, 8}, {6, 8, 8, 22, 10, 12}, {6, 8, 8, 22, 12, 8}, {6, 8, 10, 12, 22, 6}, {6, 8, 10, 12, 22, 10}, {6, 8, 10, 16, 18, 14}, {6, 8, 10, 18, 14, 16}, {6, 8, 10, 22, 10, 12}, {6, 8, 12, 10, 22, 6}, {6, 8, 12, 10, 22, 8}, {6, 8, 12, 18, 12, 16}, {6, 8, 12, 22, 8, 12}, {6, 8, 14, 16, 6, 18}, {6, 8, 14, 18, 8, 16}, {6, 8, 14, 18, 14, 14}, {6, 8, 14, 20, 6, 14}, {6, 8, 14, 22, 10, 10}, {6, 8, 18, 14, 0, 14}, {6, 8, 18, 14, 0, 16}, {6, 8, 18, 14, 8, 16}, {6, 8, 18, 16, 10, 14}, {6, 8, 18, 18, 0, 10}, {6, 8, 18, 18, 0, 12}, {6, 8, 22, 12, 8, 12}, {6, 8, 22, 12, 12, 8}, {6, 8, 22, 14, 10, 10}, {6, 10, 8, 10, 22, 12}, {6, 10, 8, 14, 18, 16}, {6, 10, 8, 18, 16, 14}, {6, 10, 8, 22, 12, 6}, {6, 10, 8, 22, 12, 10}, {6, 10, 12, 10, 22, 8}, {6, 10, 12, 18, 14, 14}, {6, 10, 12, 22, 10, 10}, {6, 10, 14, 18, 12, 14}, {6, 10, 14, 22, 8, 10}, {6, 10, 16, 18, 8, 14}, {6, 10, 16, 20, 6, 12}, {6, 10, 18, 12, 0, 14}, {6, 10, 18, 12, 0, 16}, {6, 10, 18, 16, 0, 10}, {6, 10, 20, 16, 6, 12}, {6, 10, 22, 8, 8, 12}, {6, 10, 22, 8, 12, 6}, {6, 10, 22, 8, 12, 8}, {6, 10, 22, 10, 8, 12}, {6, 10, 22, 10, 12, 8}, {6, 10, 22, 12, 6, 12}, {6, 10, 22, 12, 10, 10}, {6, 10, 22, 14, 8, 10}, {6, 12, 0, 10, 18, 14}, {6, 12, 0, 10, 18, 16}, {6, 12, 0, 14, 18, 14}, {6, 12, 0, 14, 18, 16}, {6, 12, 6, 10, 22, 12}, {6, 12, 6, 12, 22, 10}, {6, 12, 6, 14, 18, 16}, {6, 12, 6, 16, 18, 14}, {6, 12, 8, 8, 22, 12}, {6, 12, 8, 12, 18, 16}, {6, 12, 8, 22, 10, 6}, {6, 12, 8, 22, 10, 8}, {6, 12, 10, 10, 22, 10}, {6, 12, 10, 14, 18, 14}, {6, 12, 10, 22, 10, 8}, {6, 12, 12, 8, 22, 8}, {6, 12, 12, 22, 8, 8}, {6, 12, 16, 20, 6, 10}, {6, 12, 18, 12, 8, 16}, {6, 12, 18, 14, 0, 16}, {6, 12, 18, 14, 10, 14}, {6, 12, 18, 16, 6, 14}, {6, 12, 18, 18, 0, 10}, {6, 12, 18, 18, 0, 12}, {6, 12, 20, 16, 6, 10}, {6, 12, 22, 8, 8, 8}, {6, 12, 22, 8, 10, 6}, {6, 12, 22, 8, 10, 10}, {6, 12, 22, 12, 6, 10}, {6, 14, 0, 8, 18, 14}, {6, 14, 0, 8, 18, 16}, {6, 14, 0, 12, 18, 16}, {6, 14, 8, 6, 16, 18}, {6, 14, 8, 6, 20, 14}, {6, 14, 8, 8, 18, 16}, {6, 14, 8, 10, 22, 10}, {6, 14, 8, 14, 18, 14}, {6, 14, 10, 8, 22, 10}, {6, 14, 10, 12, 18, 14}, {6, 14, 14, 6, 20, 8}, {6, 14, 14, 20, 6, 8}, {6, 14, 18, 6, 16, 8}, {6, 14, 18, 10, 8, 16}, {6, 14, 18, 12, 0, 14}, {6, 14, 18, 12, 0, 16}, {6, 14, 18, 12, 6, 16}, {6, 14, 18, 12, 10, 14}, {6, 14, 18, 14, 8, 14}, {6, 14, 18, 16, 0, 10}, {6, 14, 18, 16, 0, 12}, {6, 14, 18, 16, 6, 12}, {6, 16, 0, 10, 18, 10}, {6, 16, 0, 14, 18, 10}, {6, 16, 0, 14, 18, 12}, {6, 16, 6, 8, 14, 18}, {6, 16, 6, 10, 20, 12}, {6, 16, 6, 12, 18, 14}, {6, 16, 6, 12, 20, 10}, {6, 16, 6, 14, 18, 12}, {6, 16, 6, 18, 14, 8}, {6, 16, 10, 6, 20, 12}, {6, 16, 10, 8, 18, 14}, {6, 16, 12, 6, 20, 10}, {6, 16, 18, 8, 10, 14}, {6, 16, 18, 12, 6, 14}, {6, 18, 0, 8, 18, 10}, {6, 18, 0, 8, 18, 12}, {6, 18, 0, 12, 18, 10}, {6, 18, 0, 12, 18, 12}, {6, 18, 8, 0, 14, 14}, {6, 18, 8, 0, 14, 16}, {6, 18, 8, 0, 18, 10}, {6, 18, 8, 0, 18, 12}, {6, 18, 8, 8, 14, 16}, {6, 18, 8, 10, 16, 14}, {6, 18, 10, 0, 12, 14}, {6, 18, 10, 0, 12, 16}, {6, 18, 10, 0, 16, 10}, {6, 18, 12, 0, 14, 16}, {6, 18, 12, 0, 18, 10}, {6, 18, 12, 0, 18, 12}, {6, 18, 12, 6, 16, 14}, {6, 18, 12, 8, 12, 16}, {6, 18, 12, 10, 14, 14}, {6, 18, 14, 0, 12, 14}, {6, 18, 14, 0, 12, 16}, {6, 18, 14, 0, 16, 10}, {6, 18, 14, 0, 16, 12}, {6, 18, 14, 6, 12, 16}, {6, 18, 14, 6, 16, 12}, {6, 18, 14, 8, 10, 16}, {6, 18, 14, 8, 14, 14}, {6, 18, 14, 10, 12, 14}, {6, 18, 14, 16, 6, 8}, {6, 18, 16, 6, 12, 14}, {6, 18, 16, 10, 8, 14}, {6, 20, 6, 8, 14, 14}, {6, 20, 6, 10, 16, 12}, {6, 20, 6, 12, 16, 10}, {6, 20, 6, 14, 14, 8}, {6, 20, 10, 6, 16, 12}, {6, 20, 12, 6, 16, 10}, {6, 22, 8, 8, 12, 12}, {6, 22, 8, 10, 14, 10}, {6, 22, 8, 12, 12, 8}, {6, 22, 10, 6, 12, 12}, {6, 22, 10, 8, 8, 12}, {6, 22, 10, 8, 10, 12}, {6, 22, 10, 8, 14, 10}, {6, 22, 10, 10, 12, 10}, {6, 22, 10, 12, 8, 6}, {6, 22, 10, 12, 8, 8}, {6, 22, 10, 12, 10, 8}, {6, 22, 12, 6, 12, 10}, {6, 22, 12, 8, 8, 8}, {6, 22, 12, 10, 8, 6}, {6, 22, 12, 10, 8, 10}, {8, 0, 10, 16, 10, 18}, {8, 0, 10, 16, 14, 18}, {8, 0, 10, 18, 10, 14}, {8, 0, 10, 18, 14, 14}, {8, 0, 12, 18, 14, 16}, {8, 0, 12, 20, 8, 12}, {8, 0, 12, 20, 8, 14}, {8, 0, 12, 20, 12, 12}, {8, 0, 12, 20, 12, 14}, {8, 0, 16, 18, 10, 8}, {8, 0, 16, 18, 14, 8}, {8, 0, 16, 18, 14, 12}, {8, 0, 16, 20, 8, 8}, {8, 0, 16, 20, 8, 10}, {8, 0, 16, 20, 12, 8}, {8, 0, 16, 20, 12, 10}, {8, 0, 18, 16, 10, 8}, {8, 0, 18, 16, 14, 8}, {8, 0, 18, 16, 14, 10}, {8, 0, 20, 16, 8, 8}, {8, 0, 20, 16, 8, 10}, {8, 0, 20, 16, 12, 8}, {8, 0, 20, 16, 12, 10}, {8, 6, 8, 10, 12, 22}, {8, 6, 8, 12, 8, 22}, {8, 6, 8, 22, 8, 12}, {8, 6, 8, 22, 12, 10}, {8, 6, 10, 12, 6, 22}, {8, 6, 10, 12, 10, 22}, {8, 6, 10, 16, 14, 18}, {8, 6, 10, 18, 16, 14}, {8, 6, 10, 22, 12, 10}, {8, 6, 12, 10, 6, 22}, {8, 6, 12, 10, 8, 22}, {8, 6, 12, 18, 16, 12}, {8, 6, 12, 22, 12, 8}, {8, 6, 14, 16, 18, 6}, {8, 6, 14, 18, 14, 14}, {8, 6, 14, 18, 16, 8}, {8, 6, 14, 20, 14, 6}, {8, 6, 14, 22, 10, 10}, {8, 6, 18, 14, 14, 0}, {8, 6, 18, 14, 16, 0}, {8, 6, 18, 14, 16, 8}, {8, 6, 18, 16, 14, 10}, {8, 6, 18, 18, 10, 0}, {8, 6, 18, 18, 12, 0}, {8, 6, 22, 12, 8, 12}, {8, 6, 22, 12, 12, 8}, {8, 6, 22, 14, 10, 10}, {8, 8, 6, 8, 12, 22}, {8, 8, 6, 8, 22, 12}, {8, 8, 6, 12, 10, 22}, {8, 8, 6, 12, 22, 10}, {8, 8, 8, 10, 12, 22}, {8, 8, 8, 10, 22, 12}, {8, 8, 8, 12, 10, 22}, {8, 8, 8, 12, 22, 10}, {8, 8, 8, 14, 16, 18}, {8, 8, 8, 14, 18, 16}, {8, 8, 8, 16, 14, 18}, {8, 8, 8, 16, 18, 14}, {8, 8, 8, 18, 14, 16}, {8, 8, 8, 18, 16, 14}, {8, 8, 8, 22, 10, 12}, {8, 8, 8, 22, 12, 10}, {8, 8, 10, 12, 6, 22}, {8, 8, 10, 12, 8, 22}, {8, 8, 10, 12, 22, 6}, {8, 8, 10, 12, 22, 8}, {8, 8, 10, 16, 12, 18}, {8, 8, 10, 16, 18, 12}, {8, 8, 12, 8, 6, 22}, {8, 8, 12, 8, 22, 6}, {8, 8, 12, 10, 8, 22}, {8, 8, 12, 10, 22, 8}, {8, 8, 12, 18, 10, 16}, {8, 8, 12, 18, 16, 10}, {8, 8, 12, 22, 6, 12}, {8, 8, 12, 22, 12, 6}, {8, 8, 16, 20, 0, 8}, {8, 8, 16, 20, 0, 10}, {8, 8, 16, 20, 8, 0}, {8, 8, 16, 20, 10, 0}, {8, 8, 20, 12, 0, 12}, {8, 8, 20, 12, 0, 14}, {8, 8, 20, 12, 12, 0}, {8, 8, 20, 12, 14, 0}, {8, 8, 20, 16, 0, 8}, {8, 8, 20, 16, 0, 10}, {8, 8, 20, 16, 8, 0}, {8, 8, 20, 16, 10, 0}, {8, 8, 22, 8, 6, 12}, {8, 8, 22, 8, 12, 6}, {8, 10, 0, 10, 16, 18}, {8, 10, 0, 10, 18, 14}, {8, 10, 0, 14, 16, 18}, {8, 10, 0, 14, 18, 14}, {8, 10, 6, 6, 12, 22}, {8, 10, 6, 10, 12, 22}, {8, 10, 6, 12, 22, 10}, {8, 10, 6, 14, 16, 18}, {8, 10, 6, 16, 18, 14}, {8, 10, 8, 6, 12, 22}, {8, 10, 8, 8, 12, 22}, {8, 10, 8, 12, 16, 18}, {8, 10, 8, 18, 16, 12}, {8, 10, 8, 22, 12, 6}, {8, 10, 8, 22, 12, 8}, {8, 10, 10, 10, 22, 10}, {8, 10, 10, 12, 22, 6}, {8, 10, 10, 14, 18, 14}, {8, 10, 10, 16, 18, 10}, {8, 10, 10, 18, 14, 14}, {8, 10, 10, 18, 16, 10}, {8, 10, 10, 22, 10, 10}, {8, 10, 10, 22, 12, 6}, {8, 10, 12, 6, 8, 22}, {8, 10, 12, 8, 8, 22}, {8, 10, 12, 10, 6, 22}, {8, 10, 14, 10, 20, 0}, {8, 10, 14, 18, 10, 14}, {8, 10, 14, 22, 6, 10}, {8, 10, 16, 10, 0, 18}, {8, 10, 16, 18, 0, 8}, {8, 10, 16, 20, 8, 0}, {8, 10, 18, 10, 0, 14}, {8, 10, 18, 12, 8, 16}, {8, 10, 18, 14, 10, 14}, {8, 10, 18, 16, 0, 8}, {8, 10, 18, 18, 6, 0}, {8, 10, 20, 10, 14, 0}, {8, 10, 20, 16, 8, 0}, {8, 10, 22, 8, 8, 12}, {8, 10, 22, 8, 12, 8}, {8, 10, 22, 10, 10, 10}, {8, 10, 22, 14, 6, 10}, {8, 12, 0, 8, 20, 12}, {8, 12, 0, 8, 20, 14}, {8, 12, 0, 12, 20, 12}, {8, 12, 0, 12, 20, 14}, {8, 12, 0, 14, 18, 16}, {8, 12, 6, 6, 10, 22}, {8, 12, 6, 8, 10, 22}, {8, 12, 6, 12, 22, 8}, {8, 12, 6, 16, 18, 12}, {8, 12, 8, 6, 8, 22}, {8, 12, 8, 6, 22, 12}, {8, 12, 8, 8, 10, 22}, {8, 12, 8, 10, 18, 16}, {8, 12, 8, 12, 22, 6}, {8, 12, 8, 16, 18, 10}, {8, 12, 8, 22, 8, 6}, {8, 12, 8, 22, 10, 8}, {8, 12, 10, 6, 10, 22}, {8, 12, 10, 8, 6, 22}, {8, 12, 10, 8, 8, 22}, {8, 12, 12, 6, 22, 8}, {8, 12, 12, 8, 20, 0}, {8, 12, 12, 20, 8, 0}, {8, 12, 12, 22, 6, 8}, {8, 12, 14, 8, 20, 0}, {8, 12, 16, 10, 8, 18}, {8, 12, 16, 20, 0, 8}, {8, 12, 16, 20, 0, 10}, {8, 12, 18, 18, 6, 0}, {8, 12, 20, 12, 0, 12}, {8, 12, 20, 12, 0, 14}, {8, 12, 20, 16, 0, 8}, {8, 12, 20, 16, 0, 10}, {8, 12, 22, 8, 6, 10}, {8, 12, 22, 8, 8, 10}, {8, 12, 22, 8, 10, 6}, {8, 12, 22, 8, 10, 8}, {8, 12, 22, 10, 6, 10}, {8, 12, 22, 10, 10, 6}, {8, 12, 22, 12, 6, 8}, {8, 12, 22, 12, 8, 6}, {8, 14, 6, 10, 22, 10}, {8, 14, 6, 14, 18, 14}, {8, 14, 6, 14, 20, 6}, {8, 14, 6, 16, 18, 8}, {8, 14, 6, 18, 16, 6}, {8, 14, 10, 6, 22, 10}, {8, 14, 10, 10, 18, 14}, {8, 14, 10, 20, 10, 0}, {8, 14, 12, 20, 8, 0}, {8, 14, 14, 6, 18, 0}, {8, 14, 14, 18, 6, 0}, {8, 14, 16, 6, 18, 0}, {8, 14, 16, 6, 18, 8}, {8, 14, 16, 8, 8, 18}, {8, 14, 16, 10, 0, 18}, {8, 14, 16, 10, 6, 18}, {8, 14, 16, 18, 0, 8}, {8, 14, 16, 18, 0, 10}, {8, 14, 16, 18, 6, 10}, {8, 14, 18, 8, 8, 16}, {8, 14, 18, 10, 0, 14}, {8, 14, 18, 10, 10, 14}, {8, 14, 18, 12, 0, 16}, {8, 14, 18, 14, 6, 14}, {8, 14, 18, 16, 0, 8}, {8, 14, 18, 16, 0, 12}, {8, 14, 20, 14, 6, 6}, {8, 16, 0, 8, 20, 8}, {8, 16, 0, 8, 20, 10}, {8, 16, 0, 10, 18, 8}, {8, 16, 0, 12, 20, 8}, {8, 16, 0, 12, 20, 10}, {8, 16, 0, 14, 18, 8}, {8, 16, 0, 14, 18, 12}, {8, 16, 8, 0, 20, 8}, {8, 16, 8, 0, 20, 10}, {8, 16, 8, 8, 20, 0}, {8, 16, 8, 10, 20, 0}, {8, 16, 10, 0, 10, 18}, {8, 16, 10, 0, 18, 8}, {8, 16, 10, 8, 20, 0}, {8, 16, 12, 0, 20, 8}, {8, 16, 12, 0, 20, 10}, {8, 16, 12, 8, 10, 18}, {8, 16, 14, 0, 10, 18}, {8, 16, 14, 0, 18, 8}, {8, 16, 14, 0, 18, 10}, {8, 16, 14, 6, 10, 18}, {8, 16, 14, 6, 18, 10}, {8, 16, 14, 8, 8, 18}, {8, 16, 14, 18, 6, 0}, {8, 16, 14, 18, 6, 8}, {8, 16, 18, 6, 14, 6}, {8, 16, 18, 8, 8, 14}, {8, 16, 18, 8, 10, 12}, {8, 16, 18, 10, 6, 14}, {8, 16, 18, 10, 10, 10}, {8, 16, 18, 12, 6, 12}, {8, 16, 18, 12, 8, 10}, {8, 16, 18, 14, 6, 8}, {8, 18, 0, 10, 16, 8}, {8, 18, 0, 14, 16, 8}, {8, 18, 0, 14, 16, 10}, {8, 18, 6, 10, 18, 0}, {8, 18, 6, 12, 18, 0}, {8, 18, 6, 14, 14, 0}, {8, 18, 6, 14, 16, 10}, {8, 18, 6, 16, 14, 0}, {8, 18, 6, 16, 14, 8}, {8, 18, 10, 0, 10, 14}, {8, 18, 10, 0, 16, 8}, {8, 18, 10, 6, 18, 0}, {8, 18, 10, 8, 12, 16}, {8, 18, 10, 10, 14, 14}, {8, 18, 12, 6, 18, 0}, {8, 18, 14, 0, 10, 14}, {8, 18, 14, 0, 12, 16}, {8, 18, 14, 0, 16, 8}, {8, 18, 14, 0, 16, 12}, {8, 18, 14, 6, 14, 14}, {8, 18, 14, 8, 8, 16}, {8, 18, 14, 10, 10, 14}, {8, 18, 16, 6, 10, 14}, {8, 18, 16, 6, 12, 12}, {8, 18, 16, 6, 14, 8}, {8, 18, 16, 8, 8, 14}, {8, 18, 16, 8, 12, 10}, {8, 18, 16, 10, 8, 12}, {8, 18, 16, 10, 10, 10}, {8, 18, 16, 14, 6, 6}, {8, 20, 0, 8, 16, 8}, {8, 20, 0, 8, 16, 10}, {8, 20, 0, 12, 16, 8}, {8, 20, 0, 12, 16, 10}, {8, 20, 8, 0, 12, 12}, {8, 20, 8, 0, 12, 14}, {8, 20, 8, 0, 16, 8}, {8, 20, 8, 0, 16, 10}, {8, 20, 8, 8, 16, 0}, {8, 20, 8, 10, 16, 0}, {8, 20, 8, 12, 12, 0}, {8, 20, 8, 14, 12, 0}, {8, 20, 10, 8, 16, 0}, {8, 20, 10, 14, 10, 0}, {8, 20, 12, 0, 12, 12}, {8, 20, 12, 0, 12, 14}, {8, 20, 12, 0, 16, 8}, {8, 20, 12, 0, 16, 10}, {8, 20, 14, 6, 14, 6}, {8, 22, 6, 8, 12, 12}, {8, 22, 6, 10, 14, 10}, {8, 22, 6, 12, 12, 8}, {8, 22, 8, 6, 8, 12}, {8, 22, 8, 12, 8, 6}, {8, 22, 10, 6, 14, 10}, {8, 22, 10, 8, 8, 12}, {8, 22, 10, 10, 10, 10}, {8, 22, 10, 12, 8, 8}, {8, 22, 12, 6, 8, 10}, {8, 22, 12, 6, 10, 10}, {8, 22, 12, 6, 12, 8}, {8, 22, 12, 8, 8, 10}, {8, 22, 12, 8, 12, 6}, {8, 22, 12, 10, 8, 6}, {8, 22, 12, 10, 8, 8}, {8, 22, 12, 10, 10, 6}, {10, 0, 8, 14, 10, 18}, {10, 0, 8, 14, 14, 18}, {10, 0, 8, 18, 10, 16}, {10, 0, 8, 18, 14, 16}, {10, 0, 10, 14, 8, 20}, {10, 0, 10, 14, 12, 20}, {10, 0, 10, 16, 14, 18}, {10, 0, 10, 18, 14, 16}, {10, 0, 10, 20, 8, 14}, {10, 0, 10, 20, 12, 14}, {10, 0, 16, 18, 14, 8}, {10, 0, 16, 18, 14, 10}, {10, 0, 16, 20, 8, 8}, {10, 0, 16, 20, 12, 8}, {10, 0, 18, 16, 10, 6}, {10, 0, 18, 16, 14, 6}, {10, 0, 18, 16, 14, 10}, {10, 0, 18, 18, 8, 6}, {10, 0, 18, 18, 12, 6}, {10, 0, 20, 16, 8, 8}, {10, 0, 20, 16, 12, 8}, {10, 6, 8, 10, 12, 22}, {10, 6, 8, 14, 16, 18}, {10, 6, 8, 18, 14, 16}, {10, 6, 8, 22, 6, 12}, {10, 6, 8, 22, 10, 12}, {10, 6, 12, 10, 8, 22}, {10, 6, 12, 18, 14, 14}, {10, 6, 12, 22, 10, 10}, {10, 6, 14, 18, 14, 12}, {10, 6, 14, 22, 10, 8}, {10, 6, 16, 18, 14, 8}, {10, 6, 16, 20, 12, 6}, {10, 6, 18, 12, 14, 0}, {10, 6, 18, 12, 16, 0}, {10, 6, 18, 16, 10, 0}, {10, 6, 20, 16, 12, 6}, {10, 6, 22, 8, 6, 12}, {10, 6, 22, 8, 8, 12}, {10, 6, 22, 8, 12, 8}, {10, 6, 22, 10, 8, 12}, {10, 6, 22, 10, 12, 8}, {10, 6, 22, 12, 10, 10}, {10, 6, 22, 12, 12, 6}, {10, 6, 22, 14, 10, 8}, {10, 8, 0, 10, 14, 18}, {10, 8, 0, 10, 18, 16}, {10, 8, 0, 14, 14, 18}, {10, 8, 0, 14, 18, 16}, {10, 8, 6, 6, 22, 12}, {10, 8, 6, 10, 22, 12}, {10, 8, 6, 12, 10, 22}, {10, 8, 6, 14, 18, 16}, {10, 8, 6, 16, 14, 18}, {10, 8, 8, 6, 22, 12}, {10, 8, 8, 8, 22, 12}, {10, 8, 8, 12, 18, 16}, {10, 8, 8, 18, 12, 16}, {10, 8, 8, 22, 6, 12}, {10, 8, 8, 22, 8, 12}, {10, 8, 10, 10, 10, 22}, {10, 8, 10, 12, 6, 22}, {10, 8, 10, 14, 14, 18}, {10, 8, 10, 16, 10, 18}, {10, 8, 10, 18, 10, 16}, {10, 8, 10, 18, 14, 14}, {10, 8, 10, 22, 6, 12}, {10, 8, 10, 22, 10, 10}, {10, 8, 12, 6, 22, 8}, {10, 8, 12, 8, 22, 8}, {10, 8, 12, 10, 22, 6}, {10, 8, 14, 10, 0, 20}, {10, 8, 14, 18, 14, 10}, {10, 8, 14, 22, 10, 6}, {10, 8, 16, 10, 18, 0}, {10, 8, 16, 18, 8, 0}, {10, 8, 16, 20, 0, 8}, {10, 8, 18, 10, 14, 0}, {10, 8, 18, 12, 16, 8}, {10, 8, 18, 14, 14, 10}, {10, 8, 18, 16, 8, 0}, {10, 8, 18, 18, 0, 6}, {10, 8, 20, 10, 0, 14}, {10, 8, 20, 16, 0, 8}, {10, 8, 22, 8, 8, 12}, {10, 8, 22, 8, 12, 8}, {10, 8, 22, 10, 10, 10}, {10, 8, 22, 14, 10, 6}, {10, 10, 0, 8, 14, 20}, {10, 10, 0, 8, 20, 14}, {10, 10, 0, 12, 14, 20}, {10, 10, 0, 12, 20, 14}, {10, 10, 0, 14, 16, 18}, {10, 10, 0, 14, 18, 16}, {10, 10, 8, 6, 12, 22}, {10, 10, 8, 6, 22, 12}, {10, 10, 8, 10, 10, 22}, {10, 10, 8, 10, 16, 18}, {10, 10, 8, 10, 18, 16}, {10, 10, 8, 10, 22, 10}, {10, 10, 8, 14, 14, 18}, {10, 10, 8, 14, 18, 14}, {10, 10, 10, 8, 10, 22}, {10, 10, 10, 8, 22, 10}, {10, 10, 10, 10, 8, 22}, {10, 10, 10, 10, 22, 8}, {10, 10, 10, 12, 14, 18}, {10, 10, 10, 12, 18, 14}, {10, 10, 10, 14, 12, 18}, {10, 10, 10, 14, 18, 12}, {10, 10, 10, 18, 12, 14}, {10, 10, 10, 18, 14, 12}, {10, 10, 10, 22, 8, 10}, {10, 10, 10, 22, 10, 8}, {10, 10, 12, 6, 8, 22}, {10, 10, 12, 6, 22, 8}, {10, 10, 12, 18, 10, 14}, {10, 10, 12, 18, 14, 10}, {10, 10, 12, 22, 6, 10}, {10, 10, 12, 22, 10, 6}, {10, 10, 14, 8, 0, 18}, {10, 10, 14, 8, 18, 0}, {10, 10, 14, 22, 6, 8}, {10, 10, 14, 22, 8, 6}, {10, 10, 16, 10, 8, 18}, {10, 10, 16, 10, 18, 8}, {10, 10, 16, 18, 0, 6}, {10, 10, 16, 18, 6, 0}, {10, 10, 18, 8, 0, 16}, {10, 10, 18, 8, 16, 0}, {10, 10, 18, 10, 8, 16}, {10, 10, 18, 10, 16, 8}, {10, 10, 18, 12, 10, 14}, {10, 10, 18, 12, 14, 10}, {10, 10, 22, 8, 6, 12}, {10, 10, 22, 8, 12, 6}, {10, 10, 22, 10, 8, 10}, {10, 10, 22, 10, 10, 8}, {10, 10, 22, 12, 6, 10}, {10, 10, 22, 12, 10, 6}, {10, 10, 22, 14, 6, 8}, {10, 10, 22, 14, 8, 6}, {10, 12, 6, 8, 10, 22}, {10, 12, 6, 10, 22, 10}, {10, 12, 6, 14, 18, 14}, {10, 12, 8, 22, 6, 8}, {10, 12, 8, 22, 8, 8}, {10, 12, 8, 22, 10, 6}, {10, 12, 10, 6, 22, 10}, {10, 12, 10, 8, 6, 22}, {10, 12, 10, 10, 18, 14}, {10, 12, 10, 10, 22, 6}, {10, 12, 10, 14, 18, 10}, {10, 12, 10, 22, 6, 8}, {10, 12, 12, 6, 22, 6}, {10, 12, 12, 22, 6, 6}, {10, 12, 14, 6, 18, 0}, {10, 12, 14, 10, 0, 20}, {10, 12, 14, 10, 10, 18}, {10, 12, 14, 10, 18, 10}, {10, 12, 14, 14, 14, 14}, {10, 12, 16, 6, 18, 0}, {10, 12, 16, 8, 18, 8}, {10, 12, 16, 20, 0, 8}, {10, 12, 16, 20, 6, 6}, {10, 12, 18, 8, 8, 16}, {10, 12, 18, 10, 10, 14}, {10, 12, 18, 18, 0, 6}, {10, 12, 20, 10, 0, 14}, {10, 12, 20, 16, 0, 8}, {10, 12, 20, 16, 6, 6}, {10, 14, 6, 10, 22, 8}, {10, 14, 6, 14, 18, 12}, {10, 14, 8, 0, 10, 20}, {10, 14, 8, 10, 22, 6}, {10, 14, 8, 14, 18, 10}, {10, 14, 10, 0, 8, 18}, {10, 14, 10, 6, 22, 8}, {10, 14, 10, 8, 22, 6}, {10, 14, 10, 18, 8, 0}, {10, 14, 12, 0, 10, 20}, {10, 14, 12, 10, 10, 18}, {10, 14, 12, 14, 14, 14}, {10, 14, 12, 18, 6, 0}, {10, 14, 12, 18, 10, 10}, {10, 14, 14, 0, 8, 18}, {10, 14, 14, 8, 0, 18}, {10, 14, 14, 8, 10, 18}, {10, 14, 14, 8, 18, 10}, {10, 14, 14, 10, 8, 18}, {10, 14, 14, 12, 14, 14}, {10, 14, 14, 14, 12, 14}, {10, 14, 14, 18, 8, 10}, {10, 14, 16, 6, 8, 18}, {10, 14, 16, 10, 0, 18}, {10, 14, 16, 18, 0, 6}, {10, 14, 16, 18, 0, 10}, {10, 14, 18, 8, 0, 16}, {10, 14, 18, 8, 6, 16}, {10, 14, 18, 10, 0, 16}, {10, 14, 18, 10, 8, 14}, {10, 14, 18, 10, 10, 12}, {10, 14, 18, 12, 6, 14}, {10, 14, 18, 12, 10, 10}, {10, 14, 18, 14, 6, 12}, {10, 14, 18, 14, 8, 10}, {10, 14, 18, 16, 0, 8}, {10, 14, 18, 16, 0, 10}, {10, 14, 18, 16, 6, 8}, {10, 16, 0, 8, 20, 8}, {10, 16, 0, 12, 20, 8}, {10, 16, 0, 14, 18, 8}, {10, 16, 0, 14, 18, 10}, {10, 16, 6, 12, 20, 6}, {10, 16, 6, 14, 18, 8}, {10, 16, 8, 0, 20, 8}, {10, 16, 8, 8, 18, 0}, {10, 16, 8, 18, 10, 0}, {10, 16, 10, 0, 18, 6}, {10, 16, 10, 6, 18, 0}, {10, 16, 10, 8, 10, 18}, {10, 16, 10, 18, 10, 8}, {10, 16, 12, 0, 20, 8}, {10, 16, 12, 6, 20, 6}, {10, 16, 12, 18, 6, 0}, {10, 16, 12, 18, 8, 8}, {10, 16, 14, 0, 10, 18}, {10, 16, 14, 0, 18, 6}, {10, 16, 14, 0, 18, 10}, {10, 16, 14, 8, 6, 18}, {10, 18, 0, 8, 18, 6}, {10, 18, 0, 10, 16, 6}, {10, 18, 0, 12, 18, 6}, {10, 18, 0, 14, 16, 6}, {10, 18, 0, 14, 16, 10}, {10, 18, 6, 10, 16, 0}, {10, 18, 6, 14, 12, 0}, {10, 18, 6, 16, 12, 0}, {10, 18, 8, 0, 18, 6}, {10, 18, 8, 8, 16, 0}, {10, 18, 8, 14, 10, 0}, {10, 18, 8, 14, 14, 10}, {10, 18, 8, 16, 12, 8}, {10, 18, 10, 0, 8, 16}, {10, 18, 10, 8, 10, 16}, {10, 18, 10, 10, 12, 14}, {10, 18, 10, 14, 12, 10}, {10, 18, 10, 16, 8, 0}, {10, 18, 10, 16, 10, 8}, {10, 18, 12, 0, 18, 6}, {10, 18, 12, 8, 8, 16}, {10, 18, 12, 10, 10, 14}, {10, 18, 14, 0, 8, 16}, {10, 18, 14, 0, 10, 16}, {10, 18, 14, 0, 16, 8}, {10, 18, 14, 0, 16, 10}, {10, 18, 14, 6, 8, 16}, {10, 18, 14, 6, 12, 14}, {10, 18, 14, 6, 14, 12}, {10, 18, 14, 6, 16, 8}, {10, 18, 14, 8, 10, 14}, {10, 18, 14, 8, 14, 10}, {10, 18, 14, 10, 10, 12}, {10, 18, 14, 10, 12, 10}, {10, 20, 0, 8, 16, 8}, {10, 20, 0, 12, 16, 8}, {10, 20, 6, 12, 16, 6}, {10, 20, 8, 0, 10, 14}, {10, 20, 8, 0, 16, 8}, {10, 20, 12, 0, 10, 14}, {10, 20, 12, 0, 16, 8}, {10, 20, 12, 6, 16, 6}, {10, 22, 6, 6, 8, 12}, {10, 22, 6, 8, 8, 12}, {10, 22, 6, 8, 10, 12}, {10, 22, 6, 10, 12, 10}, {10, 22, 6, 10, 14, 8}, {10, 22, 6, 12, 8, 8}, {10, 22, 6, 12, 10, 8}, {10, 22, 6, 12, 12, 6}, {10, 22, 8, 8, 8, 12}, {10, 22, 8, 10, 10, 10}, {10, 22, 8, 10, 14, 6}, {10, 22, 8, 12, 8, 8}, {10, 22, 10, 6, 8, 12}, {10, 22, 10, 6, 12, 10}, {10, 22, 10, 6, 14, 8}, {10, 22, 10, 8, 10, 10}, {10, 22, 10, 8, 14, 6}, {10, 22, 10, 10, 10, 8}, {10, 22, 10, 10, 12, 6}, {10, 22, 10, 12, 8, 6}, {12, 0, 6, 14, 10, 18}, {12, 0, 6, 14, 14, 18}, {12, 0, 6, 16, 10, 18}, {12, 0, 6, 16, 14, 18}, {12, 0, 8, 12, 8, 20}, {12, 0, 8, 12, 12, 20}, {12, 0, 8, 14, 8, 20}, {12, 0, 8, 14, 12, 20}, {12, 0, 8, 16, 14, 18}, {12, 0, 18, 16, 14, 6}, {12, 0, 18, 16, 14, 8}, {12, 0, 18, 18, 8, 6}, {12, 0, 18, 18, 12, 6}, {12, 0, 20, 12, 8, 8}, {12, 0, 20, 12, 12, 8}, {12, 6, 0, 10, 14, 18}, {12, 6, 0, 10, 16, 18}, {12, 6, 0, 14, 14, 18}, {12, 6, 0, 14, 16, 18}, {12, 6, 6, 10, 12, 22}, {12, 6, 6, 12, 10, 22}, {12, 6, 6, 14, 16, 18}, {12, 6, 6, 16, 14, 18}, {12, 6, 8, 8, 12, 22}, {12, 6, 8, 12, 16, 18}, {12, 6, 8, 22, 6, 10}, {12, 6, 8, 22, 8, 10}, {12, 6, 10, 10, 10, 22}, {12, 6, 10, 14, 14, 18}, {12, 6, 10, 22, 8, 10}, {12, 6, 12, 8, 8, 22}, {12, 6, 12, 22, 8, 8}, {12, 6, 16, 20, 10, 6}, {12, 6, 18, 12, 16, 8}, {12, 6, 18, 14, 14, 10}, {12, 6, 18, 14, 16, 0}, {12, 6, 18, 16, 14, 6}, {12, 6, 18, 18, 10, 0}, {12, 6, 18, 18, 12, 0}, {12, 6, 20, 16, 10, 6}, {12, 6, 22, 8, 6, 10}, {12, 6, 22, 8, 8, 8}, {12, 6, 22, 8, 10, 10}, {12, 6, 22, 12, 10, 6}, {12, 8, 0, 8, 12, 20}, {12, 8, 0, 8, 14, 20}, {12, 8, 0, 12, 12, 20}, {12, 8, 0, 12, 14, 20}, {12, 8, 0, 14, 16, 18}, {12, 8, 6, 6, 22, 10}, {12, 8, 6, 8, 22, 10}, {12, 8, 6, 12, 8, 22}, {12, 8, 6, 16, 12, 18}, {12, 8, 8, 6, 12, 22}, {12, 8, 8, 6, 22, 8}, {12, 8, 8, 8, 22, 10}, {12, 8, 8, 10, 16, 18}, {12, 8, 8, 12, 6, 22}, {12, 8, 8, 16, 10, 18}, {12, 8, 8, 22, 6, 8}, {12, 8, 8, 22, 8, 10}, {12, 8, 10, 6, 22, 10}, {12, 8, 10, 8, 22, 6}, {12, 8, 10, 8, 22, 8}, {12, 8, 12, 6, 8, 22}, {12, 8, 12, 8, 0, 20}, {12, 8, 12, 20, 0, 8}, {12, 8, 12, 22, 8, 6}, {12, 8, 14, 8, 0, 20}, {12, 8, 16, 10, 18, 8}, {12, 8, 16, 20, 8, 0}, {12, 8, 16, 20, 10, 0}, {12, 8, 18, 18, 0, 6}, {12, 8, 20, 12, 12, 0}, {12, 8, 20, 12, 14, 0}, {12, 8, 20, 16, 8, 0}, {12, 8, 20, 16, 10, 0}, {12, 8, 22, 8, 6, 10}, {12, 8, 22, 8, 8, 10}, {12, 8, 22, 8, 10, 6}, {12, 8, 22, 8, 10, 8}, {12, 8, 22, 10, 6, 10}, {12, 8, 22, 10, 10, 6}, {12, 8, 22, 12, 6, 8}, {12, 8, 22, 12, 8, 6}, {12, 10, 6, 8, 22, 10}, {12, 10, 6, 10, 10, 22}, {12, 10, 6, 14, 14, 18}, {12, 10, 8, 22, 6, 10}, {12, 10, 8, 22, 8, 6}, {12, 10, 8, 22, 8, 8}, {12, 10, 10, 6, 10, 22}, {12, 10, 10, 8, 22, 6}, {12, 10, 10, 10, 6, 22}, {12, 10, 10, 10, 14, 18}, {12, 10, 10, 14, 10, 18}, {12, 10, 10, 22, 8, 6}, {12, 10, 12, 6, 6, 22}, {12, 10, 12, 22, 6, 6}, {12, 10, 14, 6, 0, 18}, {12, 10, 14, 10, 10, 18}, {12, 10, 14, 10, 18, 10}, {12, 10, 14, 10, 20, 0}, {12, 10, 14, 14, 14, 14}, {12, 10, 16, 6, 0, 18}, {12, 10, 16, 8, 8, 18}, {12, 10, 16, 20, 6, 6}, {12, 10, 16, 20, 8, 0}, {12, 10, 18, 8, 16, 8}, {12, 10, 18, 10, 14, 10}, {12, 10, 18, 18, 6, 0}, {12, 10, 20, 10, 14, 0}, {12, 10, 20, 16, 6, 6}, {12, 10, 20, 16, 8, 0}, {12, 12, 6, 8, 8, 22}, {12, 12, 6, 8, 22, 8}, {12, 12, 8, 0, 8, 20}, {12, 12, 8, 0, 20, 8}, {12, 12, 8, 8, 6, 22}, {12, 12, 8, 8, 22, 6}, {12, 12, 10, 6, 6, 22}, {12, 12, 10, 6, 22, 6}, {12, 12, 12, 0, 8, 20}, {12, 12, 12, 0, 20, 8}, {12, 12, 12, 8, 0, 20}, {12, 12, 12, 8, 20, 0}, {12, 12, 12, 20, 0, 8}, {12, 12, 12, 20, 8, 0}, {12, 12, 14, 8, 0, 20}, {12, 12, 14, 8, 20, 0}, {12, 12, 16, 6, 8, 18}, {12, 12, 16, 6, 18, 8}, {12, 12, 18, 18, 0, 6}, {12, 12, 18, 18, 6, 0}, {12, 14, 8, 0, 8, 20}, {12, 14, 10, 0, 6, 18}, {12, 14, 10, 10, 10, 18}, {12, 14, 10, 14, 14, 14}, {12, 14, 10, 18, 10, 10}, {12, 14, 10, 20, 10, 0}, {12, 14, 12, 0, 8, 20}, {12, 14, 12, 20, 8, 0}, {12, 14, 14, 0, 6, 18}, {12, 14, 14, 6, 0, 18}, {12, 14, 14, 6, 10, 18}, {12, 14, 14, 6, 18, 10}, {12, 14, 14, 10, 6, 18}, {12, 14, 14, 10, 14, 14}, {12, 14, 14, 14, 10, 14}, {12, 14, 14, 18, 6, 10}, {12, 14, 16, 6, 0, 18}, {12, 14, 16, 6, 6, 18}, {12, 14, 16, 6, 18, 0}, {12, 14, 16, 8, 0, 18}, {12, 14, 16, 18, 0, 6}, {12, 14, 16, 18, 0, 8}, {12, 14, 16, 18, 6, 6}, {12, 16, 6, 10, 20, 6}, {12, 16, 8, 8, 20, 0}, {12, 16, 8, 10, 20, 0}, {12, 16, 8, 18, 10, 8}, {12, 16, 10, 0, 6, 18}, {12, 16, 10, 6, 20, 6}, {12, 16, 10, 8, 8, 18}, {12, 16, 10, 8, 20, 0}, {12, 16, 12, 8, 6, 18}, {12, 16, 12, 18, 6, 8}, {12, 16, 14, 0, 6, 18}, {12, 16, 14, 0, 8, 18}, {12, 16, 14, 0, 18, 6}, {12, 16, 14, 0, 18, 8}, {12, 16, 14, 6, 6, 18}, {12, 16, 14, 6, 18, 6}, {12, 16, 14, 18, 6, 0}, {12, 18, 0, 8, 18, 6}, {12, 18, 0, 12, 18, 6}, {12, 18, 0, 14, 16, 6}, {12, 18, 0, 14, 16, 8}, {12, 18, 6, 10, 18, 0}, {12, 18, 6, 12, 18, 0}, {12, 18, 6, 14, 14, 10}, {12, 18, 6, 14, 16, 6}, {12, 18, 6, 16, 12, 8}, {12, 18, 6, 16, 14, 0}, {12, 18, 8, 0, 18, 6}, {12, 18, 10, 6, 18, 0}, {12, 18, 10, 14, 10, 10}, {12, 18, 10, 16, 8, 8}, {12, 18, 12, 0, 18, 6}, {12, 18, 12, 6, 18, 0}, {12, 20, 0, 8, 12, 8}, {12, 20, 0, 12, 12, 8}, {12, 20, 6, 10, 16, 6}, {12, 20, 8, 8, 16, 0}, {12, 20, 8, 10, 16, 0}, {12, 20, 8, 12, 12, 0}, {12, 20, 8, 14, 12, 0}, {12, 20, 10, 6, 16, 6}, {12, 20, 10, 8, 16, 0}, {12, 20, 10, 14, 10, 0}, {12, 22, 6, 6, 8, 10}, {12, 22, 6, 8, 8, 8}, {12, 22, 6, 10, 8, 10}, {12, 22, 6, 10, 12, 6}, {12, 22, 8, 6, 8, 10}, {12, 22, 8, 6, 10, 10}, {12, 22, 8, 6, 12, 8}, {12, 22, 8, 8, 8, 10}, {12, 22, 8, 8, 12, 6}, {12, 22, 8, 10, 8, 6}, {12, 22, 8, 10, 8, 8}, {12, 22, 8, 10, 10, 6}, {14, 0, 6, 14, 8, 18}, {14, 0, 6, 16, 8, 18}, {14, 0, 6, 16, 12, 18}, {14, 0, 18, 10, 10, 8}, {14, 0, 18, 10, 14, 8}, {14, 0, 18, 12, 10, 6}, {14, 0, 18, 12, 14, 6}, {14, 0, 18, 14, 8, 6}, {14, 0, 20, 10, 8, 10}, {14, 0, 20, 10, 12, 10}, {14, 0, 20, 12, 8, 8}, {14, 0, 20, 12, 12, 8}, {14, 6, 0, 8, 14, 18}, {14, 6, 0, 8, 16, 18}, {14, 6, 0, 12, 16, 18}, {14, 6, 8, 6, 14, 20}, {14, 6, 8, 6, 18, 16}, {14, 6, 8, 8, 16, 18}, {14, 6, 8, 10, 10, 22}, {14, 6, 8, 14, 14, 18}, {14, 6, 10, 8, 10, 22}, {14, 6, 10, 12, 14, 18}, {14, 6, 14, 6, 8, 20}, {14, 6, 14, 20, 8, 6}, {14, 6, 18, 6, 8, 16}, {14, 6, 18, 10, 16, 8}, {14, 6, 18, 12, 14, 0}, {14, 6, 18, 12, 14, 10}, {14, 6, 18, 12, 16, 0}, {14, 6, 18, 12, 16, 6}, {14, 6, 18, 14, 14, 8}, {14, 6, 18, 16, 10, 0}, {14, 6, 18, 16, 12, 0}, {14, 6, 18, 16, 12, 6}, {14, 8, 6, 10, 10, 22}, {14, 8, 6, 14, 6, 20}, {14, 8, 6, 14, 14, 18}, {14, 8, 6, 16, 8, 18}, {14, 8, 6, 18, 6, 16}, {14, 8, 10, 6, 10, 22}, {14, 8, 10, 10, 14, 18}, {14, 8, 10, 20, 0, 10}, {14, 8, 12, 20, 0, 8}, {14, 8, 14, 6, 0, 18}, {14, 8, 14, 18, 0, 6}, {14, 8, 16, 6, 0, 18}, {14, 8, 16, 6, 8, 18}, {14, 8, 16, 8, 18, 8}, {14, 8, 16, 10, 18, 0}, {14, 8, 16, 10, 18, 6}, {14, 8, 16, 18, 8, 0}, {14, 8, 16, 18, 10, 0}, {14, 8, 16, 18, 10, 6}, {14, 8, 18, 8, 16, 8}, {14, 8, 18, 10, 14, 0}, {14, 8, 18, 10, 14, 10}, {14, 8, 18, 12, 16, 0}, {14, 8, 18, 14, 14, 6}, {14, 8, 18, 16, 8, 0}, {14, 8, 18, 16, 12, 0}, {14, 8, 20, 14, 6, 6}, {14, 10, 6, 10, 8, 22}, {14, 10, 6, 14, 12, 18}, {14, 10, 8, 0, 20, 10}, {14, 10, 8, 10, 6, 22}, {14, 10, 8, 14, 10, 18}, {14, 10, 10, 0, 18, 8}, {14, 10, 10, 6, 8, 22}, {14, 10, 10, 8, 6, 22}, {14, 10, 10, 18, 0, 8}, {14, 10, 12, 0, 20, 10}, {14, 10, 12, 10, 18, 10}, {14, 10, 12, 14, 14, 14}, {14, 10, 12, 18, 0, 6}, {14, 10, 12, 18, 10, 10}, {14, 10, 14, 0, 18, 8}, {14, 10, 14, 8, 10, 18}, {14, 10, 14, 8, 18, 0}, {14, 10, 14, 8, 18, 10}, {14, 10, 14, 10, 18, 8}, {14, 10, 14, 12, 14, 14}, {14, 10, 14, 14, 14, 12}, {14, 10, 14, 18, 10, 8}, {14, 10, 16, 6, 18, 8}, {14, 10, 16, 10, 18, 0}, {14, 10, 16, 18, 6, 0}, {14, 10, 16, 18, 10, 0}, {14, 10, 18, 8, 16, 0}, {14, 10, 18, 8, 16, 6}, {14, 10, 18, 10, 12, 10}, {14, 10, 18, 10, 14, 8}, {14, 10, 18, 10, 16, 0}, {14, 10, 18, 12, 10, 10}, {14, 10, 18, 12, 14, 6}, {14, 10, 18, 14, 10, 8}, {14, 10, 18, 14, 12, 6}, {14, 10, 18, 16, 8, 0}, {14, 10, 18, 16, 8, 6}, {14, 10, 18, 16, 10, 0}, {14, 12, 8, 0, 20, 8}, {14, 12, 10, 0, 18, 6}, {14, 12, 10, 10, 18, 10}, {14, 12, 10, 14, 14, 14}, {14, 12, 10, 18, 10, 10}, {14, 12, 10, 20, 0, 10}, {14, 12, 12, 0, 20, 8}, {14, 12, 12, 20, 0, 8}, {14, 12, 14, 0, 18, 6}, {14, 12, 14, 6, 10, 18}, {14, 12, 14, 6, 18, 0}, {14, 12, 14, 6, 18, 10}, {14, 12, 14, 10, 14, 14}, {14, 12, 14, 10, 18, 6}, {14, 12, 14, 14, 14, 10}, {14, 12, 14, 18, 10, 6}, {14, 12, 16, 6, 0, 18}, {14, 12, 16, 6, 18, 0}, {14, 12, 16, 6, 18, 6}, {14, 12, 16, 8, 18, 0}, {14, 12, 16, 18, 6, 0}, {14, 12, 16, 18, 6, 6}, {14, 12, 16, 18, 8, 0}, {14, 14, 6, 8, 6, 20}, {14, 14, 6, 8, 20, 6}, {14, 14, 8, 0, 6, 18}, {14, 14, 8, 0, 18, 6}, {14, 14, 10, 10, 8, 18}, {14, 14, 10, 10, 18, 8}, {14, 14, 10, 14, 12, 14}, {14, 14, 10, 14, 14, 12}, {14, 14, 10, 18, 0, 8}, {14, 14, 10, 18, 8, 0}, {14, 14, 10, 18, 8, 10}, {14, 14, 10, 18, 10, 8}, {14, 14, 12, 10, 6, 18}, {14, 14, 12, 10, 18, 6}, {14, 14, 12, 14, 10, 14}, {14, 14, 12, 14, 14, 10}, {14, 14, 12, 18, 0, 6}, {14, 14, 12, 18, 6, 0}, {14, 14, 12, 18, 6, 10}, {14, 14, 12, 18, 10, 6}, {14, 14, 14, 6, 8, 18}, {14, 14, 14, 6, 18, 8}, {14, 14, 14, 8, 6, 18}, {14, 14, 14, 8, 18, 6}, {14, 14, 14, 10, 12, 14}, {14, 14, 14, 10, 14, 12}, {14, 14, 14, 12, 10, 14}, {14, 14, 14, 12, 14, 10}, {14, 14, 14, 14, 10, 12}, {14, 14, 14, 14, 12, 10}, {14, 14, 14, 18, 6, 8}, {14, 14, 14, 18, 8, 6}, {14, 16, 8, 0, 6, 18}, {14, 16, 8, 8, 6, 18}, {14, 16, 8, 8, 18, 0}, {14, 16, 8, 10, 18, 0}, {14, 16, 8, 10, 18, 6}, {14, 16, 8, 18, 8, 8}, {14, 16, 8, 18, 10, 0}, {14, 16, 8, 18, 10, 6}, {14, 16, 10, 6, 18, 0}, {14, 16, 10, 10, 18, 0}, {14, 16, 10, 18, 6, 8}, {14, 16, 10, 18, 10, 0}, {14, 16, 12, 0, 6, 18}, {14, 16, 12, 6, 18, 0}, {14, 16, 12, 6, 18, 6}, {14, 16, 12, 8, 18, 0}, {14, 16, 12, 18, 6, 0}, {14, 16, 12, 18, 6, 6}, {14, 16, 12, 18, 8, 0}, {14, 18, 0, 8, 14, 6}, {14, 18, 0, 10, 10, 8}, {14, 18, 0, 10, 12, 6}, {14, 18, 0, 14, 10, 8}, {14, 18, 0, 14, 12, 6}, {14, 18, 6, 8, 6, 16}, {14, 18, 6, 10, 16, 0}, {14, 18, 6, 12, 16, 0}, {14, 18, 6, 12, 16, 6}, {14, 18, 6, 14, 12, 0}, {14, 18, 6, 14, 12, 10}, {14, 18, 6, 14, 14, 8}, {14, 18, 6, 16, 10, 8}, {14, 18, 6, 16, 12, 0}, {14, 18, 6, 16, 12, 6}, {14, 18, 8, 8, 16, 0}, {14, 18, 8, 12, 16, 0}, {14, 18, 8, 14, 10, 0}, {14, 18, 8, 14, 10, 10}, {14, 18, 8, 14, 14, 6}, {14, 18, 8, 16, 8, 8}, {14, 18, 8, 16, 12, 0}, {14, 18, 10, 8, 16, 0}, {14, 18, 10, 8, 16, 6}, {14, 18, 10, 10, 12, 10}, {14, 18, 10, 10, 14, 8}, {14, 18, 10, 10, 16, 0}, {14, 18, 10, 12, 10, 10}, {14, 18, 10, 12, 14, 6}, {14, 18, 10, 14, 10, 8}, {14, 18, 10, 14, 12, 6}, {14, 18, 10, 16, 8, 0}, {14, 18, 10, 16, 8, 6}, {14, 18, 10, 16, 10, 0}, {14, 20, 0, 8, 10, 10}, {14, 20, 0, 8, 12, 8}, {14, 20, 0, 12, 10, 10}, {14, 20, 0, 12, 12, 8}, {14, 20, 8, 6, 14, 6}, {16, 0, 6, 10, 10, 18}, {16, 0, 6, 10, 14, 18}, {16, 0, 6, 12, 14, 18}, {16, 0, 8, 8, 8, 20}, {16, 0, 8, 8, 10, 18}, {16, 0, 8, 8, 12, 20}, {16, 0, 8, 8, 14, 18}, {16, 0, 8, 10, 8, 20}, {16, 0, 8, 10, 12, 20}, {16, 0, 8, 12, 14, 18}, {16, 0, 10, 8, 8, 20}, {16, 0, 10, 8, 12, 20}, {16, 0, 10, 8, 14, 18}, {16, 0, 10, 10, 14, 18}, {16, 0, 18, 8, 10, 10}, {16, 0, 18, 8, 14, 10}, {16, 0, 18, 10, 14, 10}, {16, 0, 18, 12, 10, 6}, {16, 0, 18, 12, 14, 6}, {16, 0, 18, 12, 14, 8}, {16, 0, 18, 14, 8, 6}, {16, 0, 18, 14, 12, 6}, {16, 6, 0, 10, 10, 18}, {16, 6, 0, 14, 10, 18}, {16, 6, 0, 14, 12, 18}, {16, 6, 6, 8, 18, 14}, {16, 6, 6, 10, 12, 20}, {16, 6, 6, 12, 10, 20}, {16, 6, 6, 12, 14, 18}, {16, 6, 6, 14, 12, 18}, {16, 6, 6, 18, 8, 14}, {16, 6, 10, 6, 12, 20}, {16, 6, 10, 8, 14, 18}, {16, 6, 12, 6, 10, 20}, {16, 6, 18, 8, 14, 10}, {16, 6, 18, 12, 14, 6}, {16, 8, 0, 8, 8, 20}, {16, 8, 0, 8, 10, 20}, {16, 8, 0, 10, 8, 18}, {16, 8, 0, 12, 8, 20}, {16, 8, 0, 12, 10, 20}, {16, 8, 0, 14, 8, 18}, {16, 8, 0, 14, 12, 18}, {16, 8, 8, 0, 8, 20}, {16, 8, 8, 0, 10, 20}, {16, 8, 8, 8, 0, 20}, {16, 8, 8, 10, 0, 20}, {16, 8, 10, 0, 8, 18}, {16, 8, 10, 0, 18, 10}, {16, 8, 10, 8, 0, 20}, {16, 8, 12, 0, 8, 20}, {16, 8, 12, 0, 10, 20}, {16, 8, 12, 8, 18, 10}, {16, 8, 14, 0, 8, 18}, {16, 8, 14, 0, 10, 18}, {16, 8, 14, 0, 18, 10}, {16, 8, 14, 6, 10, 18}, {16, 8, 14, 6, 18, 10}, {16, 8, 14, 8, 18, 8}, {16, 8, 14, 18, 0, 6}, {16, 8, 14, 18, 8, 6}, {16, 8, 18, 6, 6, 14}, {16, 8, 18, 8, 12, 10}, {16, 8, 18, 8, 14, 8}, {16, 8, 18, 10, 10, 10}, {16, 8, 18, 10, 14, 6}, {16, 8, 18, 12, 10, 8}, {16, 8, 18, 12, 12, 6}, {16, 8, 18, 14, 8, 6}, {16, 10, 0, 8, 8, 20}, {16, 10, 0, 12, 8, 20}, {16, 10, 0, 14, 8, 18}, {16, 10, 0, 14, 10, 18}, {16, 10, 6, 12, 6, 20}, {16, 10, 6, 14, 8, 18}, {16, 10, 8, 0, 8, 20}, {16, 10, 8, 8, 0, 18}, {16, 10, 8, 18, 0, 10}, {16, 10, 10, 0, 6, 18}, {16, 10, 10, 6, 0, 18}, {16, 10, 10, 8, 18, 10}, {16, 10, 10, 18, 8, 10}, {16, 10, 12, 0, 8, 20}, {16, 10, 12, 6, 6, 20}, {16, 10, 12, 18, 0, 6}, {16, 10, 12, 18, 8, 8}, {16, 10, 14, 0, 6, 18}, {16, 10, 14, 0, 10, 18}, {16, 10, 14, 0, 18, 10}, {16, 10, 14, 8, 18, 6}, {16, 12, 6, 10, 6, 20}, {16, 12, 8, 8, 0, 20}, {16, 12, 8, 10, 0, 20}, {16, 12, 8, 18, 8, 10}, {16, 12, 10, 0, 18, 6}, {16, 12, 10, 6, 6, 20}, {16, 12, 10, 8, 0, 20}, {16, 12, 10, 8, 18, 8}, {16, 12, 12, 8, 18, 6}, {16, 12, 12, 18, 8, 6}, {16, 12, 14, 0, 6, 18}, {16, 12, 14, 0, 8, 18}, {16, 12, 14, 0, 18, 6}, {16, 12, 14, 0, 18, 8}, {16, 12, 14, 6, 6, 18}, {16, 12, 14, 6, 18, 6}, {16, 12, 14, 18, 0, 6}, {16, 14, 8, 0, 18, 6}, {16, 14, 8, 8, 0, 18}, {16, 14, 8, 8, 18, 6}, {16, 14, 8, 10, 0, 18}, {16, 14, 8, 10, 6, 18}, {16, 14, 8, 18, 0, 10}, {16, 14, 8, 18, 6, 10}, {16, 14, 8, 18, 8, 8}, {16, 14, 10, 6, 0, 18}, {16, 14, 10, 10, 0, 18}, {16, 14, 10, 18, 0, 10}, {16, 14, 10, 18, 8, 6}, {16, 14, 12, 0, 18, 6}, {16, 14, 12, 6, 0, 18}, {16, 14, 12, 6, 6, 18}, {16, 14, 12, 8, 0, 18}, {16, 14, 12, 18, 0, 6}, {16, 14, 12, 18, 0, 8}, {16, 14, 12, 18, 6, 6}, {16, 18, 0, 8, 14, 6}, {16, 18, 0, 10, 8, 10}, {16, 18, 0, 10, 12, 6}, {16, 18, 0, 12, 14, 6}, {16, 18, 0, 14, 8, 10}, {16, 18, 0, 14, 10, 10}, {16, 18, 0, 14, 12, 6}, {16, 18, 0, 14, 12, 8}, {16, 18, 6, 14, 8, 10}, {16, 18, 6, 14, 12, 6}, {16, 18, 8, 6, 6, 14}, {16, 18, 8, 8, 14, 6}, {16, 18, 8, 10, 10, 10}, {16, 18, 8, 10, 12, 8}, {16, 18, 8, 12, 8, 10}, {16, 18, 8, 12, 12, 6}, {16, 18, 8, 14, 8, 8}, {16, 18, 8, 14, 10, 6}, {18, 0, 6, 10, 8, 18}, {18, 0, 6, 10, 12, 18}, {18, 0, 6, 12, 8, 18}, {18, 0, 6, 12, 12, 18}, {18, 0, 8, 8, 10, 16}, {18, 0, 8, 8, 14, 16}, {18, 0, 8, 10, 14, 16}, {18, 0, 10, 6, 8, 18}, {18, 0, 10, 6, 10, 16}, {18, 0, 10, 6, 12, 18}, {18, 0, 10, 6, 14, 16}, {18, 0, 10, 10, 14, 16}, {18, 0, 12, 6, 8, 18}, {18, 0, 12, 6, 12, 18}, {18, 0, 12, 6, 14, 16}, {18, 0, 12, 8, 14, 16}, {18, 0, 14, 6, 8, 14}, {18, 0, 14, 6, 10, 12}, {18, 0, 14, 6, 14, 12}, {18, 0, 14, 8, 10, 10}, {18, 0, 14, 8, 14, 10}, {18, 0, 16, 6, 8, 14}, {18, 0, 16, 6, 10, 12}, {18, 0, 16, 6, 12, 14}, {18, 0, 16, 6, 14, 12}, {18, 0, 16, 8, 14, 12}, {18, 0, 16, 10, 10, 8}, {18, 0, 16, 10, 14, 8}, {18, 0, 16, 10, 14, 10}, {18, 6, 0, 8, 10, 18}, {18, 6, 0, 8, 12, 18}, {18, 6, 0, 12, 10, 18}, {18, 6, 0, 12, 12, 18}, {18, 6, 8, 0, 10, 18}, {18, 6, 8, 0, 12, 18}, {18, 6, 8, 0, 14, 14}, {18, 6, 8, 0, 16, 14}, {18, 6, 8, 8, 16, 14}, {18, 6, 8, 10, 14, 16}, {18, 6, 10, 0, 10, 16}, {18, 6, 10, 0, 14, 12}, {18, 6, 10, 0, 16, 12}, {18, 6, 12, 0, 10, 18}, {18, 6, 12, 0, 12, 18}, {18, 6, 12, 0, 16, 14}, {18, 6, 12, 6, 14, 16}, {18, 6, 12, 8, 16, 12}, {18, 6, 12, 10, 14, 14}, {18, 6, 14, 0, 10, 16}, {18, 6, 14, 0, 12, 16}, {18, 6, 14, 0, 14, 12}, {18, 6, 14, 0, 16, 12}, {18, 6, 14, 6, 12, 16}, {18, 6, 14, 6, 16, 12}, {18, 6, 14, 8, 14, 14}, {18, 6, 14, 8, 16, 10}, {18, 6, 14, 10, 14, 12}, {18, 6, 14, 16, 8, 6}, {18, 6, 16, 6, 14, 12}, {18, 6, 16, 10, 14, 8}, {18, 8, 0, 10, 8, 16}, {18, 8, 0, 14, 8, 16}, {18, 8, 0, 14, 10, 16}, {18, 8, 6, 10, 0, 18}, {18, 8, 6, 12, 0, 18}, {18, 8, 6, 14, 0, 14}, {18, 8, 6, 14, 10, 16}, {18, 8, 6, 16, 0, 14}, {18, 8, 6, 16, 8, 14}, {18, 8, 10, 0, 8, 16}, {18, 8, 10, 0, 14, 10}, {18, 8, 10, 6, 0, 18}, {18, 8, 10, 8, 16, 12}, {18, 8, 10, 10, 14, 14}, {18, 8, 12, 6, 0, 18}, {18, 8, 14, 0, 8, 16}, {18, 8, 14, 0, 12, 16}, {18, 8, 14, 0, 14, 10}, {18, 8, 14, 0, 16, 12}, {18, 8, 14, 6, 14, 14}, {18, 8, 14, 8, 16, 8}, {18, 8, 14, 10, 14, 10}, {18, 8, 16, 6, 8, 14}, {18, 8, 16, 6, 12, 12}, {18, 8, 16, 6, 14, 10}, {18, 8, 16, 8, 10, 12}, {18, 8, 16, 8, 14, 8}, {18, 8, 16, 10, 10, 10}, {18, 8, 16, 10, 12, 8}, {18, 8, 16, 14, 6, 6}, {18, 10, 0, 8, 6, 18}, {18, 10, 0, 10, 6, 16}, {18, 10, 0, 12, 6, 18}, {18, 10, 0, 14, 6, 16}, {18, 10, 0, 14, 10, 16}, {18, 10, 6, 10, 0, 16}, {18, 10, 6, 14, 0, 12}, {18, 10, 6, 16, 0, 12}, {18, 10, 8, 0, 6, 18}, {18, 10, 8, 8, 0, 16}, {18, 10, 8, 14, 0, 10}, {18, 10, 8, 14, 10, 14}, {18, 10, 8, 16, 8, 12}, {18, 10, 10, 0, 16, 8}, {18, 10, 10, 8, 16, 10}, {18, 10, 10, 10, 14, 12}, {18, 10, 10, 14, 10, 12}, {18, 10, 10, 16, 0, 8}, {18, 10, 10, 16, 8, 10}, {18, 10, 12, 0, 6, 18}, {18, 10, 12, 8, 16, 8}, {18, 10, 12, 10, 14, 10}, {18, 10, 14, 0, 8, 16}, {18, 10, 14, 0, 10, 16}, {18, 10, 14, 0, 16, 8}, {18, 10, 14, 0, 16, 10}, {18, 10, 14, 6, 8, 16}, {18, 10, 14, 6, 12, 14}, {18, 10, 14, 6, 14, 12}, {18, 10, 14, 6, 16, 8}, {18, 10, 14, 8, 10, 14}, {18, 10, 14, 8, 14, 10}, {18, 10, 14, 10, 10, 12}, {18, 10, 14, 10, 12, 10}, {18, 12, 0, 8, 6, 18}, {18, 12, 0, 12, 6, 18}, {18, 12, 0, 14, 6, 16}, {18, 12, 0, 14, 8, 16}, {18, 12, 6, 10, 0, 18}, {18, 12, 6, 12, 0, 18}, {18, 12, 6, 14, 6, 16}, {18, 12, 6, 14, 10, 14}, {18, 12, 6, 16, 0, 14}, {18, 12, 6, 16, 8, 12}, {18, 12, 8, 0, 6, 18}, {18, 12, 10, 6, 0, 18}, {18, 12, 10, 14, 10, 10}, {18, 12, 10, 16, 8, 8}, {18, 12, 12, 0, 6, 18}, {18, 12, 12, 6, 0, 18}, {18, 14, 0, 8, 6, 14}, {18, 14, 0, 10, 6, 12}, {18, 14, 0, 10, 8, 10}, {18, 14, 0, 14, 6, 12}, {18, 14, 0, 14, 8, 10}, {18, 14, 6, 8, 16, 6}, {18, 14, 6, 10, 0, 16}, {18, 14, 6, 12, 0, 16}, {18, 14, 6, 12, 6, 16}, {18, 14, 6, 14, 0, 12}, {18, 14, 6, 14, 8, 14}, {18, 14, 6, 14, 10, 12}, {18, 14, 6, 16, 0, 12}, {18, 14, 6, 16, 6, 12}, {18, 14, 6, 16, 8, 10}, {18, 14, 8, 8, 0, 16}, {18, 14, 8, 12, 0, 16}, {18, 14, 8, 14, 0, 10}, {18, 14, 8, 14, 6, 14}, {18, 14, 8, 14, 10, 10}, {18, 14, 8, 16, 0, 12}, {18, 14, 8, 16, 8, 8}, {18, 14, 10, 8, 0, 16}, {18, 14, 10, 8, 6, 16}, {18, 14, 10, 10, 0, 16}, {18, 14, 10, 10, 8, 14}, {18, 14, 10, 10, 10, 12}, {18, 14, 10, 12, 6, 14}, {18, 14, 10, 12, 10, 10}, {18, 14, 10, 14, 6, 12}, {18, 14, 10, 14, 8, 10}, {18, 14, 10, 16, 0, 8}, {18, 14, 10, 16, 0, 10}, {18, 14, 10, 16, 6, 8}, {18, 16, 0, 8, 6, 14}, {18, 16, 0, 10, 6, 12}, {18, 16, 0, 10, 10, 8}, {18, 16, 0, 12, 6, 14}, {18, 16, 0, 14, 6, 12}, {18, 16, 0, 14, 8, 12}, {18, 16, 0, 14, 10, 8}, {18, 16, 0, 14, 10, 10}, {18, 16, 6, 14, 6, 12}, {18, 16, 6, 14, 10, 8}, {18, 16, 8, 6, 14, 6}, {18, 16, 8, 8, 6, 14}, {18, 16, 8, 10, 8, 12}, {18, 16, 8, 10, 10, 10}, {18, 16, 8, 12, 6, 12}, {18, 16, 8, 12, 10, 8}, {18, 16, 8, 14, 6, 10}, {18, 16, 8, 14, 8, 8}, {20, 0, 8, 8, 8, 16}, {20, 0, 8, 8, 12, 16}, {20, 0, 8, 10, 8, 16}, {20, 0, 8, 10, 12, 16}, {20, 0, 10, 8, 8, 16}, {20, 0, 10, 8, 12, 16}, {20, 0, 12, 8, 8, 12}, {20, 0, 12, 8, 12, 12}, {20, 0, 14, 8, 8, 12}, {20, 0, 14, 8, 12, 12}, {20, 0, 14, 10, 8, 10}, {20, 0, 14, 10, 12, 10}, {20, 6, 6, 8, 14, 14}, {20, 6, 6, 10, 12, 16}, {20, 6, 6, 12, 10, 16}, {20, 6, 6, 14, 8, 14}, {20, 6, 10, 6, 12, 16}, {20, 6, 12, 6, 10, 16}, {20, 8, 0, 8, 8, 16}, {20, 8, 0, 8, 10, 16}, {20, 8, 0, 12, 8, 16}, {20, 8, 0, 12, 10, 16}, {20, 8, 8, 0, 8, 16}, {20, 8, 8, 0, 10, 16}, {20, 8, 8, 0, 12, 12}, {20, 8, 8, 0, 14, 12}, {20, 8, 8, 8, 0, 16}, {20, 8, 8, 10, 0, 16}, {20, 8, 8, 12, 0, 12}, {20, 8, 8, 14, 0, 12}, {20, 8, 10, 8, 0, 16}, {20, 8, 10, 14, 0, 10}, {20, 8, 12, 0, 8, 16}, {20, 8, 12, 0, 10, 16}, {20, 8, 12, 0, 12, 12}, {20, 8, 12, 0, 14, 12}, {20, 8, 14, 6, 6, 14}, {20, 10, 0, 8, 8, 16}, {20, 10, 0, 12, 8, 16}, {20, 10, 6, 12, 6, 16}, {20, 10, 8, 0, 8, 16}, {20, 10, 8, 0, 14, 10}, {20, 10, 12, 0, 8, 16}, {20, 10, 12, 0, 14, 10}, {20, 10, 12, 6, 6, 16}, {20, 12, 0, 8, 8, 12}, {20, 12, 0, 12, 8, 12}, {20, 12, 6, 10, 6, 16}, {20, 12, 8, 8, 0, 16}, {20, 12, 8, 10, 0, 16}, {20, 12, 8, 12, 0, 12}, {20, 12, 8, 14, 0, 12}, {20, 12, 10, 6, 6, 16}, {20, 12, 10, 8, 0, 16}, {20, 12, 10, 14, 0, 10}, {20, 14, 0, 8, 8, 12}, {20, 14, 0, 8, 10, 10}, {20, 14, 0, 12, 8, 12}, {20, 14, 0, 12, 10, 10}, {20, 14, 8, 6, 6, 14}, {22, 6, 8, 8, 12, 12}, {22, 6, 8, 10, 10, 14}, {22, 6, 8, 12, 8, 12}, {22, 6, 10, 6, 12, 12}, {22, 6, 10, 8, 10, 14}, {22, 6, 10, 8, 12, 8}, {22, 6, 10, 8, 12, 10}, {22, 6, 10, 10, 10, 12}, {22, 6, 10, 12, 6, 8}, {22, 6, 10, 12, 8, 8}, {22, 6, 10, 12, 8, 10}, {22, 6, 12, 6, 10, 12}, {22, 6, 12, 8, 8, 8}, {22, 6, 12, 10, 6, 8}, {22, 6, 12, 10, 10, 8}, {22, 8, 6, 8, 12, 12}, {22, 8, 6, 10, 10, 14}, {22, 8, 6, 12, 8, 12}, {22, 8, 8, 6, 12, 8}, {22, 8, 8, 12, 6, 8}, {22, 8, 10, 6, 10, 14}, {22, 8, 10, 8, 12, 8}, {22, 8, 10, 10, 10, 10}, {22, 8, 10, 12, 8, 8}, {22, 8, 12, 6, 8, 12}, {22, 8, 12, 6, 10, 8}, {22, 8, 12, 6, 10, 10}, {22, 8, 12, 8, 6, 12}, {22, 8, 12, 8, 10, 8}, {22, 8, 12, 10, 6, 8}, {22, 8, 12, 10, 6, 10}, {22, 8, 12, 10, 8, 8}, {22, 10, 6, 6, 12, 8}, {22, 10, 6, 8, 12, 8}, {22, 10, 6, 8, 12, 10}, {22, 10, 6, 10, 8, 14}, {22, 10, 6, 10, 10, 12}, {22, 10, 6, 12, 6, 12}, {22, 10, 6, 12, 8, 8}, {22, 10, 6, 12, 8, 10}, {22, 10, 8, 8, 12, 8}, {22, 10, 8, 10, 6, 14}, {22, 10, 8, 10, 10, 10}, {22, 10, 8, 12, 8, 8}, {22, 10, 10, 6, 8, 14}, {22, 10, 10, 6, 10, 12}, {22, 10, 10, 6, 12, 8}, {22, 10, 10, 8, 6, 14}, {22, 10, 10, 8, 10, 10}, {22, 10, 10, 10, 6, 12}, {22, 10, 10, 10, 8, 10}, {22, 10, 10, 12, 6, 8}, {22, 12, 6, 6, 10, 8}, {22, 12, 6, 8, 8, 8}, {22, 12, 6, 10, 6, 12}, {22, 12, 6, 10, 10, 8}, {22, 12, 8, 6, 8, 12}, {22, 12, 8, 6, 10, 8}, {22, 12, 8, 6, 10, 10}, {22, 12, 8, 8, 6, 12}, {22, 12, 8, 8, 10, 8}, {22, 12, 8, 10, 6, 8}, {22, 12, 8, 10, 6, 10}, {22, 12, 8, 10, 8, 8}, {4, 6, 8, 14, 16, 18}, {4, 6, 8, 16, 12, 18}, {4, 6, 8, 16, 18, 10}, {4, 6, 8, 18, 14, 10}, {4, 6, 10, 16, 14, 18}, {4, 6, 12, 22, 8, 12}, {4, 6, 12, 22, 10, 6}, {4, 6, 12, 22, 10, 12}, {4, 6, 12, 22, 12, 6}, {4, 6, 14, 16, 6, 18}, {4, 6, 14, 16, 10, 18}, {4, 6, 14, 16, 18, 10}, {4, 6, 14, 18, 12, 16}, {4, 6, 14, 18, 16, 12}, {4, 6, 14, 20, 10, 14}, {4, 6, 14, 20, 14, 10}, {4, 6, 14, 22, 6, 8}, {4, 6, 14, 22, 6, 10}, {4, 6, 16, 14, 6, 18}, {4, 6, 16, 14, 8, 18}, {4, 6, 16, 14, 18, 8}, {4, 6, 18, 18, 12, 12}, {4, 6, 20, 14, 14, 8}, {4, 6, 22, 14, 6, 8}, {4, 6, 22, 14, 6, 10}, {4, 8, 6, 12, 16, 18}, {4, 8, 6, 14, 18, 10}, {4, 8, 6, 16, 14, 18}, {4, 8, 6, 18, 16, 10}, {4, 8, 8, 14, 16, 18}, {4, 8, 8, 16, 14, 18}, {4, 8, 10, 12, 22, 8}, {4, 8, 10, 12, 22, 10}, {4, 8, 10, 22, 10, 12}, {4, 8, 10, 22, 12, 6}, {4, 8, 12, 18, 16, 14}, {4, 8, 12, 22, 8, 12}, {4, 8, 12, 22, 12, 10}, {4, 8, 14, 16, 6, 18}, {4, 8, 14, 16, 8, 18}, {4, 8, 14, 18, 10, 16}, {4, 8, 14, 20, 8, 14}, {4, 8, 16, 14, 8, 18}, {4, 8, 16, 18, 12, 14}, {4, 8, 16, 20, 10, 12}, {4, 8, 20, 14, 8, 14}, {4, 8, 20, 16, 10, 12}, {4, 8, 22, 12, 6, 12}, {4, 8, 22, 12, 8, 12}, {4, 8, 22, 12, 12, 8}, {4, 10, 6, 14, 16, 18}, {4, 10, 8, 10, 22, 12}, {4, 10, 8, 12, 22, 6}, {4, 10, 8, 22, 12, 8}, {4, 10, 8, 22, 12, 10}, {4, 10, 10, 12, 22, 10}, {4, 10, 10, 16, 18, 14}, {4, 10, 10, 18, 16, 14}, {4, 10, 10, 22, 12, 10}, {4, 10, 12, 10, 22, 8}, {4, 10, 16, 14, 6, 18}, {4, 10, 16, 18, 10, 14}, {4, 10, 16, 20, 8, 12}, {4, 10, 18, 14, 8, 16}, {4, 10, 18, 16, 10, 14}, {4, 10, 20, 14, 6, 14}, {4, 10, 20, 16, 8, 12}, {4, 10, 22, 10, 8, 12}, {4, 10, 22, 10, 12, 8}, {4, 10, 22, 12, 6, 6}, {4, 10, 22, 12, 6, 12}, {4, 12, 6, 8, 22, 12}, {4, 12, 6, 10, 22, 6}, {4, 12, 6, 10, 22, 12}, {4, 12, 6, 12, 22, 6}, {4, 12, 8, 8, 22, 12}, {4, 12, 8, 12, 22, 10}, {4, 12, 8, 16, 18, 14}, {4, 12, 10, 22, 10, 8}, {4, 12, 12, 8, 22, 8}, {4, 12, 12, 22, 8, 8}, {4, 12, 16, 8, 6, 18}, {4, 12, 18, 14, 6, 16}, {4, 12, 18, 16, 8, 14}, {4, 12, 18, 18, 6, 12}, {4, 12, 22, 8, 10, 8}, {4, 12, 22, 8, 10, 10}, {4, 12, 22, 10, 8, 6}, {4, 12, 22, 10, 10, 10}, {4, 12, 22, 12, 6, 6}, {4, 12, 22, 12, 8, 10}, {4, 14, 6, 6, 16, 18}, {4, 14, 6, 6, 22, 8}, {4, 14, 6, 6, 22, 10}, {4, 14, 6, 10, 16, 18}, {4, 14, 6, 10, 20, 14}, {4, 14, 6, 12, 18, 16}, {4, 14, 6, 14, 20, 10}, {4, 14, 6, 16, 18, 12}, {4, 14, 6, 18, 16, 10}, {4, 14, 8, 6, 16, 18}, {4, 14, 8, 8, 16, 18}, {4, 14, 8, 8, 20, 14}, {4, 14, 8, 10, 18, 16}, {4, 14, 14, 6, 20, 8}, {4, 14, 14, 20, 6, 8}, {4, 14, 16, 6, 8, 18}, {4, 14, 16, 8, 8, 18}, {4, 14, 16, 10, 6, 18}, {4, 14, 18, 6, 16, 8}, {4, 14, 18, 8, 6, 10}, {4, 14, 20, 14, 6, 10}, {4, 16, 6, 6, 14, 18}, {4, 16, 6, 8, 14, 18}, {4, 16, 6, 18, 14, 8}, {4, 16, 8, 8, 14, 18}, {4, 16, 8, 10, 20, 12}, {4, 16, 8, 12, 18, 14}, {4, 16, 10, 6, 14, 18}, {4, 16, 10, 8, 20, 12}, {4, 16, 10, 10, 18, 14}, {4, 16, 12, 6, 8, 18}, {4, 16, 14, 6, 10, 18}, {4, 16, 14, 8, 6, 18}, {4, 16, 14, 8, 8, 18}, {4, 16, 18, 6, 8, 10}, {4, 16, 18, 6, 14, 10}, {4, 16, 18, 10, 10, 14}, {4, 16, 18, 12, 8, 14}, {4, 16, 18, 14, 6, 12}, {4, 18, 6, 12, 18, 12}, {4, 18, 10, 8, 14, 16}, {4, 18, 10, 10, 16, 14}, {4, 18, 12, 6, 14, 16}, {4, 18, 12, 6, 18, 12}, {4, 18, 12, 8, 16, 14}, {4, 18, 14, 6, 8, 10}, {4, 18, 14, 16, 6, 8}, {4, 18, 16, 6, 14, 12}, {4, 18, 16, 8, 6, 10}, {4, 18, 16, 8, 12, 14}, {4, 18, 16, 10, 10, 14}, {4, 18, 16, 14, 6, 10}, {4, 20, 6, 14, 14, 8}, {4, 20, 8, 8, 14, 14}, {4, 20, 8, 10, 16, 12}, {4, 20, 10, 6, 14, 14}, {4, 20, 10, 8, 16, 12}, {4, 20, 14, 6, 14, 10}, {4, 22, 6, 6, 14, 8}, {4, 22, 6, 6, 14, 10}, {4, 22, 8, 6, 12, 12}, {4, 22, 8, 8, 12, 12}, {4, 22, 8, 12, 12, 8}, {4, 22, 10, 6, 12, 6}, {4, 22, 10, 6, 12, 12}, {4, 22, 10, 8, 10, 12}, {4, 22, 10, 12, 10, 8}, {4, 22, 12, 6, 12, 6}, {4, 22, 12, 8, 10, 6}, {4, 22, 12, 8, 12, 10}, {4, 22, 12, 10, 8, 8}, {4, 22, 12, 10, 8, 10}, {4, 22, 12, 10, 10, 10}, {6, 4, 8, 14, 18, 16}, {6, 4, 8, 16, 10, 18}, {6, 4, 8, 16, 18, 12}, {6, 4, 8, 18, 10, 14}, {6, 4, 10, 16, 18, 14}, {6, 4, 12, 22, 6, 10}, {6, 4, 12, 22, 6, 12}, {6, 4, 12, 22, 12, 8}, {6, 4, 12, 22, 12, 10}, {6, 4, 14, 16, 10, 18}, {6, 4, 14, 16, 18, 6}, {6, 4, 14, 16, 18, 10}, {6, 4, 14, 18, 12, 16}, {6, 4, 14, 18, 16, 12}, {6, 4, 14, 20, 10, 14}, {6, 4, 14, 20, 14, 10}, {6, 4, 14, 22, 8, 6}, {6, 4, 14, 22, 10, 6}, {6, 4, 16, 14, 8, 18}, {6, 4, 16, 14, 18, 6}, {6, 4, 16, 14, 18, 8}, {6, 4, 18, 18, 12, 12}, {6, 4, 20, 14, 8, 14}, {6, 4, 22, 14, 8, 6}, {6, 4, 22, 14, 10, 6}, {6, 6, 22, 12, 4, 10}, {6, 6, 22, 12, 4, 12}, {6, 6, 22, 12, 10, 4}, {6, 6, 22, 12, 12, 4}, {6, 8, 4, 10, 16, 18}, {6, 8, 4, 10, 18, 14}, {6, 8, 4, 18, 14, 16}, {6, 8, 4, 18, 16, 12}, {6, 8, 14, 16, 4, 18}, {6, 8, 14, 20, 4, 14}, {6, 8, 14, 22, 4, 6}, {6, 8, 22, 10, 12, 4}, {6, 8, 22, 14, 4, 6}, {6, 10, 4, 18, 16, 14}, {6, 10, 12, 8, 22, 4}, {6, 10, 12, 22, 6, 4}, {6, 10, 14, 22, 4, 6}, {6, 10, 16, 8, 4, 18}, {6, 10, 16, 14, 4, 18}, {6, 10, 18, 8, 4, 14}, {6, 10, 20, 14, 4, 14}, {6, 10, 22, 14, 4, 6}, {6, 12, 4, 6, 22, 10}, {6, 12, 4, 6, 22, 12}, {6, 12, 4, 12, 22, 8}, {6, 12, 4, 12, 22, 10}, {6, 12, 10, 6, 22, 4}, {6, 12, 10, 22, 8, 4}, {6, 12, 12, 6, 22, 4}, {6, 12, 12, 22, 6, 4}, {6, 12, 18, 14, 4, 16}, {6, 12, 18, 18, 4, 12}, {6, 12, 22, 12, 4, 8}, {6, 12, 22, 12, 4, 10}, {6, 14, 4, 8, 22, 6}, {6, 14, 4, 10, 16, 18}, {6, 14, 4, 10, 20, 14}, {6, 14, 4, 10, 22, 6}, {6, 14, 4, 12, 18, 16}, {6, 14, 4, 14, 20, 10}, {6, 14, 4, 16, 18, 12}, {6, 14, 4, 18, 16, 6}, {6, 14, 4, 18, 16, 10}, {6, 14, 8, 4, 16, 18}, {6, 14, 8, 4, 20, 14}, {6, 14, 8, 4, 22, 6}, {6, 14, 10, 4, 22, 6}, {6, 14, 18, 4, 8, 16}, {6, 14, 18, 4, 16, 6}, {6, 14, 18, 4, 16, 8}, {6, 14, 20, 14, 4, 10}, {6, 16, 4, 8, 14, 18}, {6, 16, 4, 18, 14, 6}, {6, 16, 4, 18, 14, 8}, {6, 16, 10, 4, 8, 18}, {6, 16, 10, 4, 14, 18}, {6, 16, 18, 4, 8, 12}, {6, 16, 18, 4, 10, 14}, {6, 16, 18, 4, 14, 6}, {6, 16, 18, 4, 14, 10}, {6, 16, 18, 14, 4, 12}, {6, 18, 4, 12, 18, 12}, {6, 18, 10, 4, 8, 14}, {6, 18, 12, 4, 14, 16}, {6, 18, 12, 4, 18, 12}, {6, 18, 14, 8, 4, 16}, {6, 18, 14, 16, 4, 6}, {6, 18, 14, 16, 4, 8}, {6, 18, 16, 4, 14, 12}, {6, 18, 16, 8, 4, 12}, {6, 18, 16, 10, 4, 14}, {6, 18, 16, 14, 4, 6}, {6, 18, 16, 14, 4, 10}, {6, 20, 4, 8, 14, 14}, {6, 20, 10, 4, 14, 14}, {6, 20, 14, 4, 14, 10}, {6, 22, 4, 8, 14, 6}, {6, 22, 4, 10, 14, 6}, {6, 22, 6, 4, 12, 10}, {6, 22, 6, 4, 12, 12}, {6, 22, 6, 10, 12, 4}, {6, 22, 6, 12, 12, 4}, {6, 22, 8, 4, 14, 6}, {6, 22, 8, 12, 10, 4}, {6, 22, 10, 4, 14, 6}, {6, 22, 12, 4, 12, 8}, {6, 22, 12, 4, 12, 10}, {8, 4, 6, 12, 18, 16}, {8, 4, 6, 14, 10, 18}, {8, 4, 6, 16, 18, 14}, {8, 4, 6, 18, 10, 16}, {8, 4, 8, 14, 18, 16}, {8, 4, 8, 16, 18, 14}, {8, 4, 10, 12, 8, 22}, {8, 4, 10, 12, 10, 22}, {8, 4, 10, 22, 6, 12}, {8, 4, 10, 22, 12, 10}, {8, 4, 12, 18, 14, 16}, {8, 4, 12, 22, 10, 12}, {8, 4, 12, 22, 12, 8}, {8, 4, 14, 16, 18, 6}, {8, 4, 14, 16, 18, 8}, {8, 4, 14, 18, 16, 10}, {8, 4, 14, 20, 14, 8}, {8, 4, 16, 14, 18, 8}, {8, 4, 16, 18, 14, 12}, {8, 4, 16, 20, 12, 10}, {8, 4, 20, 14, 14, 8}, {8, 4, 20, 16, 12, 10}, {8, 4, 22, 12, 8, 12}, {8, 4, 22, 12, 12, 6}, {8, 4, 22, 12, 12, 8}, {8, 6, 4, 10, 14, 18}, {8, 6, 4, 10, 18, 16}, {8, 6, 4, 18, 12, 16}, {8, 6, 4, 18, 16, 14}, {8, 6, 14, 16, 18, 4}, {8, 6, 14, 20, 14, 4}, {8, 6, 14, 22, 6, 4}, {8, 6, 22, 10, 4, 12}, {8, 6, 22, 14, 6, 4}, {8, 8, 4, 18, 14, 16}, {8, 8, 4, 18, 16, 14}, {8, 8, 12, 10, 4, 22}, {8, 8, 12, 10, 22, 4}, {8, 8, 12, 22, 4, 12}, {8, 8, 12, 22, 12, 4}, {8, 10, 4, 6, 22, 12}, {8, 10, 4, 8, 12, 22}, {8, 10, 4, 10, 12, 22}, {8, 10, 4, 12, 22, 10}, {8, 10, 10, 12, 22, 4}, {8, 10, 10, 22, 12, 4}, {8, 10, 12, 10, 4, 22}, {8, 10, 14, 6, 4, 18}, {8, 10, 18, 6, 4, 16}, {8, 10, 22, 8, 12, 4}, {8, 10, 22, 12, 4, 12}, {8, 12, 4, 10, 22, 12}, {8, 12, 4, 12, 22, 8}, {8, 12, 4, 14, 18, 16}, {8, 12, 8, 4, 10, 22}, {8, 12, 8, 4, 22, 12}, {8, 12, 8, 12, 22, 4}, {8, 12, 8, 22, 10, 4}, {8, 12, 10, 4, 10, 22}, {8, 12, 12, 4, 22, 6}, {8, 12, 12, 4, 22, 8}, {8, 12, 12, 22, 4, 6}, {8, 12, 12, 22, 4, 8}, {8, 12, 16, 20, 4, 10}, {8, 12, 18, 4, 6, 16}, {8, 12, 20, 16, 4, 10}, {8, 12, 22, 10, 4, 10}, {8, 12, 22, 10, 10, 4}, {8, 12, 22, 12, 4, 8}, {8, 12, 22, 12, 8, 4}, {8, 14, 4, 14, 20, 8}, {8, 14, 4, 16, 18, 10}, {8, 14, 4, 18, 16, 6}, {8, 14, 4, 18, 16, 8}, {8, 14, 6, 6, 22, 4}, {8, 14, 6, 14, 20, 4}, {8, 14, 6, 18, 16, 4}, {8, 14, 10, 4, 6, 18}, {8, 14, 14, 4, 20, 8}, {8, 14, 14, 20, 4, 8}, {8, 14, 18, 4, 8, 16}, {8, 14, 18, 4, 16, 8}, {8, 14, 18, 12, 4, 16}, {8, 14, 18, 16, 4, 12}, {8, 14, 20, 14, 4, 8}, {8, 14, 20, 14, 6, 4}, {8, 16, 4, 12, 20, 10}, {8, 16, 4, 14, 18, 12}, {8, 16, 4, 18, 14, 8}, {8, 16, 12, 4, 20, 10}, {8, 16, 18, 4, 6, 14}, {8, 16, 18, 4, 8, 14}, {8, 16, 18, 4, 14, 6}, {8, 16, 18, 4, 14, 8}, {8, 16, 18, 6, 14, 4}, {8, 16, 18, 14, 4, 10}, {8, 18, 10, 4, 6, 16}, {8, 18, 12, 6, 4, 16}, {8, 18, 14, 4, 12, 16}, {8, 18, 14, 4, 16, 12}, {8, 18, 14, 8, 4, 16}, {8, 18, 14, 16, 4, 8}, {8, 18, 16, 4, 14, 10}, {8, 18, 16, 6, 4, 14}, {8, 18, 16, 8, 4, 14}, {8, 18, 16, 14, 4, 6}, {8, 18, 16, 14, 4, 8}, {8, 18, 16, 14, 6, 4}, {8, 20, 4, 12, 16, 10}, {8, 20, 4, 14, 14, 8}, {8, 20, 12, 4, 16, 10}, {8, 20, 14, 4, 14, 8}, {8, 20, 14, 6, 14, 4}, {8, 22, 4, 8, 12, 12}, {8, 22, 4, 12, 12, 6}, {8, 22, 4, 12, 12, 8}, {8, 22, 6, 4, 10, 12}, {8, 22, 6, 6, 14, 4}, {8, 22, 10, 4, 12, 12}, {8, 22, 10, 12, 8, 4}, {8, 22, 12, 4, 10, 10}, {8, 22, 12, 4, 12, 8}, {8, 22, 12, 8, 12, 4}, {8, 22, 12, 10, 10, 4}, {10, 4, 6, 14, 18, 16}, {10, 4, 8, 10, 12, 22}, {10, 4, 8, 12, 6, 22}, {10, 4, 8, 22, 8, 12}, {10, 4, 8, 22, 10, 12}, {10, 4, 10, 12, 10, 22}, {10, 4, 10, 16, 14, 18}, {10, 4, 10, 18, 14, 16}, {10, 4, 10, 22, 10, 12}, {10, 4, 12, 10, 8, 22}, {10, 4, 16, 14, 18, 6}, {10, 4, 16, 18, 14, 10}, {10, 4, 16, 20, 12, 8}, {10, 4, 18, 14, 16, 8}, {10, 4, 18, 16, 14, 10}, {10, 4, 20, 14, 14, 6}, {10, 4, 20, 16, 12, 8}, {10, 4, 22, 10, 8, 12}, {10, 4, 22, 10, 12, 8}, {10, 4, 22, 12, 6, 6}, {10, 4, 22, 12, 12, 6}, {10, 6, 4, 18, 14, 16}, {10, 6, 12, 8, 4, 22}, {10, 6, 12, 22, 4, 6}, {10, 6, 14, 22, 6, 4}, {10, 6, 16, 8, 18, 4}, {10, 6, 16, 14, 18, 4}, {10, 6, 18, 8, 14, 4}, {10, 6, 20, 14, 14, 4}, {10, 6, 22, 14, 6, 4}, {10, 8, 4, 6, 12, 22}, {10, 8, 4, 8, 22, 12}, {10, 8, 4, 10, 22, 12}, {10, 8, 4, 12, 10, 22}, {10, 8, 10, 12, 4, 22}, {10, 8, 10, 22, 4, 12}, {10, 8, 12, 10, 22, 4}, {10, 8, 14, 6, 18, 4}, {10, 8, 18, 6, 16, 4}, {10, 8, 22, 8, 4, 12}, {10, 8, 22, 12, 12, 4}, {10, 10, 4, 10, 12, 22}, {10, 10, 4, 10, 22, 12}, {10, 10, 4, 14, 16, 18}, {10, 10, 4, 14, 18, 16}, {10, 10, 8, 4, 12, 22}, {10, 10, 8, 4, 22, 12}, {10, 10, 12, 4, 8, 22}, {10, 10, 12, 4, 22, 8}, {10, 10, 12, 10, 4, 22}, {10, 10, 12, 10, 22, 4}, {10, 10, 22, 8, 4, 12}, {10, 10, 22, 8, 12, 4}, {10, 10, 22, 10, 4, 12}, {10, 10, 22, 10, 12, 4}, {10, 12, 4, 8, 10, 22}, {10, 12, 6, 4, 8, 22}, {10, 12, 6, 4, 22, 6}, {10, 12, 8, 22, 10, 4}, {10, 12, 10, 4, 10, 22}, {10, 12, 10, 8, 4, 22}, {10, 12, 10, 22, 4, 8}, {10, 12, 10, 22, 10, 4}, {10, 12, 12, 4, 22, 6}, {10, 12, 12, 8, 22, 4}, {10, 12, 12, 22, 4, 6}, {10, 12, 12, 22, 8, 4}, {10, 12, 16, 20, 4, 8}, {10, 12, 20, 16, 4, 8}, {10, 14, 6, 6, 22, 4}, {10, 14, 8, 18, 6, 4}, {10, 14, 14, 4, 20, 6}, {10, 14, 14, 6, 20, 4}, {10, 14, 14, 20, 4, 6}, {10, 14, 14, 20, 6, 4}, {10, 14, 16, 4, 18, 8}, {10, 14, 16, 10, 4, 18}, {10, 14, 16, 18, 4, 10}, {10, 14, 18, 4, 6, 16}, {10, 14, 18, 4, 16, 6}, {10, 14, 18, 6, 16, 4}, {10, 14, 18, 10, 4, 16}, {10, 14, 18, 16, 4, 10}, {10, 16, 4, 12, 20, 8}, {10, 16, 4, 14, 18, 10}, {10, 16, 4, 18, 14, 6}, {10, 16, 6, 18, 8, 4}, {10, 16, 6, 18, 14, 4}, {10, 16, 12, 4, 20, 8}, {10, 16, 14, 4, 10, 18}, {10, 16, 14, 4, 18, 10}, {10, 16, 14, 18, 4, 8}, {10, 18, 4, 14, 16, 10}, {10, 18, 4, 16, 14, 8}, {10, 18, 6, 14, 8, 4}, {10, 18, 8, 16, 6, 4}, {10, 18, 14, 4, 10, 16}, {10, 18, 14, 4, 16, 10}, {10, 18, 14, 6, 4, 16}, {10, 18, 14, 16, 4, 6}, {10, 18, 14, 16, 6, 4}, {10, 20, 4, 12, 16, 8}, {10, 20, 4, 14, 14, 6}, {10, 20, 6, 14, 14, 4}, {10, 20, 12, 4, 16, 8}, {10, 22, 4, 6, 12, 6}, {10, 22, 4, 8, 10, 12}, {10, 22, 4, 12, 10, 8}, {10, 22, 4, 12, 12, 6}, {10, 22, 6, 6, 14, 4}, {10, 22, 8, 4, 8, 12}, {10, 22, 8, 12, 12, 4}, {10, 22, 10, 4, 8, 12}, {10, 22, 10, 4, 10, 12}, {10, 22, 10, 12, 8, 4}, {10, 22, 10, 12, 10, 4}, {12, 4, 6, 8, 12, 22}, {12, 4, 6, 10, 6, 22}, {12, 4, 6, 10, 12, 22}, {12, 4, 6, 12, 6, 22}, {12, 4, 8, 8, 12, 22}, {12, 4, 8, 12, 10, 22}, {12, 4, 8, 16, 14, 18}, {12, 4, 10, 22, 8, 10}, {12, 4, 12, 8, 8, 22}, {12, 4, 12, 22, 8, 8}, {12, 4, 16, 8, 18, 6}, {12, 4, 18, 14, 16, 6}, {12, 4, 18, 16, 14, 8}, {12, 4, 18, 18, 12, 6}, {12, 4, 22, 8, 8, 10}, {12, 4, 22, 8, 10, 10}, {12, 4, 22, 10, 6, 8}, {12, 4, 22, 10, 10, 10}, {12, 4, 22, 12, 6, 6}, {12, 4, 22, 12, 10, 8}, {12, 6, 4, 6, 10, 22}, {12, 6, 4, 6, 12, 22}, {12, 6, 4, 12, 8, 22}, {12, 6, 4, 12, 10, 22}, {12, 6, 10, 6, 4, 22}, {12, 6, 10, 22, 4, 8}, {12, 6, 12, 6, 4, 22}, {12, 6, 12, 22, 4, 6}, {12, 6, 18, 14, 16, 4}, {12, 6, 18, 18, 12, 4}, {12, 6, 22, 12, 8, 4}, {12, 6, 22, 12, 10, 4}, {12, 8, 4, 10, 12, 22}, {12, 8, 4, 12, 8, 22}, {12, 8, 4, 14, 16, 18}, {12, 8, 8, 4, 12, 22}, {12, 8, 8, 4, 22, 10}, {12, 8, 8, 12, 4, 22}, {12, 8, 8, 22, 4, 10}, {12, 8, 10, 4, 22, 10}, {12, 8, 12, 4, 6, 22}, {12, 8, 12, 4, 8, 22}, {12, 8, 12, 22, 6, 4}, {12, 8, 12, 22, 8, 4}, {12, 8, 16, 20, 10, 4}, {12, 8, 18, 4, 16, 6}, {12, 8, 20, 16, 10, 4}, {12, 8, 22, 10, 4, 10}, {12, 8, 22, 10, 10, 4}, {12, 8, 22, 12, 4, 8}, {12, 8, 22, 12, 8, 4}, {12, 10, 4, 8, 22, 10}, {12, 10, 6, 4, 6, 22}, {12, 10, 6, 4, 22, 8}, {12, 10, 8, 22, 4, 10}, {12, 10, 10, 4, 22, 10}, {12, 10, 10, 8, 22, 4}, {12, 10, 10, 22, 4, 10}, {12, 10, 10, 22, 8, 4}, {12, 10, 12, 4, 6, 22}, {12, 10, 12, 8, 4, 22}, {12, 10, 12, 22, 4, 8}, {12, 10, 12, 22, 6, 4}, {12, 10, 16, 20, 8, 4}, {12, 10, 20, 16, 8, 4}, {12, 12, 4, 8, 8, 22}, {12, 12, 4, 8, 22, 8}, {12, 12, 6, 4, 6, 22}, {12, 12, 6, 4, 22, 6}, {12, 12, 8, 6, 4, 22}, {12, 12, 8, 6, 22, 4}, {12, 12, 8, 8, 4, 22}, {12, 12, 8, 8, 22, 4}, {12, 12, 10, 4, 8, 22}, {12, 12, 10, 4, 22, 8}, {12, 12, 10, 6, 4, 22}, {12, 12, 10, 6, 22, 4}, {12, 12, 18, 18, 4, 6}, {12, 12, 18, 18, 6, 4}, {12, 14, 16, 4, 18, 6}, {12, 14, 16, 6, 18, 4}, {12, 14, 16, 8, 4, 18}, {12, 14, 16, 18, 4, 8}, {12, 16, 4, 18, 8, 6}, {12, 16, 8, 10, 20, 4}, {12, 16, 10, 8, 20, 4}, {12, 16, 14, 4, 8, 18}, {12, 16, 14, 4, 18, 8}, {12, 16, 14, 18, 4, 6}, {12, 16, 14, 18, 6, 4}, {12, 18, 4, 12, 18, 6}, {12, 18, 4, 14, 16, 8}, {12, 18, 4, 16, 14, 6}, {12, 18, 6, 12, 18, 4}, {12, 18, 6, 16, 14, 4}, {12, 18, 8, 16, 4, 6}, {12, 18, 12, 4, 18, 6}, {12, 18, 12, 6, 18, 4}, {12, 20, 8, 10, 16, 4}, {12, 20, 10, 8, 16, 4}, {12, 22, 4, 6, 10, 8}, {12, 22, 4, 6, 12, 6}, {12, 22, 4, 8, 8, 10}, {12, 22, 4, 10, 8, 10}, {12, 22, 4, 10, 10, 10}, {12, 22, 4, 10, 12, 8}, {12, 22, 6, 8, 12, 4}, {12, 22, 6, 10, 12, 4}, {12, 22, 8, 4, 10, 10}, {12, 22, 8, 4, 12, 8}, {12, 22, 8, 8, 12, 4}, {12, 22, 8, 10, 10, 4}, {14, 4, 6, 6, 8, 22}, {14, 4, 6, 6, 10, 22}, {14, 4, 6, 6, 18, 16}, {14, 4, 6, 10, 14, 20}, {14, 4, 6, 10, 18, 16}, {14, 4, 6, 12, 16, 18}, {14, 4, 6, 14, 10, 20}, {14, 4, 6, 16, 12, 18}, {14, 4, 6, 18, 10, 16}, {14, 4, 8, 6, 18, 16}, {14, 4, 8, 8, 14, 20}, {14, 4, 8, 8, 18, 16}, {14, 4, 8, 10, 16, 18}, {14, 4, 14, 6, 8, 20}, {14, 4, 14, 20, 8, 6}, {14, 4, 16, 6, 18, 8}, {14, 4, 16, 8, 18, 8}, {14, 4, 16, 10, 18, 6}, {14, 4, 18, 6, 8, 16}, {14, 4, 18, 8, 10, 6}, {14, 4, 20, 14, 10, 6}, {14, 6, 4, 8, 6, 22}, {14, 6, 4, 10, 6, 22}, {14, 6, 4, 10, 14, 20}, {14, 6, 4, 10, 18, 16}, {14, 6, 4, 12, 16, 18}, {14, 6, 4, 14, 10, 20}, {14, 6, 4, 16, 12, 18}, {14, 6, 4, 18, 6, 16}, {14, 6, 4, 18, 10, 16}, {14, 6, 8, 4, 6, 22}, {14, 6, 8, 4, 14, 20}, {14, 6, 8, 4, 18, 16}, {14, 6, 10, 4, 6, 22}, {14, 6, 18, 4, 6, 16}, {14, 6, 18, 4, 8, 16}, {14, 6, 18, 4, 16, 8}, {14, 6, 20, 14, 10, 4}, {14, 8, 4, 14, 8, 20}, {14, 8, 4, 16, 10, 18}, {14, 8, 4, 18, 6, 16}, {14, 8, 4, 18, 8, 16}, {14, 8, 6, 6, 4, 22}, {14, 8, 6, 14, 4, 20}, {14, 8, 6, 18, 4, 16}, {14, 8, 10, 4, 18, 6}, {14, 8, 14, 4, 8, 20}, {14, 8, 14, 20, 8, 4}, {14, 8, 18, 4, 8, 16}, {14, 8, 18, 4, 16, 8}, {14, 8, 18, 12, 16, 4}, {14, 8, 18, 16, 12, 4}, {14, 8, 20, 14, 4, 6}, {14, 8, 20, 14, 8, 4}, {14, 10, 6, 6, 4, 22}, {14, 10, 8, 18, 4, 6}, {14, 10, 14, 4, 6, 20}, {14, 10, 14, 6, 4, 20}, {14, 10, 14, 20, 4, 6}, {14, 10, 14, 20, 6, 4}, {14, 10, 16, 4, 8, 18}, {14, 10, 16, 10, 18, 4}, {14, 10, 16, 18, 10, 4}, {14, 10, 18, 4, 6, 16}, {14, 10, 18, 4, 16, 6}, {14, 10, 18, 6, 4, 16}, {14, 10, 18, 10, 16, 4}, {14, 10, 18, 16, 10, 4}, {14, 12, 16, 4, 6, 18}, {14, 12, 16, 6, 4, 18}, {14, 12, 16, 8, 18, 4}, {14, 12, 16, 18, 8, 4}, {14, 14, 4, 8, 6, 20}, {14, 14, 4, 8, 20, 6}, {14, 14, 8, 8, 4, 20}, {14, 14, 8, 8, 20, 4}, {14, 14, 10, 4, 6, 20}, {14, 14, 10, 4, 20, 6}, {14, 14, 10, 6, 4, 20}, {14, 14, 10, 6, 20, 4}, {14, 16, 4, 18, 6, 8}, {14, 16, 4, 18, 8, 8}, {14, 16, 4, 18, 10, 6}, {14, 16, 10, 8, 4, 18}, {14, 16, 10, 10, 18, 4}, {14, 16, 10, 18, 10, 4}, {14, 16, 12, 4, 6, 18}, {14, 16, 12, 6, 4, 18}, {14, 16, 12, 8, 18, 4}, {14, 16, 12, 18, 8, 4}, {14, 18, 4, 8, 6, 16}, {14, 18, 4, 10, 8, 6}, {14, 18, 6, 6, 4, 16}, {14, 18, 6, 8, 4, 16}, {14, 18, 6, 16, 4, 8}, {14, 18, 8, 8, 4, 16}, {14, 18, 8, 12, 16, 4}, {14, 18, 8, 16, 4, 8}, {14, 18, 8, 16, 12, 4}, {14, 18, 10, 4, 6, 16}, {14, 18, 10, 6, 4, 16}, {14, 18, 10, 10, 16, 4}, {14, 18, 10, 16, 4, 6}, {14, 18, 10, 16, 10, 4}, {14, 20, 4, 10, 14, 6}, {14, 20, 6, 10, 14, 4}, {14, 20, 8, 4, 14, 6}, {14, 20, 8, 8, 14, 4}, {16, 4, 6, 6, 18, 14}, {16, 4, 6, 8, 18, 14}, {16, 4, 6, 18, 8, 14}, {16, 4, 8, 8, 18, 14}, {16, 4, 8, 10, 12, 20}, {16, 4, 8, 12, 14, 18}, {16, 4, 10, 6, 18, 14}, {16, 4, 10, 8, 12, 20}, {16, 4, 10, 10, 14, 18}, {16, 4, 12, 6, 18, 8}, {16, 4, 14, 6, 18, 10}, {16, 4, 14, 8, 18, 6}, {16, 4, 14, 8, 18, 8}, {16, 4, 18, 6, 10, 8}, {16, 4, 18, 6, 10, 14}, {16, 4, 18, 10, 14, 10}, {16, 4, 18, 12, 14, 8}, {16, 4, 18, 14, 12, 6}, {16, 6, 4, 8, 18, 14}, {16, 6, 4, 18, 6, 14}, {16, 6, 4, 18, 8, 14}, {16, 6, 10, 4, 18, 8}, {16, 6, 10, 4, 18, 14}, {16, 6, 18, 4, 6, 14}, {16, 6, 18, 4, 10, 14}, {16, 6, 18, 4, 12, 8}, {16, 6, 18, 4, 14, 10}, {16, 6, 18, 14, 12, 4}, {16, 8, 4, 12, 10, 20}, {16, 8, 4, 14, 12, 18}, {16, 8, 4, 18, 8, 14}, {16, 8, 12, 4, 10, 20}, {16, 8, 18, 4, 6, 14}, {16, 8, 18, 4, 8, 14}, {16, 8, 18, 4, 14, 6}, {16, 8, 18, 4, 14, 8}, {16, 8, 18, 6, 4, 14}, {16, 8, 18, 14, 10, 4}, {16, 10, 4, 12, 8, 20}, {16, 10, 4, 14, 10, 18}, {16, 10, 4, 18, 6, 14}, {16, 10, 6, 18, 4, 8}, {16, 10, 6, 18, 4, 14}, {16, 10, 12, 4, 8, 20}, {16, 10, 14, 4, 10, 18}, {16, 10, 14, 4, 18, 10}, {16, 10, 14, 18, 8, 4}, {16, 12, 4, 18, 6, 8}, {16, 12, 8, 10, 4, 20}, {16, 12, 10, 8, 4, 20}, {16, 12, 14, 4, 8, 18}, {16, 12, 14, 4, 18, 8}, {16, 12, 14, 18, 4, 6}, {16, 12, 14, 18, 6, 4}, {16, 14, 4, 18, 6, 10}, {16, 14, 4, 18, 8, 6}, {16, 14, 4, 18, 8, 8}, {16, 14, 10, 8, 18, 4}, {16, 14, 10, 10, 4, 18}, {16, 14, 10, 18, 4, 10}, {16, 14, 12, 4, 18, 6}, {16, 14, 12, 6, 18, 4}, {16, 14, 12, 8, 4, 18}, {16, 14, 12, 18, 4, 8}, {16, 18, 4, 10, 6, 8}, {16, 18, 4, 10, 6, 14}, {16, 18, 4, 12, 14, 6}, {16, 18, 4, 14, 10, 10}, {16, 18, 4, 14, 12, 8}, {16, 18, 6, 6, 4, 14}, {16, 18, 6, 10, 4, 14}, {16, 18, 6, 12, 4, 8}, {16, 18, 6, 12, 14, 4}, {16, 18, 6, 14, 4, 10}, {16, 18, 8, 4, 6, 14}, {16, 18, 8, 6, 4, 14}, {16, 18, 8, 8, 4, 14}, {16, 18, 8, 10, 14, 4}, {16, 18, 8, 14, 4, 6}, {16, 18, 8, 14, 4, 8}, {18, 4, 6, 12, 12, 18}, {18, 4, 10, 8, 16, 14}, {18, 4, 10, 10, 14, 16}, {18, 4, 12, 6, 12, 18}, {18, 4, 12, 6, 16, 14}, {18, 4, 12, 8, 14, 16}, {18, 4, 14, 6, 10, 8}, {18, 4, 14, 16, 8, 6}, {18, 4, 16, 6, 12, 14}, {18, 4, 16, 8, 10, 6}, {18, 4, 16, 8, 14, 12}, {18, 4, 16, 10, 14, 10}, {18, 4, 16, 14, 10, 6}, {18, 6, 4, 12, 12, 18}, {18, 6, 10, 4, 14, 8}, {18, 6, 12, 4, 12, 18}, {18, 6, 12, 4, 16, 14}, {18, 6, 14, 8, 16, 4}, {18, 6, 14, 16, 6, 4}, {18, 6, 14, 16, 8, 4}, {18, 6, 16, 4, 12, 14}, {18, 6, 16, 8, 12, 4}, {18, 6, 16, 10, 14, 4}, {18, 6, 16, 14, 6, 4}, {18, 6, 16, 14, 10, 4}, {18, 8, 10, 4, 16, 6}, {18, 8, 12, 6, 16, 4}, {18, 8, 14, 4, 12, 16}, {18, 8, 14, 4, 16, 12}, {18, 8, 14, 8, 16, 4}, {18, 8, 14, 16, 8, 4}, {18, 8, 16, 4, 10, 14}, {18, 8, 16, 6, 14, 4}, {18, 8, 16, 8, 14, 4}, {18, 8, 16, 14, 4, 6}, {18, 8, 16, 14, 6, 4}, {18, 8, 16, 14, 8, 4}, {18, 10, 4, 14, 10, 16}, {18, 10, 4, 16, 8, 14}, {18, 10, 6, 14, 4, 8}, {18, 10, 8, 16, 4, 6}, {18, 10, 14, 4, 10, 16}, {18, 10, 14, 4, 16, 10}, {18, 10, 14, 6, 16, 4}, {18, 10, 14, 16, 4, 6}, {18, 10, 14, 16, 6, 4}, {18, 12, 4, 12, 6, 18}, {18, 12, 4, 14, 8, 16}, {18, 12, 4, 16, 6, 14}, {18, 12, 6, 12, 4, 18}, {18, 12, 6, 16, 4, 14}, {18, 12, 8, 16, 6, 4}, {18, 12, 12, 4, 6, 18}, {18, 12, 12, 6, 4, 18}, {18, 14, 4, 8, 16, 6}, {18, 14, 4, 10, 6, 8}, {18, 14, 6, 6, 16, 4}, {18, 14, 6, 8, 16, 4}, {18, 14, 6, 16, 8, 4}, {18, 14, 8, 8, 16, 4}, {18, 14, 8, 12, 4, 16}, {18, 14, 8, 16, 4, 12}, {18, 14, 8, 16, 8, 4}, {18, 14, 10, 4, 16, 6}, {18, 14, 10, 6, 16, 4}, {18, 14, 10, 10, 4, 16}, {18, 14, 10, 16, 4, 10}, {18, 14, 10, 16, 6, 4}, {18, 16, 4, 10, 8, 6}, {18, 16, 4, 10, 14, 6}, {18, 16, 4, 12, 6, 14}, {18, 16, 4, 14, 8, 12}, {18, 16, 4, 14, 10, 10}, {18, 16, 6, 6, 14, 4}, {18, 16, 6, 10, 14, 4}, {18, 16, 6, 12, 4, 14}, {18, 16, 6, 12, 8, 4}, {18, 16, 6, 14, 10, 4}, {18, 16, 8, 4, 14, 6}, {18, 16, 8, 6, 14, 4}, {18, 16, 8, 8, 14, 4}, {18, 16, 8, 10, 4, 14}, {18, 16, 8, 14, 6, 4}, {18, 16, 8, 14, 8, 4}, {20, 4, 6, 14, 8, 14}, {20, 4, 8, 8, 14, 14}, {20, 4, 8, 10, 12, 16}, {20, 4, 10, 6, 14, 14}, {20, 4, 10, 8, 12, 16}, {20, 4, 14, 6, 10, 14}, {20, 6, 4, 8, 14, 14}, {20, 6, 10, 4, 14, 14}, {20, 6, 14, 4, 10, 14}, {20, 8, 4, 12, 10, 16}, {20, 8, 4, 14, 8, 14}, {20, 8, 12, 4, 10, 16}, {20, 8, 14, 4, 8, 14}, {20, 8, 14, 6, 4, 14}, {20, 10, 4, 12, 8, 16}, {20, 10, 4, 14, 6, 14}, {20, 10, 6, 14, 4, 14}, {20, 10, 12, 4, 8, 16}, {20, 12, 8, 10, 4, 16}, {20, 12, 10, 8, 4, 16}, {20, 14, 4, 10, 6, 14}, {20, 14, 6, 10, 4, 14}, {20, 14, 8, 4, 6, 14}, {20, 14, 8, 8, 4, 14}, {22, 4, 6, 6, 8, 14}, {22, 4, 6, 6, 10, 14}, {22, 4, 8, 6, 12, 12}, {22, 4, 8, 8, 12, 12}, {22, 4, 8, 12, 8, 12}, {22, 4, 10, 6, 6, 12}, {22, 4, 10, 6, 12, 12}, {22, 4, 10, 8, 12, 10}, {22, 4, 10, 12, 8, 10}, {22, 4, 12, 6, 6, 12}, {22, 4, 12, 8, 6, 10}, {22, 4, 12, 8, 10, 12}, {22, 4, 12, 10, 8, 8}, {22, 4, 12, 10, 10, 8}, {22, 4, 12, 10, 10, 10}, {22, 6, 4, 8, 6, 14}, {22, 6, 4, 10, 6, 14}, {22, 6, 6, 4, 10, 12}, {22, 6, 6, 4, 12, 12}, {22, 6, 6, 10, 4, 12}, {22, 6, 6, 12, 4, 12}, {22, 6, 8, 4, 6, 14}, {22, 6, 8, 12, 4, 10}, {22, 6, 10, 4, 6, 14}, {22, 6, 12, 4, 8, 12}, {22, 6, 12, 4, 10, 12}, {22, 8, 4, 8, 12, 12}, {22, 8, 4, 12, 6, 12}, {22, 8, 4, 12, 8, 12}, {22, 8, 6, 4, 12, 10}, {22, 8, 6, 6, 4, 14}, {22, 8, 10, 4, 12, 12}, {22, 8, 10, 12, 4, 8}, {22, 8, 12, 4, 8, 12}, {22, 8, 12, 4, 10, 10}, {22, 8, 12, 8, 4, 12}, {22, 8, 12, 10, 4, 10}, {22, 10, 4, 6, 6, 12}, {22, 10, 4, 8, 12, 10}, {22, 10, 4, 12, 6, 12}, {22, 10, 4, 12, 8, 10}, {22, 10, 6, 6, 4, 14}, {22, 10, 8, 4, 12, 8}, {22, 10, 8, 12, 4, 12}, {22, 10, 10, 4, 12, 8}, {22, 10, 10, 4, 12, 10}, {22, 10, 10, 12, 4, 8}, {22, 10, 10, 12, 4, 10}, {22, 12, 4, 6, 6, 12}, {22, 12, 4, 6, 8, 10}, {22, 12, 4, 8, 10, 8}, {22, 12, 4, 10, 8, 12}, {22, 12, 4, 10, 10, 8}, {22, 12, 4, 10, 10, 10}, {22, 12, 6, 8, 4, 12}, {22, 12, 6, 10, 4, 12}, {22, 12, 8, 4, 8, 12}, {22, 12, 8, 4, 10, 10}, {22, 12, 8, 8, 4, 12}, {22, 12, 8, 10, 4, 10}, {4, 4, 10, 16, 12, 18}, {4, 4, 10, 16, 14, 18}, {4, 4, 10, 16, 18, 12}, {4, 4, 10, 16, 18, 14}, {4, 4, 10, 18, 10, 14}, {4, 4, 10, 18, 10, 16}, {4, 4, 10, 18, 14, 10}, {4, 4, 10, 18, 16, 10}, {4, 4, 12, 20, 8, 12}, {4, 4, 12, 20, 8, 14}, {4, 4, 12, 20, 12, 8}, {4, 4, 12, 20, 14, 8}, {4, 4, 14, 16, 8, 18}, {4, 4, 14, 16, 10, 18}, {4, 4, 14, 16, 18, 8}, {4, 4, 14, 16, 18, 10}, {4, 4, 14, 18, 6, 14}, {4, 4, 14, 18, 6, 16}, {4, 4, 14, 18, 14, 6}, {4, 4, 14, 18, 16, 6}, {4, 4, 14, 20, 6, 12}, {4, 4, 14, 20, 6, 14}, {4, 4, 14, 20, 12, 6}, {4, 4, 14, 20, 14, 6}, {4, 6, 14, 16, 16, 4}, {4, 6, 14, 16, 18, 4}, {4, 6, 14, 20, 12, 4}, {4, 6, 14, 20, 14, 4}, {4, 6, 16, 14, 16, 4}, {4, 6, 16, 14, 18, 4}, {4, 6, 18, 14, 4, 14}, {4, 6, 18, 14, 4, 16}, {4, 6, 20, 14, 4, 12}, {4, 6, 20, 14, 4, 14}, {4, 6, 20, 14, 12, 4}, {4, 6, 20, 14, 14, 4}, {4, 8, 12, 22, 10, 4}, {4, 8, 12, 22, 12, 4}, {4, 8, 16, 14, 4, 18}, {4, 8, 20, 12, 4, 12}, {4, 8, 20, 12, 4, 14}, {4, 8, 22, 12, 10, 4}, {4, 8, 22, 12, 12, 4}, {4, 10, 4, 10, 18, 14}, {4, 10, 4, 10, 18, 16}, {4, 10, 4, 12, 16, 18}, {4, 10, 4, 14, 16, 18}, {4, 10, 4, 14, 18, 10}, {4, 10, 4, 16, 18, 10}, {4, 10, 4, 18, 16, 12}, {4, 10, 4, 18, 16, 14}, {4, 10, 10, 12, 22, 4}, {4, 10, 10, 22, 12, 4}, {4, 10, 12, 10, 22, 4}, {4, 10, 12, 22, 8, 4}, {4, 10, 16, 14, 4, 18}, {4, 10, 18, 10, 4, 14}, {4, 10, 18, 10, 4, 16}, {4, 10, 22, 10, 12, 4}, {4, 10, 22, 12, 8, 4}, {4, 12, 4, 8, 20, 12}, {4, 12, 4, 8, 20, 14}, {4, 12, 4, 12, 20, 8}, {4, 12, 4, 14, 20, 8}, {4, 12, 8, 10, 22, 4}, {4, 12, 8, 12, 22, 4}, {4, 12, 10, 8, 22, 4}, {4, 12, 10, 22, 10, 4}, {4, 12, 12, 8, 22, 4}, {4, 12, 12, 22, 8, 4}, {4, 12, 14, 20, 6, 4}, {4, 12, 16, 10, 4, 18}, {4, 12, 20, 12, 4, 8}, {4, 12, 20, 14, 4, 6}, {4, 12, 20, 14, 6, 4}, {4, 12, 22, 10, 10, 4}, {4, 12, 22, 12, 8, 4}, {4, 14, 4, 6, 18, 14}, {4, 14, 4, 6, 18, 16}, {4, 14, 4, 6, 20, 12}, {4, 14, 4, 6, 20, 14}, {4, 14, 4, 8, 16, 18}, {4, 14, 4, 10, 16, 18}, {4, 14, 4, 12, 20, 6}, {4, 14, 4, 14, 18, 6}, {4, 14, 4, 14, 20, 6}, {4, 14, 4, 16, 18, 6}, {4, 14, 4, 18, 16, 8}, {4, 14, 4, 18, 16, 10}, {4, 14, 6, 12, 20, 4}, {4, 14, 6, 14, 20, 4}, {4, 14, 6, 16, 16, 4}, {4, 14, 6, 18, 16, 4}, {4, 14, 12, 6, 20, 4}, {4, 14, 14, 6, 20, 4}, {4, 14, 14, 20, 6, 4}, {4, 14, 16, 6, 16, 4}, {4, 14, 16, 10, 4, 18}, {4, 14, 18, 6, 16, 4}, {4, 14, 18, 10, 4, 10}, {4, 14, 18, 14, 4, 6}, {4, 14, 20, 12, 4, 8}, {4, 14, 20, 14, 4, 6}, {4, 14, 20, 14, 6, 4}, {4, 16, 6, 16, 14, 4}, {4, 16, 6, 18, 14, 4}, {4, 16, 8, 4, 14, 18}, {4, 16, 10, 4, 14, 18}, {4, 16, 12, 4, 10, 18}, {4, 16, 14, 4, 10, 18}, {4, 16, 14, 16, 6, 4}, {4, 16, 16, 6, 14, 4}, {4, 16, 16, 14, 6, 4}, {4, 16, 18, 4, 10, 12}, {4, 16, 18, 4, 10, 14}, {4, 16, 18, 4, 14, 8}, {4, 16, 18, 4, 14, 10}, {4, 16, 18, 6, 14, 4}, {4, 16, 18, 10, 4, 10}, {4, 16, 18, 14, 4, 6}, {4, 18, 6, 4, 14, 14}, {4, 18, 6, 4, 14, 16}, {4, 18, 10, 4, 10, 14}, {4, 18, 10, 4, 10, 16}, {4, 18, 14, 4, 10, 10}, {4, 18, 14, 4, 14, 6}, {4, 18, 14, 16, 6, 4}, {4, 18, 16, 4, 10, 10}, {4, 18, 16, 4, 14, 6}, {4, 18, 16, 10, 4, 12}, {4, 18, 16, 10, 4, 14}, {4, 18, 16, 14, 4, 8}, {4, 18, 16, 14, 4, 10}, {4, 18, 16, 14, 6, 4}, {4, 20, 6, 4, 14, 12}, {4, 20, 6, 4, 14, 14}, {4, 20, 6, 12, 14, 4}, {4, 20, 6, 14, 14, 4}, {4, 20, 8, 4, 12, 12}, {4, 20, 8, 4, 12, 14}, {4, 20, 12, 4, 12, 8}, {4, 20, 12, 4, 14, 6}, {4, 20, 12, 6, 14, 4}, {4, 20, 14, 4, 12, 8}, {4, 20, 14, 4, 14, 6}, {4, 20, 14, 6, 14, 4}, {4, 22, 8, 10, 12, 4}, {4, 22, 8, 12, 12, 4}, {4, 22, 10, 8, 12, 4}, {4, 22, 10, 12, 10, 4}, {4, 22, 12, 8, 12, 4}, {4, 22, 12, 10, 10, 4}, {6, 4, 14, 16, 4, 16}, {6, 4, 14, 16, 4, 18}, {6, 4, 14, 20, 4, 12}, {6, 4, 14, 20, 4, 14}, {6, 4, 16, 14, 4, 16}, {6, 4, 16, 14, 4, 18}, {6, 4, 18, 14, 14, 4}, {6, 4, 18, 14, 16, 4}, {6, 4, 20, 14, 4, 12}, {6, 4, 20, 14, 4, 14}, {6, 4, 20, 14, 12, 4}, {6, 4, 20, 14, 14, 4}, {6, 12, 14, 20, 4, 4}, {6, 14, 4, 4, 16, 16}, {6, 14, 4, 4, 16, 18}, {6, 14, 4, 4, 20, 12}, {6, 14, 4, 4, 20, 14}, {6, 14, 12, 4, 20, 4}, {6, 14, 14, 4, 18, 4}, {6, 14, 14, 4, 20, 4}, {6, 14, 14, 18, 4, 4}, {6, 14, 14, 20, 4, 4}, {6, 14, 16, 4, 18, 4}, {6, 16, 4, 4, 14, 16}, {6, 16, 4, 4, 14, 18}, {6, 16, 14, 18, 4, 4}, {6, 18, 4, 14, 14, 4}, {6, 18, 4, 16, 14, 4}, {6, 20, 4, 4, 14, 12}, {6, 20, 4, 4, 14, 14}, {6, 20, 4, 12, 14, 4}, {6, 20, 4, 14, 14, 4}, {8, 4, 12, 22, 4, 10}, {8, 4, 12, 22, 4, 12}, {8, 4, 16, 14, 18, 4}, {8, 4, 20, 12, 12, 4}, {8, 4, 20, 12, 14, 4}, {8, 4, 22, 12, 4, 10}, {8, 4, 22, 12, 4, 12}, {8, 12, 4, 4, 22, 10}, {8, 12, 4, 4, 22, 12}, {8, 12, 12, 4, 20, 4}, {8, 12, 12, 20, 4, 4}, {8, 12, 14, 4, 20, 4}, {8, 14, 12, 20, 4, 4}, {8, 14, 18, 4, 16, 4}, {8, 16, 4, 18, 14, 4}, {8, 18, 14, 16, 4, 4}, {8, 20, 4, 12, 12, 4}, {8, 20, 4, 14, 12, 4}, {8, 22, 4, 4, 12, 10}, {8, 22, 4, 4, 12, 12}, {10, 4, 4, 10, 14, 18}, {10, 4, 4, 10, 16, 18}, {10, 4, 4, 12, 18, 16}, {10, 4, 4, 14, 10, 18}, {10, 4, 4, 14, 18, 16}, {10, 4, 4, 16, 10, 18}, {10, 4, 4, 18, 12, 16}, {10, 4, 4, 18, 14, 16}, {10, 4, 10, 12, 4, 22}, {10, 4, 10, 22, 4, 12}, {10, 4, 12, 10, 4, 22}, {10, 4, 12, 22, 4, 8}, {10, 4, 16, 14, 18, 4}, {10, 4, 18, 10, 14, 4}, {10, 4, 18, 10, 16, 4}, {10, 4, 22, 10, 4, 12}, {10, 4, 22, 12, 4, 8}, {10, 10, 4, 4, 12, 22}, {10, 10, 4, 4, 22, 12}, {10, 10, 14, 4, 4, 18}, {10, 10, 14, 4, 18, 4}, {10, 10, 16, 4, 4, 18}, {10, 10, 16, 4, 18, 4}, {10, 12, 4, 4, 10, 22}, {10, 12, 4, 4, 22, 8}, {10, 12, 18, 4, 4, 16}, {10, 14, 10, 4, 4, 18}, {10, 14, 10, 18, 4, 4}, {10, 14, 18, 4, 4, 16}, {10, 14, 18, 4, 16, 4}, {10, 16, 4, 18, 14, 4}, {10, 16, 10, 4, 4, 18}, {10, 16, 10, 18, 4, 4}, {10, 18, 4, 14, 10, 4}, {10, 18, 4, 16, 10, 4}, {10, 18, 12, 4, 4, 16}, {10, 18, 14, 4, 4, 16}, {10, 18, 14, 16, 4, 4}, {10, 22, 4, 4, 10, 12}, {10, 22, 4, 4, 12, 8}, {12, 4, 4, 8, 12, 20}, {12, 4, 4, 8, 14, 20}, {12, 4, 4, 12, 8, 20}, {12, 4, 4, 14, 8, 20}, {12, 4, 8, 10, 4, 22}, {12, 4, 8, 12, 4, 22}, {12, 4, 10, 8, 4, 22}, {12, 4, 10, 22, 4, 10}, {12, 4, 12, 8, 4, 22}, {12, 4, 12, 22, 4, 8}, {12, 4, 14, 20, 4, 6}, {12, 4, 16, 10, 18, 4}, {12, 4, 20, 12, 8, 4}, {12, 4, 20, 14, 4, 6}, {12, 4, 20, 14, 6, 4}, {12, 4, 22, 10, 4, 10}, {12, 4, 22, 12, 4, 8}, {12, 6, 14, 20, 4, 4}, {12, 8, 4, 4, 10, 22}, {12, 8, 4, 4, 12, 22}, {12, 8, 12, 4, 4, 20}, {12, 8, 12, 20, 4, 4}, {12, 8, 14, 4, 4, 20}, {12, 10, 4, 4, 8, 22}, {12, 10, 4, 4, 22, 10}, {12, 10, 18, 4, 16, 4}, {12, 12, 4, 4, 8, 22}, {12, 12, 4, 4, 22, 8}, {12, 12, 8, 4, 4, 20}, {12, 12, 8, 4, 20, 4}, {12, 14, 4, 4, 20, 6}, {12, 14, 6, 4, 20, 4}, {12, 14, 8, 4, 4, 20}, {12, 16, 4, 18, 10, 4}, {12, 18, 10, 16, 4, 4}, {12, 20, 4, 4, 14, 6}, {12, 20, 4, 6, 14, 4}, {12, 20, 4, 8, 12, 4}, {12, 22, 4, 4, 10, 10}, {12, 22, 4, 4, 12, 8}, {14, 4, 4, 6, 12, 20}, {14, 4, 4, 6, 14, 18}, {14, 4, 4, 6, 14, 20}, {14, 4, 4, 6, 16, 18}, {14, 4, 4, 8, 18, 16}, {14, 4, 4, 10, 18, 16}, {14, 4, 4, 12, 6, 20}, {14, 4, 4, 14, 6, 18}, {14, 4, 4, 14, 6, 20}, {14, 4, 4, 16, 6, 18}, {14, 4, 4, 18, 8, 16}, {14, 4, 4, 18, 10, 16}, {14, 4, 6, 12, 4, 20}, {14, 4, 6, 14, 4, 20}, {14, 4, 6, 16, 4, 16}, {14, 4, 6, 18, 4, 16}, {14, 4, 12, 6, 4, 20}, {14, 4, 14, 6, 4, 20}, {14, 4, 14, 20, 4, 6}, {14, 4, 16, 6, 4, 16}, {14, 4, 16, 10, 18, 4}, {14, 4, 18, 6, 4, 16}, {14, 4, 18, 10, 10, 4}, {14, 4, 18, 14, 6, 4}, {14, 4, 20, 12, 8, 4}, {14, 4, 20, 14, 4, 6}, {14, 4, 20, 14, 6, 4}, {14, 6, 4, 4, 12, 20}, {14, 6, 4, 4, 14, 20}, {14, 6, 4, 4, 16, 16}, {14, 6, 4, 4, 18, 16}, {14, 6, 12, 4, 4, 20}, {14, 6, 14, 4, 4, 18}, {14, 6, 14, 4, 4, 20}, {14, 6, 14, 18, 4, 4}, {14, 6, 14, 20, 4, 4}, {14, 6, 16, 4, 4, 18}, {14, 8, 12, 20, 4, 4}, {14, 8, 18, 4, 4, 16}, {14, 10, 10, 4, 18, 4}, {14, 10, 10, 18, 4, 4}, {14, 10, 18, 4, 4, 16}, {14, 10, 18, 4, 16, 4}, {14, 12, 4, 4, 6, 20}, {14, 12, 6, 4, 4, 20}, {14, 12, 8, 4, 20, 4}, {14, 14, 4, 4, 6, 20}, {14, 14, 4, 4, 20, 6}, {14, 14, 6, 4, 4, 18}, {14, 14, 6, 4, 4, 20}, {14, 14, 6, 4, 18, 4}, {14, 14, 6, 4, 20, 4}, {14, 16, 4, 4, 6, 16}, {14, 16, 4, 18, 10, 4}, {14, 16, 6, 4, 4, 18}, {14, 18, 4, 4, 6, 16}, {14, 18, 4, 6, 14, 4}, {14, 18, 4, 10, 10, 4}, {14, 18, 8, 4, 4, 16}, {14, 18, 10, 4, 4, 16}, {14, 18, 10, 16, 4, 4}, {14, 20, 4, 4, 14, 6}, {14, 20, 4, 6, 14, 4}, {14, 20, 4, 8, 12, 4}, {16, 4, 6, 16, 4, 14}, {16, 4, 6, 18, 4, 14}, {16, 4, 8, 4, 18, 14}, {16, 4, 10, 4, 18, 14}, {16, 4, 12, 4, 18, 10}, {16, 4, 14, 4, 18, 10}, {16, 4, 14, 16, 4, 6}, {16, 4, 16, 6, 4, 14}, {16, 4, 16, 14, 4, 6}, {16, 4, 18, 4, 8, 14}, {16, 4, 18, 4, 10, 14}, {16, 4, 18, 4, 12, 10}, {16, 4, 18, 4, 14, 10}, {16, 4, 18, 6, 4, 14}, {16, 4, 18, 10, 10, 4}, {16, 4, 18, 14, 6, 4}, {16, 6, 4, 4, 16, 14}, {16, 6, 4, 4, 18, 14}, {16, 6, 14, 18, 4, 4}, {16, 8, 4, 18, 4, 14}, {16, 10, 4, 18, 4, 14}, {16, 10, 10, 4, 18, 4}, {16, 10, 10, 18, 4, 4}, {16, 12, 4, 18, 4, 10}, {16, 14, 4, 4, 16, 6}, {16, 14, 4, 18, 4, 10}, {16, 14, 6, 4, 18, 4}, {16, 16, 4, 4, 6, 14}, {16, 16, 4, 4, 14, 6}, {16, 18, 4, 4, 6, 14}, {16, 18, 4, 6, 14, 4}, {16, 18, 4, 8, 4, 14}, {16, 18, 4, 10, 4, 14}, {16, 18, 4, 10, 10, 4}, {16, 18, 4, 12, 4, 10}, {16, 18, 4, 14, 4, 10}, {18, 4, 6, 4, 14, 14}, {18, 4, 6, 4, 16, 14}, {18, 4, 10, 4, 14, 10}, {18, 4, 10, 4, 16, 10}, {18, 4, 14, 4, 6, 14}, {18, 4, 14, 4, 10, 10}, {18, 4, 14, 16, 4, 6}, {18, 4, 16, 4, 6, 14}, {18, 4, 16, 4, 10, 10}, {18, 4, 16, 10, 12, 4}, {18, 4, 16, 10, 14, 4}, {18, 4, 16, 14, 4, 6}, {18, 4, 16, 14, 8, 4}, {18, 4, 16, 14, 10, 4}, {18, 6, 4, 14, 4, 14}, {18, 6, 4, 16, 4, 14}, {18, 8, 14, 16, 4, 4}, {18, 10, 4, 14, 4, 10}, {18, 10, 4, 16, 4, 10}, {18, 10, 12, 4, 16, 4}, {18, 10, 14, 4, 16, 4}, {18, 10, 14, 16, 4, 4}, {18, 12, 10, 16, 4, 4}, {18, 14, 4, 4, 16, 6}, {18, 14, 4, 6, 4, 14}, {18, 14, 4, 10, 4, 10}, {18, 14, 8, 4, 16, 4}, {18, 14, 10, 4, 16, 4}, {18, 14, 10, 16, 4, 4}, {18, 16, 4, 4, 14, 6}, {18, 16, 4, 6, 4, 14}, {18, 16, 4, 8, 14, 4}, {18, 16, 4, 10, 4, 10}, {18, 16, 4, 10, 14, 4}, {18, 16, 4, 12, 10, 4}, {18, 16, 4, 14, 10, 4}, {20, 4, 6, 4, 12, 14}, {20, 4, 6, 4, 14, 14}, {20, 4, 6, 12, 4, 14}, {20, 4, 6, 14, 4, 14}, {20, 4, 8, 4, 12, 12}, {20, 4, 8, 4, 14, 12}, {20, 4, 12, 4, 6, 14}, {20, 4, 12, 4, 8, 12}, {20, 4, 12, 6, 4, 14}, {20, 4, 14, 4, 6, 14}, {20, 4, 14, 4, 8, 12}, {20, 4, 14, 6, 4, 14}, {20, 6, 4, 4, 12, 14}, {20, 6, 4, 4, 14, 14}, {20, 6, 4, 12, 4, 14}, {20, 6, 4, 14, 4, 14}, {20, 8, 4, 12, 4, 12}, {20, 8, 4, 14, 4, 12}, {20, 12, 4, 4, 6, 14}, {20, 12, 4, 6, 4, 14}, {20, 12, 4, 8, 4, 12}, {20, 14, 4, 4, 6, 14}, {20, 14, 4, 6, 4, 14}, {20, 14, 4, 8, 4, 12}, {22, 4, 8, 10, 4, 12}, {22, 4, 8, 12, 4, 12}, {22, 4, 10, 8, 4, 12}, {22, 4, 10, 12, 4, 10}, {22, 4, 12, 8, 4, 12}, {22, 4, 12, 10, 4, 10}, {22, 8, 4, 4, 10, 12}, {22, 8, 4, 4, 12, 12}, {22, 10, 4, 4, 8, 12}, {22, 10, 4, 4, 12, 10}, {22, 12, 4, 4, 8, 12}, {22, 12, 4, 4, 10, 10}, {2, 6, 10, 16, 18, 10}, {2, 6, 10, 18, 12, 16}, {2, 6, 12, 18, 14, 16}, {2, 6, 12, 20, 10, 14}, {2, 6, 12, 20, 12, 14}, {2, 6, 14, 16, 16, 6}, {2, 6, 14, 16, 18, 6}, {2, 6, 14, 16, 18, 10}, {2, 6, 14, 18, 8, 16}, {2, 6, 14, 18, 12, 16}, {2, 6, 14, 20, 8, 14}, {2, 6, 14, 20, 10, 14}, {2, 6, 14, 20, 12, 6}, {2, 6, 14, 20, 14, 6}, {2, 6, 14, 20, 14, 10}, {2, 6, 16, 18, 6, 12}, {2, 6, 16, 18, 6, 14}, {2, 6, 16, 20, 6, 10}, {2, 6, 16, 20, 6, 12}, {2, 6, 16, 20, 10, 6}, {2, 6, 16, 20, 12, 6}, {2, 6, 16, 20, 12, 10}, {2, 6, 18, 16, 6, 12}, {2, 6, 18, 16, 6, 14}, {2, 6, 20, 16, 6, 10}, {2, 6, 20, 16, 6, 12}, {2, 6, 20, 16, 10, 6}, {2, 6, 20, 16, 12, 6}, {2, 6, 20, 16, 12, 10}, {2, 8, 8, 14, 18, 10}, {2, 8, 8, 14, 18, 16}, {2, 8, 8, 18, 14, 10}, {2, 8, 8, 18, 14, 16}, {2, 8, 10, 18, 14, 16}, {2, 8, 10, 20, 12, 14}, {2, 8, 12, 22, 10, 6}, {2, 8, 12, 22, 10, 10}, {2, 8, 12, 22, 12, 6}, {2, 8, 12, 22, 12, 10}, {2, 8, 14, 18, 8, 16}, {2, 8, 14, 18, 10, 16}, {2, 8, 14, 20, 8, 14}, {2, 8, 14, 22, 8, 6}, {2, 8, 14, 22, 8, 10}, {2, 8, 14, 22, 10, 6}, {2, 8, 14, 22, 10, 10}, {2, 8, 18, 14, 6, 16}, {2, 8, 18, 14, 8, 16}, {2, 8, 20, 14, 6, 14}, {2, 8, 20, 14, 8, 14}, {2, 8, 22, 14, 8, 6}, {2, 8, 22, 14, 8, 10}, {2, 8, 22, 14, 10, 6}, {2, 8, 22, 14, 10, 10}, {2, 10, 6, 12, 18, 16}, {2, 10, 6, 18, 16, 10}, {2, 10, 8, 12, 20, 14}, {2, 10, 8, 14, 18, 16}, {2, 10, 10, 12, 22, 6}, {2, 10, 10, 12, 22, 10}, {2, 10, 10, 22, 12, 6}, {2, 10, 10, 22, 12, 10}, {2, 10, 14, 22, 8, 6}, {2, 10, 14, 22, 8, 10}, {2, 10, 16, 20, 6, 6}, {2, 10, 18, 14, 8, 16}, {2, 10, 20, 12, 6, 14}, {2, 10, 20, 14, 6, 14}, {2, 10, 20, 16, 6, 6}, {2, 10, 22, 12, 8, 6}, {2, 10, 22, 12, 8, 10}, {2, 10, 22, 14, 8, 6}, {2, 10, 22, 14, 8, 10}, {2, 12, 6, 10, 20, 14}, {2, 12, 6, 12, 20, 14}, {2, 12, 6, 14, 18, 16}, {2, 12, 8, 10, 22, 6}, {2, 12, 8, 10, 22, 10}, {2, 12, 8, 12, 22, 6}, {2, 12, 8, 12, 22, 10}, {2, 12, 16, 20, 6, 6}, {2, 12, 16, 20, 6, 10}, {2, 12, 18, 10, 6, 16}, {2, 12, 18, 14, 6, 16}, {2, 12, 20, 10, 8, 14}, {2, 12, 20, 12, 6, 14}, {2, 12, 20, 14, 6, 6}, {2, 12, 20, 16, 6, 6}, {2, 12, 20, 16, 6, 10}, {2, 12, 22, 10, 10, 6}, {2, 12, 22, 10, 10, 10}, {2, 12, 22, 12, 8, 6}, {2, 12, 22, 12, 8, 10}, {2, 14, 6, 8, 18, 16}, {2, 14, 6, 8, 20, 14}, {2, 14, 6, 10, 20, 14}, {2, 14, 6, 12, 18, 16}, {2, 14, 6, 12, 20, 6}, {2, 14, 6, 14, 20, 6}, {2, 14, 6, 14, 20, 10}, {2, 14, 6, 16, 16, 6}, {2, 14, 6, 18, 16, 6}, {2, 14, 6, 18, 16, 10}, {2, 14, 8, 8, 18, 16}, {2, 14, 8, 8, 20, 14}, {2, 14, 8, 8, 22, 6}, {2, 14, 8, 8, 22, 10}, {2, 14, 8, 10, 18, 16}, {2, 14, 8, 10, 22, 6}, {2, 14, 8, 10, 22, 10}, {2, 14, 10, 8, 22, 6}, {2, 14, 10, 8, 22, 10}, {2, 14, 18, 8, 8, 10}, {2, 14, 18, 8, 8, 16}, {2, 14, 18, 10, 8, 16}, {2, 14, 18, 12, 6, 16}, {2, 14, 20, 14, 6, 6}, {2, 14, 20, 14, 6, 10}, {2, 16, 6, 6, 18, 12}, {2, 16, 6, 6, 18, 14}, {2, 16, 6, 6, 20, 10}, {2, 16, 6, 6, 20, 12}, {2, 16, 6, 10, 20, 6}, {2, 16, 6, 12, 20, 6}, {2, 16, 6, 12, 20, 10}, {2, 16, 10, 6, 20, 6}, {2, 16, 12, 6, 20, 6}, {2, 16, 12, 6, 20, 10}, {2, 16, 16, 6, 14, 6}, {2, 16, 16, 14, 6, 6}, {2, 16, 18, 6, 10, 10}, {2, 16, 18, 6, 14, 6}, {2, 16, 18, 6, 14, 10}, {2, 18, 6, 6, 16, 12}, {2, 18, 6, 6, 16, 14}, {2, 18, 8, 6, 14, 16}, {2, 18, 8, 8, 14, 16}, {2, 18, 10, 8, 14, 16}, {2, 18, 12, 6, 10, 16}, {2, 18, 12, 6, 14, 16}, {2, 18, 14, 6, 12, 16}, {2, 18, 14, 8, 8, 10}, {2, 18, 14, 8, 8, 16}, {2, 18, 14, 8, 10, 16}, {2, 18, 16, 10, 6, 10}, {2, 18, 16, 14, 6, 6}, {2, 18, 16, 14, 6, 10}, {2, 20, 6, 6, 16, 10}, {2, 20, 6, 6, 16, 12}, {2, 20, 6, 10, 16, 6}, {2, 20, 6, 12, 16, 6}, {2, 20, 6, 12, 16, 10}, {2, 20, 8, 6, 14, 14}, {2, 20, 8, 8, 14, 14}, {2, 20, 10, 6, 12, 14}, {2, 20, 10, 6, 14, 14}, {2, 20, 10, 6, 16, 6}, {2, 20, 12, 6, 12, 14}, {2, 20, 12, 6, 14, 6}, {2, 20, 12, 6, 16, 6}, {2, 20, 12, 6, 16, 10}, {2, 20, 12, 8, 10, 14}, {2, 20, 14, 6, 14, 6}, {2, 20, 14, 6, 14, 10}, {2, 22, 8, 8, 14, 6}, {2, 22, 8, 8, 14, 10}, {2, 22, 8, 10, 14, 6}, {2, 22, 8, 10, 14, 10}, {2, 22, 10, 8, 12, 6}, {2, 22, 10, 8, 12, 10}, {2, 22, 10, 8, 14, 6}, {2, 22, 10, 8, 14, 10}, {2, 22, 12, 8, 12, 6}, {2, 22, 12, 8, 12, 10}, {2, 22, 12, 10, 10, 6}, {2, 22, 12, 10, 10, 10}, {6, 2, 10, 16, 10, 18}, {6, 2, 10, 18, 16, 12}, {6, 2, 12, 18, 16, 14}, {6, 2, 12, 20, 14, 10}, {6, 2, 12, 20, 14, 12}, {6, 2, 14, 16, 6, 16}, {6, 2, 14, 16, 6, 18}, {6, 2, 14, 16, 10, 18}, {6, 2, 14, 18, 16, 8}, {6, 2, 14, 18, 16, 12}, {6, 2, 14, 20, 6, 12}, {6, 2, 14, 20, 6, 14}, {6, 2, 14, 20, 10, 14}, {6, 2, 14, 20, 14, 8}, {6, 2, 14, 20, 14, 10}, {6, 2, 16, 18, 12, 6}, {6, 2, 16, 18, 14, 6}, {6, 2, 16, 20, 6, 10}, {6, 2, 16, 20, 6, 12}, {6, 2, 16, 20, 10, 6}, {6, 2, 16, 20, 10, 12}, {6, 2, 16, 20, 12, 6}, {6, 2, 18, 16, 12, 6}, {6, 2, 18, 16, 14, 6}, {6, 2, 20, 16, 6, 10}, {6, 2, 20, 16, 6, 12}, {6, 2, 20, 16, 10, 6}, {6, 2, 20, 16, 10, 12}, {6, 2, 20, 16, 12, 6}, {6, 6, 16, 14, 2, 16}, {6, 6, 16, 14, 2, 18}, {6, 6, 16, 14, 16, 2}, {6, 6, 16, 14, 18, 2}, {6, 6, 16, 20, 2, 10}, {6, 6, 16, 20, 2, 12}, {6, 6, 16, 20, 10, 2}, {6, 6, 16, 20, 12, 2}, {6, 6, 20, 14, 2, 12}, {6, 6, 20, 14, 2, 14}, {6, 6, 20, 14, 12, 2}, {6, 6, 20, 14, 14, 2}, {6, 6, 20, 16, 2, 10}, {6, 6, 20, 16, 2, 12}, {6, 6, 20, 16, 10, 2}, {6, 6, 20, 16, 12, 2}, {6, 8, 14, 22, 8, 2}, {6, 8, 14, 22, 10, 2}, {6, 8, 22, 12, 10, 2}, {6, 8, 22, 12, 12, 2}, {6, 8, 22, 14, 8, 2}, {6, 8, 22, 14, 10, 2}, {6, 10, 2, 10, 16, 18}, {6, 10, 2, 16, 18, 12}, {6, 10, 12, 10, 22, 2}, {6, 10, 12, 22, 8, 2}, {6, 10, 14, 22, 8, 2}, {6, 10, 16, 10, 2, 18}, {6, 10, 16, 14, 2, 18}, {6, 10, 16, 20, 2, 6}, {6, 10, 16, 20, 2, 12}, {6, 10, 16, 20, 6, 2}, {6, 10, 20, 14, 2, 14}, {6, 10, 20, 16, 2, 6}, {6, 10, 20, 16, 2, 12}, {6, 10, 20, 16, 6, 2}, {6, 10, 22, 10, 12, 2}, {6, 10, 22, 14, 8, 2}, {6, 12, 2, 14, 20, 10}, {6, 12, 2, 14, 20, 12}, {6, 12, 2, 16, 18, 14}, {6, 12, 10, 8, 22, 2}, {6, 12, 10, 22, 10, 2}, {6, 12, 12, 8, 22, 2}, {6, 12, 12, 22, 8, 2}, {6, 12, 14, 20, 6, 2}, {6, 12, 16, 18, 2, 6}, {6, 12, 16, 20, 2, 6}, {6, 12, 16, 20, 6, 2}, {6, 12, 18, 16, 2, 6}, {6, 12, 20, 16, 2, 6}, {6, 12, 20, 16, 6, 2}, {6, 14, 2, 6, 16, 16}, {6, 14, 2, 6, 16, 18}, {6, 14, 2, 6, 20, 12}, {6, 14, 2, 6, 20, 14}, {6, 14, 2, 10, 16, 18}, {6, 14, 2, 10, 20, 14}, {6, 14, 2, 14, 20, 8}, {6, 14, 2, 14, 20, 10}, {6, 14, 2, 16, 18, 8}, {6, 14, 2, 16, 18, 12}, {6, 14, 8, 8, 22, 2}, {6, 14, 8, 10, 22, 2}, {6, 14, 10, 8, 22, 2}, {6, 14, 12, 6, 20, 2}, {6, 14, 14, 6, 20, 2}, {6, 14, 14, 20, 6, 2}, {6, 14, 16, 6, 16, 2}, {6, 14, 16, 18, 2, 6}, {6, 14, 18, 6, 16, 2}, {6, 14, 18, 16, 2, 6}, {6, 14, 20, 12, 2, 10}, {6, 14, 20, 12, 2, 12}, {6, 14, 20, 14, 2, 8}, {6, 14, 20, 14, 2, 10}, {6, 16, 2, 6, 20, 10}, {6, 16, 2, 6, 20, 12}, {6, 16, 2, 10, 20, 6}, {6, 16, 2, 10, 20, 12}, {6, 16, 2, 12, 18, 6}, {6, 16, 2, 12, 20, 6}, {6, 16, 2, 14, 18, 6}, {6, 16, 6, 2, 14, 16}, {6, 16, 6, 2, 14, 18}, {6, 16, 6, 2, 20, 10}, {6, 16, 6, 2, 20, 12}, {6, 16, 6, 10, 20, 2}, {6, 16, 6, 12, 20, 2}, {6, 16, 6, 16, 14, 2}, {6, 16, 6, 18, 14, 2}, {6, 16, 10, 2, 10, 18}, {6, 16, 10, 2, 14, 18}, {6, 16, 10, 2, 20, 6}, {6, 16, 10, 2, 20, 12}, {6, 16, 10, 6, 20, 2}, {6, 16, 12, 2, 18, 6}, {6, 16, 12, 2, 20, 6}, {6, 16, 12, 6, 20, 2}, {6, 16, 14, 2, 18, 6}, {6, 16, 14, 16, 6, 2}, {6, 16, 18, 10, 2, 12}, {6, 16, 18, 12, 2, 14}, {6, 16, 18, 14, 2, 8}, {6, 16, 18, 14, 2, 12}, {6, 18, 2, 12, 16, 6}, {6, 18, 2, 14, 16, 6}, {6, 18, 12, 2, 16, 6}, {6, 18, 14, 2, 16, 6}, {6, 18, 14, 16, 6, 2}, {6, 18, 16, 2, 10, 12}, {6, 18, 16, 2, 12, 14}, {6, 18, 16, 2, 14, 8}, {6, 18, 16, 2, 14, 12}, {6, 20, 2, 6, 16, 10}, {6, 20, 2, 6, 16, 12}, {6, 20, 2, 10, 16, 6}, {6, 20, 2, 10, 16, 12}, {6, 20, 2, 12, 16, 6}, {6, 20, 6, 2, 14, 12}, {6, 20, 6, 2, 14, 14}, {6, 20, 6, 2, 16, 10}, {6, 20, 6, 2, 16, 12}, {6, 20, 6, 10, 16, 2}, {6, 20, 6, 12, 14, 2}, {6, 20, 6, 12, 16, 2}, {6, 20, 6, 14, 14, 2}, {6, 20, 10, 2, 14, 14}, {6, 20, 10, 2, 16, 6}, {6, 20, 10, 2, 16, 12}, {6, 20, 10, 6, 16, 2}, {6, 20, 12, 2, 16, 6}, {6, 20, 12, 6, 16, 2}, {6, 20, 14, 2, 12, 10}, {6, 20, 14, 2, 12, 12}, {6, 20, 14, 2, 14, 8}, {6, 20, 14, 2, 14, 10}, {6, 22, 8, 8, 14, 2}, {6, 22, 8, 10, 12, 2}, {6, 22, 8, 10, 14, 2}, {6, 22, 8, 12, 12, 2}, {6, 22, 10, 8, 14, 2}, {6, 22, 10, 12, 10, 2}, {8, 2, 8, 14, 10, 18}, {8, 2, 8, 14, 16, 18}, {8, 2, 8, 18, 10, 14}, {8, 2, 8, 18, 16, 14}, {8, 2, 10, 18, 16, 14}, {8, 2, 10, 20, 14, 12}, {8, 2, 12, 22, 6, 10}, {8, 2, 12, 22, 6, 12}, {8, 2, 12, 22, 10, 10}, {8, 2, 12, 22, 10, 12}, {8, 2, 14, 18, 16, 8}, {8, 2, 14, 18, 16, 10}, {8, 2, 14, 20, 14, 8}, {8, 2, 14, 22, 6, 8}, {8, 2, 14, 22, 6, 10}, {8, 2, 14, 22, 10, 8}, {8, 2, 14, 22, 10, 10}, {8, 2, 18, 14, 16, 6}, {8, 2, 18, 14, 16, 8}, {8, 2, 20, 14, 14, 6}, {8, 2, 20, 14, 14, 8}, {8, 2, 22, 14, 6, 8}, {8, 2, 22, 14, 6, 10}, {8, 2, 22, 14, 10, 8}, {8, 2, 22, 14, 10, 10}, {8, 6, 14, 22, 2, 8}, {8, 6, 14, 22, 2, 10}, {8, 6, 22, 12, 2, 10}, {8, 6, 22, 12, 2, 12}, {8, 6, 22, 14, 2, 8}, {8, 6, 22, 14, 2, 10}, {8, 8, 2, 10, 14, 18}, {8, 8, 2, 10, 18, 14}, {8, 8, 2, 16, 14, 18}, {8, 8, 2, 16, 18, 14}, {8, 10, 2, 14, 20, 12}, {8, 10, 2, 16, 18, 14}, {8, 10, 14, 8, 2, 18}, {8, 10, 14, 22, 2, 8}, {8, 10, 14, 22, 2, 10}, {8, 10, 18, 8, 2, 14}, {8, 10, 22, 12, 2, 10}, {8, 10, 22, 12, 2, 12}, {8, 10, 22, 14, 2, 8}, {8, 10, 22, 14, 2, 10}, {8, 12, 2, 6, 22, 10}, {8, 12, 2, 6, 22, 12}, {8, 12, 2, 10, 22, 10}, {8, 12, 2, 10, 22, 12}, {8, 14, 2, 6, 22, 8}, {8, 14, 2, 6, 22, 10}, {8, 14, 2, 10, 22, 8}, {8, 14, 2, 10, 22, 10}, {8, 14, 2, 14, 20, 8}, {8, 14, 2, 16, 18, 8}, {8, 14, 2, 16, 18, 10}, {8, 14, 6, 2, 22, 8}, {8, 14, 6, 2, 22, 10}, {8, 14, 10, 2, 8, 18}, {8, 14, 10, 2, 22, 8}, {8, 14, 10, 2, 22, 10}, {8, 14, 14, 2, 20, 6}, {8, 14, 14, 2, 20, 8}, {8, 14, 14, 20, 2, 6}, {8, 14, 14, 20, 2, 8}, {8, 14, 16, 2, 8, 18}, {8, 14, 16, 2, 18, 6}, {8, 14, 16, 2, 18, 8}, {8, 14, 20, 10, 2, 12}, {8, 14, 20, 14, 2, 8}, {8, 16, 14, 8, 2, 18}, {8, 16, 14, 18, 2, 6}, {8, 16, 14, 18, 2, 8}, {8, 16, 18, 8, 2, 14}, {8, 16, 18, 10, 2, 14}, {8, 16, 18, 14, 2, 8}, {8, 16, 18, 14, 2, 10}, {8, 18, 2, 16, 14, 6}, {8, 18, 2, 16, 14, 8}, {8, 18, 10, 2, 8, 14}, {8, 18, 16, 2, 8, 14}, {8, 18, 16, 2, 10, 14}, {8, 18, 16, 2, 14, 8}, {8, 18, 16, 2, 14, 10}, {8, 20, 2, 14, 14, 6}, {8, 20, 2, 14, 14, 8}, {8, 20, 14, 2, 10, 12}, {8, 20, 14, 2, 14, 8}, {8, 22, 2, 6, 14, 8}, {8, 22, 2, 6, 14, 10}, {8, 22, 2, 10, 14, 8}, {8, 22, 2, 10, 14, 10}, {8, 22, 6, 2, 12, 10}, {8, 22, 6, 2, 12, 12}, {8, 22, 6, 2, 14, 8}, {8, 22, 6, 2, 14, 10}, {8, 22, 10, 2, 12, 10}, {8, 22, 10, 2, 12, 12}, {8, 22, 10, 2, 14, 8}, {8, 22, 10, 2, 14, 10}, {10, 2, 6, 12, 16, 18}, {10, 2, 6, 18, 10, 16}, {10, 2, 8, 12, 14, 20}, {10, 2, 8, 14, 16, 18}, {10, 2, 10, 12, 6, 22}, {10, 2, 10, 12, 10, 22}, {10, 2, 10, 22, 6, 12}, {10, 2, 10, 22, 10, 12}, {10, 2, 14, 22, 6, 8}, {10, 2, 14, 22, 10, 8}, {10, 2, 16, 20, 6, 6}, {10, 2, 18, 14, 16, 8}, {10, 2, 20, 12, 14, 6}, {10, 2, 20, 14, 14, 6}, {10, 2, 20, 16, 6, 6}, {10, 2, 22, 12, 6, 8}, {10, 2, 22, 12, 10, 8}, {10, 2, 22, 14, 6, 8}, {10, 2, 22, 14, 10, 8}, {10, 6, 2, 10, 18, 16}, {10, 6, 2, 16, 12, 18}, {10, 6, 12, 10, 2, 22}, {10, 6, 12, 22, 2, 8}, {10, 6, 14, 22, 2, 8}, {10, 6, 16, 10, 18, 2}, {10, 6, 16, 14, 18, 2}, {10, 6, 16, 20, 2, 6}, {10, 6, 16, 20, 6, 2}, {10, 6, 16, 20, 12, 2}, {10, 6, 20, 14, 14, 2}, {10, 6, 20, 16, 2, 6}, {10, 6, 20, 16, 6, 2}, {10, 6, 20, 16, 12, 2}, {10, 6, 22, 10, 2, 12}, {10, 6, 22, 14, 2, 8}, {10, 8, 2, 14, 12, 20}, {10, 8, 2, 16, 14, 18}, {10, 8, 14, 8, 18, 2}, {10, 8, 14, 22, 8, 2}, {10, 8, 14, 22, 10, 2}, {10, 8, 18, 8, 14, 2}, {10, 8, 22, 12, 10, 2}, {10, 8, 22, 12, 12, 2}, {10, 8, 22, 14, 8, 2}, {10, 8, 22, 14, 10, 2}, {10, 10, 2, 6, 12, 22}, {10, 10, 2, 6, 22, 12}, {10, 10, 2, 10, 12, 22}, {10, 10, 2, 10, 22, 12}, {10, 10, 12, 10, 2, 22}, {10, 10, 12, 10, 22, 2}, {10, 10, 12, 22, 2, 8}, {10, 10, 12, 22, 8, 2}, {10, 10, 14, 22, 2, 8}, {10, 10, 14, 22, 8, 2}, {10, 10, 18, 6, 2, 16}, {10, 10, 18, 6, 16, 2}, {10, 10, 22, 10, 2, 12}, {10, 10, 22, 10, 12, 2}, {10, 10, 22, 14, 2, 8}, {10, 10, 22, 14, 8, 2}, {10, 12, 6, 2, 10, 22}, {10, 12, 6, 2, 22, 8}, {10, 12, 10, 2, 10, 22}, {10, 12, 10, 2, 22, 8}, {10, 12, 10, 8, 22, 2}, {10, 12, 10, 22, 10, 2}, {10, 12, 12, 8, 22, 2}, {10, 12, 12, 22, 8, 2}, {10, 12, 14, 2, 8, 20}, {10, 12, 14, 2, 20, 6}, {10, 12, 16, 2, 6, 18}, {10, 12, 16, 20, 6, 2}, {10, 12, 20, 16, 6, 2}, {10, 14, 2, 6, 22, 8}, {10, 14, 2, 10, 22, 8}, {10, 14, 6, 2, 22, 8}, {10, 14, 8, 8, 22, 2}, {10, 14, 8, 10, 22, 2}, {10, 14, 8, 18, 8, 2}, {10, 14, 10, 2, 22, 8}, {10, 14, 10, 8, 22, 2}, {10, 14, 12, 8, 2, 20}, {10, 14, 12, 20, 2, 6}, {10, 14, 14, 2, 20, 6}, {10, 14, 14, 6, 20, 2}, {10, 14, 14, 20, 2, 6}, {10, 14, 14, 20, 6, 2}, {10, 14, 16, 2, 8, 18}, {10, 14, 16, 2, 18, 8}, {10, 14, 18, 6, 16, 2}, {10, 16, 2, 6, 20, 6}, {10, 16, 6, 2, 20, 6}, {10, 16, 6, 6, 20, 2}, {10, 16, 6, 12, 20, 2}, {10, 16, 6, 18, 10, 2}, {10, 16, 6, 18, 14, 2}, {10, 16, 12, 6, 2, 18}, {10, 16, 12, 6, 20, 2}, {10, 16, 14, 8, 2, 18}, {10, 16, 14, 18, 2, 8}, {10, 18, 2, 16, 14, 8}, {10, 18, 8, 14, 8, 2}, {10, 18, 10, 2, 6, 16}, {10, 18, 10, 16, 6, 2}, {10, 18, 14, 16, 6, 2}, {10, 20, 2, 6, 16, 6}, {10, 20, 2, 14, 12, 6}, {10, 20, 2, 14, 14, 6}, {10, 20, 6, 2, 16, 6}, {10, 20, 6, 6, 16, 2}, {10, 20, 6, 12, 16, 2}, {10, 20, 6, 14, 14, 2}, {10, 20, 12, 6, 16, 2}, {10, 22, 2, 6, 12, 8}, {10, 22, 2, 6, 14, 8}, {10, 22, 2, 10, 12, 8}, {10, 22, 2, 10, 14, 8}, {10, 22, 6, 2, 10, 12}, {10, 22, 6, 2, 14, 8}, {10, 22, 8, 8, 14, 2}, {10, 22, 8, 10, 12, 2}, {10, 22, 8, 10, 14, 2}, {10, 22, 8, 12, 12, 2}, {10, 22, 10, 2, 10, 12}, {10, 22, 10, 2, 14, 8}, {10, 22, 10, 8, 14, 2}, {10, 22, 10, 12, 10, 2}, {12, 2, 6, 10, 14, 20}, {12, 2, 6, 12, 14, 20}, {12, 2, 6, 14, 16, 18}, {12, 2, 8, 10, 6, 22}, {12, 2, 8, 10, 10, 22}, {12, 2, 8, 12, 6, 22}, {12, 2, 8, 12, 10, 22}, {12, 2, 16, 20, 6, 6}, {12, 2, 16, 20, 10, 6}, {12, 2, 18, 10, 16, 6}, {12, 2, 18, 14, 16, 6}, {12, 2, 20, 10, 14, 8}, {12, 2, 20, 12, 14, 6}, {12, 2, 20, 14, 6, 6}, {12, 2, 20, 16, 6, 6}, {12, 2, 20, 16, 10, 6}, {12, 2, 22, 10, 6, 10}, {12, 2, 22, 10, 10, 10}, {12, 2, 22, 12, 6, 8}, {12, 2, 22, 12, 10, 8}, {12, 6, 2, 14, 10, 20}, {12, 6, 2, 14, 12, 20}, {12, 6, 2, 16, 14, 18}, {12, 6, 10, 8, 2, 22}, {12, 6, 10, 22, 2, 10}, {12, 6, 12, 8, 2, 22}, {12, 6, 12, 22, 2, 8}, {12, 6, 14, 20, 2, 6}, {12, 6, 16, 18, 6, 2}, {12, 6, 16, 20, 2, 6}, {12, 6, 16, 20, 6, 2}, {12, 6, 18, 16, 6, 2}, {12, 6, 20, 16, 2, 6}, {12, 6, 20, 16, 6, 2}, {12, 8, 2, 6, 10, 22}, {12, 8, 2, 6, 12, 22}, {12, 8, 2, 10, 10, 22}, {12, 8, 2, 10, 12, 22}, {12, 10, 6, 2, 8, 22}, {12, 10, 6, 2, 22, 10}, {12, 10, 10, 2, 8, 22}, {12, 10, 10, 2, 22, 10}, {12, 10, 10, 8, 2, 22}, {12, 10, 10, 22, 2, 10}, {12, 10, 12, 8, 2, 22}, {12, 10, 12, 22, 2, 8}, {12, 10, 14, 2, 6, 20}, {12, 10, 14, 2, 20, 8}, {12, 10, 16, 2, 18, 6}, {12, 10, 16, 20, 2, 6}, {12, 10, 20, 16, 2, 6}, {12, 12, 6, 2, 8, 22}, {12, 12, 6, 2, 22, 8}, {12, 12, 10, 2, 8, 22}, {12, 12, 10, 2, 22, 8}, {12, 12, 14, 2, 6, 20}, {12, 12, 14, 2, 20, 6}, {12, 14, 6, 2, 20, 6}, {12, 14, 10, 6, 2, 20}, {12, 14, 10, 20, 2, 8}, {12, 14, 12, 6, 2, 20}, {12, 14, 12, 20, 2, 6}, {12, 14, 16, 2, 6, 18}, {12, 14, 16, 2, 18, 6}, {12, 16, 2, 6, 20, 6}, {12, 16, 2, 10, 20, 6}, {12, 16, 6, 2, 20, 6}, {12, 16, 6, 6, 18, 2}, {12, 16, 6, 6, 20, 2}, {12, 16, 10, 2, 20, 6}, {12, 16, 10, 18, 2, 6}, {12, 16, 14, 6, 2, 18}, {12, 16, 14, 18, 2, 6}, {12, 18, 2, 16, 10, 6}, {12, 18, 2, 16, 14, 6}, {12, 18, 6, 6, 16, 2}, {12, 20, 2, 6, 14, 6}, {12, 20, 2, 6, 16, 6}, {12, 20, 2, 10, 16, 6}, {12, 20, 2, 14, 10, 8}, {12, 20, 2, 14, 12, 6}, {12, 20, 6, 2, 16, 6}, {12, 20, 6, 6, 16, 2}, {12, 20, 10, 2, 16, 6}, {12, 22, 2, 6, 10, 10}, {12, 22, 2, 6, 12, 8}, {12, 22, 2, 10, 10, 10}, {12, 22, 2, 10, 12, 8}, {14, 2, 6, 8, 14, 20}, {14, 2, 6, 8, 16, 18}, {14, 2, 6, 10, 14, 20}, {14, 2, 6, 12, 6, 20}, {14, 2, 6, 12, 16, 18}, {14, 2, 6, 14, 6, 20}, {14, 2, 6, 14, 10, 20}, {14, 2, 6, 16, 6, 16}, {14, 2, 6, 18, 6, 16}, {14, 2, 6, 18, 10, 16}, {14, 2, 8, 8, 6, 22}, {14, 2, 8, 8, 10, 22}, {14, 2, 8, 8, 14, 20}, {14, 2, 8, 8, 16, 18}, {14, 2, 8, 10, 6, 22}, {14, 2, 8, 10, 10, 22}, {14, 2, 8, 10, 16, 18}, {14, 2, 10, 8, 6, 22}, {14, 2, 10, 8, 10, 22}, {14, 2, 18, 8, 10, 8}, {14, 2, 18, 8, 16, 8}, {14, 2, 18, 10, 16, 8}, {14, 2, 18, 12, 16, 6}, {14, 2, 20, 14, 6, 6}, {14, 2, 20, 14, 10, 6}, {14, 6, 2, 6, 12, 20}, {14, 6, 2, 6, 14, 20}, {14, 6, 2, 6, 16, 16}, {14, 6, 2, 6, 18, 16}, {14, 6, 2, 10, 14, 20}, {14, 6, 2, 10, 18, 16}, {14, 6, 2, 14, 8, 20}, {14, 6, 2, 14, 10, 20}, {14, 6, 2, 16, 8, 18}, {14, 6, 2, 16, 12, 18}, {14, 6, 8, 8, 2, 22}, {14, 6, 8, 10, 2, 22}, {14, 6, 10, 8, 2, 22}, {14, 6, 12, 6, 2, 20}, {14, 6, 14, 6, 2, 20}, {14, 6, 14, 20, 2, 6}, {14, 6, 16, 6, 2, 16}, {14, 6, 16, 18, 6, 2}, {14, 6, 18, 6, 2, 16}, {14, 6, 18, 16, 6, 2}, {14, 6, 20, 12, 10, 2}, {14, 6, 20, 12, 12, 2}, {14, 6, 20, 14, 8, 2}, {14, 6, 20, 14, 10, 2}, {14, 8, 2, 6, 8, 22}, {14, 8, 2, 6, 10, 22}, {14, 8, 2, 10, 8, 22}, {14, 8, 2, 10, 10, 22}, {14, 8, 2, 14, 8, 20}, {14, 8, 2, 16, 8, 18}, {14, 8, 2, 16, 10, 18}, {14, 8, 6, 2, 8, 22}, {14, 8, 6, 2, 10, 22}, {14, 8, 10, 2, 8, 22}, {14, 8, 10, 2, 10, 22}, {14, 8, 10, 2, 18, 8}, {14, 8, 14, 2, 6, 20}, {14, 8, 14, 2, 8, 20}, {14, 8, 14, 20, 6, 2}, {14, 8, 14, 20, 8, 2}, {14, 8, 16, 2, 6, 18}, {14, 8, 16, 2, 8, 18}, {14, 8, 16, 2, 18, 8}, {14, 8, 20, 10, 12, 2}, {14, 8, 20, 14, 8, 2}, {14, 10, 2, 6, 8, 22}, {14, 10, 2, 10, 8, 22}, {14, 10, 6, 2, 8, 22}, {14, 10, 8, 8, 2, 22}, {14, 10, 8, 10, 2, 22}, {14, 10, 8, 18, 2, 8}, {14, 10, 10, 2, 8, 22}, {14, 10, 10, 8, 2, 22}, {14, 10, 12, 8, 20, 2}, {14, 10, 12, 20, 6, 2}, {14, 10, 14, 2, 6, 20}, {14, 10, 14, 6, 2, 20}, {14, 10, 14, 20, 2, 6}, {14, 10, 14, 20, 6, 2}, {14, 10, 16, 2, 8, 18}, {14, 10, 16, 2, 18, 8}, {14, 10, 18, 6, 2, 16}, {14, 12, 6, 2, 6, 20}, {14, 12, 10, 6, 20, 2}, {14, 12, 10, 20, 8, 2}, {14, 12, 12, 6, 20, 2}, {14, 12, 12, 20, 6, 2}, {14, 12, 16, 2, 6, 18}, {14, 12, 16, 2, 18, 6}, {14, 14, 6, 2, 6, 20}, {14, 14, 6, 2, 20, 6}, {14, 14, 8, 6, 2, 20}, {14, 14, 8, 6, 20, 2}, {14, 14, 8, 8, 2, 20}, {14, 14, 8, 8, 20, 2}, {14, 14, 10, 2, 6, 20}, {14, 14, 10, 2, 20, 6}, {14, 14, 10, 6, 2, 20}, {14, 14, 10, 6, 20, 2}, {14, 16, 6, 2, 6, 16}, {14, 16, 6, 6, 18, 2}, {14, 16, 8, 6, 2, 18}, {14, 16, 8, 8, 2, 18}, {14, 16, 8, 18, 2, 8}, {14, 16, 10, 8, 2, 18}, {14, 16, 10, 18, 2, 8}, {14, 16, 12, 6, 2, 18}, {14, 16, 12, 18, 2, 6}, {14, 18, 2, 10, 8, 8}, {14, 18, 2, 16, 8, 8}, {14, 18, 2, 16, 10, 8}, {14, 18, 2, 16, 12, 6}, {14, 18, 6, 2, 6, 16}, {14, 18, 6, 6, 16, 2}, {14, 18, 10, 2, 6, 16}, {14, 20, 2, 6, 14, 6}, {14, 20, 2, 10, 14, 6}, {14, 20, 6, 8, 14, 2}, {14, 20, 6, 10, 12, 2}, {14, 20, 6, 10, 14, 2}, {14, 20, 6, 12, 12, 2}, {14, 20, 8, 8, 14, 2}, {14, 20, 8, 12, 10, 2}, {16, 2, 6, 6, 10, 20}, {16, 2, 6, 6, 12, 18}, {16, 2, 6, 6, 12, 20}, {16, 2, 6, 6, 14, 18}, {16, 2, 6, 10, 6, 20}, {16, 2, 6, 12, 6, 20}, {16, 2, 6, 12, 10, 20}, {16, 2, 10, 6, 6, 20}, {16, 2, 12, 6, 6, 20}, {16, 2, 12, 6, 10, 20}, {16, 2, 16, 6, 6, 14}, {16, 2, 16, 14, 6, 6}, {16, 2, 18, 6, 6, 14}, {16, 2, 18, 6, 10, 10}, {16, 2, 18, 6, 10, 14}, {16, 6, 2, 6, 10, 20}, {16, 6, 2, 6, 12, 20}, {16, 6, 2, 10, 6, 20}, {16, 6, 2, 10, 12, 20}, {16, 6, 2, 12, 6, 18}, {16, 6, 2, 12, 6, 20}, {16, 6, 2, 14, 6, 18}, {16, 6, 6, 2, 10, 20}, {16, 6, 6, 2, 12, 20}, {16, 6, 6, 2, 16, 14}, {16, 6, 6, 2, 18, 14}, {16, 6, 6, 10, 2, 20}, {16, 6, 6, 12, 2, 20}, {16, 6, 6, 16, 2, 14}, {16, 6, 6, 18, 2, 14}, {16, 6, 10, 2, 6, 20}, {16, 6, 10, 2, 12, 20}, {16, 6, 10, 2, 18, 10}, {16, 6, 10, 2, 18, 14}, {16, 6, 10, 6, 2, 20}, {16, 6, 12, 2, 6, 18}, {16, 6, 12, 2, 6, 20}, {16, 6, 12, 6, 2, 20}, {16, 6, 14, 2, 6, 18}, {16, 6, 14, 16, 2, 6}, {16, 6, 18, 10, 12, 2}, {16, 6, 18, 12, 14, 2}, {16, 6, 18, 14, 8, 2}, {16, 6, 18, 14, 12, 2}, {16, 8, 14, 8, 18, 2}, {16, 8, 14, 18, 6, 2}, {16, 8, 14, 18, 8, 2}, {16, 8, 18, 8, 14, 2}, {16, 8, 18, 10, 14, 2}, {16, 8, 18, 14, 8, 2}, {16, 8, 18, 14, 10, 2}, {16, 10, 2, 6, 6, 20}, {16, 10, 6, 2, 6, 20}, {16, 10, 6, 6, 2, 20}, {16, 10, 6, 12, 2, 20}, {16, 10, 6, 18, 2, 10}, {16, 10, 6, 18, 2, 14}, {16, 10, 12, 6, 2, 20}, {16, 10, 12, 6, 18, 2}, {16, 10, 14, 8, 18, 2}, {16, 10, 14, 18, 8, 2}, {16, 12, 2, 6, 6, 20}, {16, 12, 2, 10, 6, 20}, {16, 12, 6, 2, 6, 20}, {16, 12, 6, 6, 2, 18}, {16, 12, 6, 6, 2, 20}, {16, 12, 10, 2, 6, 20}, {16, 12, 10, 18, 6, 2}, {16, 12, 14, 6, 18, 2}, {16, 12, 14, 18, 6, 2}, {16, 14, 6, 2, 16, 6}, {16, 14, 6, 6, 2, 18}, {16, 14, 8, 6, 18, 2}, {16, 14, 8, 8, 18, 2}, {16, 14, 8, 18, 8, 2}, {16, 14, 10, 8, 18, 2}, {16, 14, 10, 18, 8, 2}, {16, 14, 12, 6, 18, 2}, {16, 14, 12, 18, 6, 2}, {16, 16, 2, 6, 6, 14}, {16, 16, 2, 6, 14, 6}, {16, 18, 2, 6, 6, 14}, {16, 18, 2, 10, 6, 10}, {16, 18, 2, 10, 6, 14}, {16, 18, 6, 8, 14, 2}, {16, 18, 6, 12, 10, 2}, {16, 18, 6, 12, 14, 2}, {16, 18, 6, 14, 12, 2}, {16, 18, 8, 8, 14, 2}, {16, 18, 8, 10, 14, 2}, {16, 18, 8, 14, 8, 2}, {16, 18, 8, 14, 10, 2}, {18, 2, 6, 6, 12, 16}, {18, 2, 6, 6, 14, 16}, {18, 2, 8, 6, 16, 14}, {18, 2, 8, 8, 16, 14}, {18, 2, 10, 8, 16, 14}, {18, 2, 12, 6, 16, 10}, {18, 2, 12, 6, 16, 14}, {18, 2, 14, 6, 16, 12}, {18, 2, 14, 8, 10, 8}, {18, 2, 14, 8, 16, 8}, {18, 2, 14, 8, 16, 10}, {18, 2, 16, 10, 10, 6}, {18, 2, 16, 14, 6, 6}, {18, 2, 16, 14, 10, 6}, {18, 6, 2, 12, 6, 16}, {18, 6, 2, 14, 6, 16}, {18, 6, 12, 2, 6, 16}, {18, 6, 14, 2, 6, 16}, {18, 6, 14, 16, 2, 6}, {18, 6, 16, 2, 8, 14}, {18, 6, 16, 2, 12, 10}, {18, 6, 16, 2, 12, 14}, {18, 6, 16, 2, 14, 12}, {18, 8, 2, 16, 6, 14}, {18, 8, 2, 16, 8, 14}, {18, 8, 10, 2, 14, 8}, {18, 8, 16, 2, 8, 14}, {18, 8, 16, 2, 10, 14}, {18, 8, 16, 2, 14, 8}, {18, 8, 16, 2, 14, 10}, {18, 10, 2, 16, 8, 14}, {18, 10, 8, 14, 2, 8}, {18, 10, 10, 2, 16, 6}, {18, 10, 10, 16, 2, 6}, {18, 10, 14, 16, 2, 6}, {18, 12, 2, 16, 6, 10}, {18, 12, 2, 16, 6, 14}, {18, 12, 6, 6, 2, 16}, {18, 14, 2, 10, 8, 8}, {18, 14, 2, 16, 6, 12}, {18, 14, 2, 16, 8, 8}, {18, 14, 2, 16, 8, 10}, {18, 14, 6, 2, 16, 6}, {18, 14, 6, 6, 2, 16}, {18, 14, 10, 2, 16, 6}, {18, 16, 2, 6, 14, 6}, {18, 16, 2, 10, 10, 6}, {18, 16, 2, 10, 14, 6}, {18, 16, 6, 8, 2, 14}, {18, 16, 6, 12, 2, 10}, {18, 16, 6, 12, 2, 14}, {18, 16, 6, 14, 2, 12}, {18, 16, 8, 8, 2, 14}, {18, 16, 8, 10, 2, 14}, {18, 16, 8, 14, 2, 8}, {18, 16, 8, 14, 2, 10}, {20, 2, 6, 6, 10, 16}, {20, 2, 6, 6, 12, 16}, {20, 2, 6, 10, 6, 16}, {20, 2, 6, 12, 6, 16}, {20, 2, 6, 12, 10, 16}, {20, 2, 8, 6, 14, 14}, {20, 2, 8, 8, 14, 14}, {20, 2, 10, 6, 6, 16}, {20, 2, 10, 6, 14, 12}, {20, 2, 10, 6, 14, 14}, {20, 2, 12, 6, 6, 14}, {20, 2, 12, 6, 6, 16}, {20, 2, 12, 6, 10, 16}, {20, 2, 12, 6, 14, 12}, {20, 2, 12, 8, 14, 10}, {20, 2, 14, 6, 6, 14}, {20, 2, 14, 6, 10, 14}, {20, 6, 2, 6, 10, 16}, {20, 6, 2, 6, 12, 16}, {20, 6, 2, 10, 6, 16}, {20, 6, 2, 10, 12, 16}, {20, 6, 2, 12, 6, 16}, {20, 6, 6, 2, 10, 16}, {20, 6, 6, 2, 12, 14}, {20, 6, 6, 2, 12, 16}, {20, 6, 6, 2, 14, 14}, {20, 6, 6, 10, 2, 16}, {20, 6, 6, 12, 2, 14}, {20, 6, 6, 12, 2, 16}, {20, 6, 6, 14, 2, 14}, {20, 6, 10, 2, 6, 16}, {20, 6, 10, 2, 12, 16}, {20, 6, 10, 2, 14, 14}, {20, 6, 10, 6, 2, 16}, {20, 6, 12, 2, 6, 16}, {20, 6, 12, 6, 2, 16}, {20, 6, 14, 2, 8, 14}, {20, 6, 14, 2, 10, 12}, {20, 6, 14, 2, 10, 14}, {20, 6, 14, 2, 12, 12}, {20, 8, 2, 14, 6, 14}, {20, 8, 2, 14, 8, 14}, {20, 8, 14, 2, 8, 14}, {20, 8, 14, 2, 12, 10}, {20, 10, 2, 6, 6, 16}, {20, 10, 2, 14, 6, 12}, {20, 10, 2, 14, 6, 14}, {20, 10, 6, 2, 6, 16}, {20, 10, 6, 6, 2, 16}, {20, 10, 6, 12, 2, 16}, {20, 10, 6, 14, 2, 14}, {20, 10, 12, 6, 2, 16}, {20, 12, 2, 6, 6, 14}, {20, 12, 2, 6, 6, 16}, {20, 12, 2, 10, 6, 16}, {20, 12, 2, 14, 6, 12}, {20, 12, 2, 14, 8, 10}, {20, 12, 6, 2, 6, 16}, {20, 12, 6, 6, 2, 16}, {20, 12, 10, 2, 6, 16}, {20, 14, 2, 6, 6, 14}, {20, 14, 2, 10, 6, 14}, {20, 14, 6, 8, 2, 14}, {20, 14, 6, 10, 2, 12}, {20, 14, 6, 10, 2, 14}, {20, 14, 6, 12, 2, 12}, {20, 14, 8, 8, 2, 14}, {20, 14, 8, 12, 2, 10}, {22, 2, 8, 8, 6, 14}, {22, 2, 8, 8, 10, 14}, {22, 2, 8, 10, 6, 14}, {22, 2, 8, 10, 10, 14}, {22, 2, 10, 8, 6, 12}, {22, 2, 10, 8, 6, 14}, {22, 2, 10, 8, 10, 12}, {22, 2, 10, 8, 10, 14}, {22, 2, 12, 8, 6, 12}, {22, 2, 12, 8, 10, 12}, {22, 2, 12, 10, 6, 10}, {22, 2, 12, 10, 10, 10}, {22, 6, 8, 8, 2, 14}, {22, 6, 8, 10, 2, 12}, {22, 6, 8, 10, 2, 14}, {22, 6, 8, 12, 2, 12}, {22, 6, 10, 8, 2, 14}, {22, 6, 10, 12, 2, 10}, {22, 8, 2, 6, 8, 14}, {22, 8, 2, 6, 10, 14}, {22, 8, 2, 10, 8, 14}, {22, 8, 2, 10, 10, 14}, {22, 8, 6, 2, 8, 14}, {22, 8, 6, 2, 10, 12}, {22, 8, 6, 2, 10, 14}, {22, 8, 6, 2, 12, 12}, {22, 8, 10, 2, 8, 14}, {22, 8, 10, 2, 10, 12}, {22, 8, 10, 2, 10, 14}, {22, 8, 10, 2, 12, 12}, {22, 10, 2, 6, 8, 12}, {22, 10, 2, 6, 8, 14}, {22, 10, 2, 10, 8, 12}, {22, 10, 2, 10, 8, 14}, {22, 10, 6, 2, 8, 14}, {22, 10, 6, 2, 12, 10}, {22, 10, 8, 8, 2, 14}, {22, 10, 8, 10, 2, 12}, {22, 10, 8, 10, 2, 14}, {22, 10, 8, 12, 2, 12}, {22, 10, 10, 2, 8, 14}, {22, 10, 10, 2, 12, 10}, {22, 10, 10, 8, 2, 14}, {22, 10, 10, 12, 2, 10}, {22, 12, 2, 6, 8, 12}, {22, 12, 2, 6, 10, 10}, {22, 12, 2, 10, 8, 12}, {22, 12, 2, 10, 10, 10}, {2, 4, 12, 18, 12, 16}, {2, 4, 12, 18, 14, 10}, {2, 4, 12, 18, 14, 16}, {2, 4, 12, 18, 16, 10}, {2, 4, 14, 18, 10, 16}, {2, 4, 14, 18, 12, 16}, {2, 4, 14, 18, 14, 8}, {2, 4, 14, 18, 16, 8}, {2, 4, 16, 18, 8, 12}, {2, 4, 16, 18, 8, 14}, {2, 4, 18, 18, 8, 10}, {2, 4, 18, 18, 8, 12}, {2, 8, 18, 16, 4, 12}, {2, 8, 18, 16, 4, 14}, {2, 8, 18, 18, 4, 10}, {2, 8, 18, 18, 4, 12}, {2, 10, 18, 14, 4, 16}, {2, 12, 4, 12, 18, 16}, {2, 12, 4, 14, 18, 10}, {2, 12, 4, 14, 18, 16}, {2, 12, 4, 16, 18, 10}, {2, 12, 18, 12, 4, 16}, {2, 12, 18, 14, 4, 16}, {2, 14, 4, 10, 18, 16}, {2, 14, 4, 12, 18, 16}, {2, 14, 4, 14, 18, 8}, {2, 14, 4, 16, 18, 8}, {2, 14, 18, 12, 4, 10}, {2, 14, 18, 12, 4, 16}, {2, 14, 18, 14, 4, 8}, {2, 16, 4, 8, 18, 12}, {2, 16, 4, 8, 18, 14}, {2, 16, 18, 12, 4, 10}, {2, 16, 18, 14, 4, 8}, {2, 18, 4, 8, 18, 10}, {2, 18, 4, 8, 18, 12}, {2, 18, 8, 4, 16, 12}, {2, 18, 8, 4, 16, 14}, {2, 18, 8, 4, 18, 10}, {2, 18, 8, 4, 18, 12}, {2, 18, 10, 4, 14, 16}, {2, 18, 12, 4, 12, 16}, {2, 18, 12, 4, 14, 16}, {2, 18, 14, 4, 12, 10}, {2, 18, 14, 4, 12, 16}, {2, 18, 14, 4, 14, 8}, {2, 18, 16, 4, 12, 10}, {2, 18, 16, 4, 14, 8}, {4, 2, 12, 18, 10, 14}, {4, 2, 12, 18, 10, 16}, {4, 2, 12, 18, 16, 12}, {4, 2, 12, 18, 16, 14}, {4, 2, 14, 18, 8, 14}, {4, 2, 14, 18, 8, 16}, {4, 2, 14, 18, 16, 10}, {4, 2, 14, 18, 16, 12}, {4, 2, 16, 18, 12, 8}, {4, 2, 16, 18, 14, 8}, {4, 2, 18, 18, 10, 8}, {4, 2, 18, 18, 12, 8}, {4, 8, 18, 14, 2, 14}, {4, 8, 18, 14, 2, 16}, {4, 10, 18, 12, 2, 14}, {4, 10, 18, 12, 2, 16}, {4, 10, 18, 18, 2, 8}, {4, 12, 2, 10, 18, 14}, {4, 12, 2, 10, 18, 16}, {4, 12, 2, 16, 18, 12}, {4, 12, 2, 16, 18, 14}, {4, 12, 18, 16, 2, 8}, {4, 12, 18, 18, 2, 8}, {4, 14, 2, 8, 18, 14}, {4, 14, 2, 8, 18, 16}, {4, 14, 2, 16, 18, 10}, {4, 14, 2, 16, 18, 12}, {4, 14, 18, 16, 2, 8}, {4, 16, 2, 12, 18, 8}, {4, 16, 2, 14, 18, 8}, {4, 16, 18, 12, 2, 12}, {4, 16, 18, 12, 2, 14}, {4, 16, 18, 14, 2, 10}, {4, 16, 18, 14, 2, 12}, {4, 18, 2, 10, 18, 8}, {4, 18, 2, 12, 18, 8}, {4, 18, 8, 2, 14, 14}, {4, 18, 8, 2, 14, 16}, {4, 18, 10, 2, 12, 14}, {4, 18, 10, 2, 12, 16}, {4, 18, 10, 2, 18, 8}, {4, 18, 12, 2, 16, 8}, {4, 18, 12, 2, 18, 8}, {4, 18, 14, 2, 16, 8}, {4, 18, 16, 2, 12, 12}, {4, 18, 16, 2, 12, 14}, {4, 18, 16, 2, 14, 10}, {4, 18, 16, 2, 14, 12}, {8, 2, 18, 16, 12, 4}, {8, 2, 18, 16, 14, 4}, {8, 2, 18, 18, 10, 4}, {8, 2, 18, 18, 12, 4}, {8, 4, 18, 14, 14, 2}, {8, 4, 18, 14, 16, 2}, {8, 10, 18, 18, 2, 4}, {8, 12, 16, 18, 2, 4}, {8, 12, 18, 18, 2, 4}, {8, 14, 14, 4, 18, 2}, {8, 14, 14, 18, 4, 2}, {8, 14, 16, 4, 18, 2}, {8, 14, 16, 18, 2, 4}, {8, 16, 12, 2, 18, 4}, {8, 16, 14, 2, 18, 4}, {8, 16, 14, 18, 4, 2}, {8, 18, 2, 10, 18, 4}, {8, 18, 2, 12, 16, 4}, {8, 18, 2, 12, 18, 4}, {8, 18, 2, 14, 16, 4}, {8, 18, 4, 14, 14, 2}, {8, 18, 4, 16, 14, 2}, {8, 18, 10, 2, 18, 4}, {8, 18, 12, 2, 18, 4}, {10, 2, 18, 14, 16, 4}, {10, 4, 18, 12, 14, 2}, {10, 4, 18, 12, 16, 2}, {10, 4, 18, 18, 8, 2}, {10, 8, 18, 18, 4, 2}, {10, 12, 14, 4, 18, 2}, {10, 12, 16, 4, 18, 2}, {10, 14, 12, 18, 4, 2}, {10, 14, 16, 2, 18, 4}, {10, 16, 12, 18, 4, 2}, {10, 16, 14, 18, 2, 4}, {10, 18, 2, 16, 14, 4}, {10, 18, 4, 8, 18, 2}, {10, 18, 4, 14, 12, 2}, {10, 18, 4, 16, 12, 2}, {10, 18, 8, 4, 18, 2}, {12, 2, 4, 12, 16, 18}, {12, 2, 4, 14, 10, 18}, {12, 2, 4, 14, 16, 18}, {12, 2, 4, 16, 10, 18}, {12, 2, 18, 12, 16, 4}, {12, 2, 18, 14, 16, 4}, {12, 4, 2, 10, 14, 18}, {12, 4, 2, 10, 16, 18}, {12, 4, 2, 16, 12, 18}, {12, 4, 2, 16, 14, 18}, {12, 4, 18, 16, 8, 2}, {12, 4, 18, 18, 8, 2}, {12, 8, 16, 18, 4, 2}, {12, 8, 18, 18, 4, 2}, {12, 10, 14, 4, 2, 18}, {12, 10, 16, 4, 2, 18}, {12, 12, 16, 2, 4, 18}, {12, 12, 16, 2, 18, 4}, {12, 14, 10, 2, 4, 18}, {12, 14, 16, 2, 4, 18}, {12, 14, 16, 2, 18, 4}, {12, 16, 8, 4, 18, 2}, {12, 16, 10, 2, 4, 18}, {12, 16, 12, 4, 2, 18}, {12, 16, 12, 18, 2, 4}, {12, 16, 14, 4, 2, 18}, {12, 16, 14, 18, 2, 4}, {12, 18, 2, 16, 12, 4}, {12, 18, 2, 16, 14, 4}, {12, 18, 4, 8, 16, 2}, {12, 18, 4, 8, 18, 2}, {12, 18, 8, 4, 18, 2}, {14, 2, 4, 10, 16, 18}, {14, 2, 4, 12, 16, 18}, {14, 2, 4, 14, 8, 18}, {14, 2, 4, 16, 8, 18}, {14, 2, 18, 12, 10, 4}, {14, 2, 18, 12, 16, 4}, {14, 2, 18, 14, 8, 4}, {14, 4, 2, 8, 14, 18}, {14, 4, 2, 8, 16, 18}, {14, 4, 2, 16, 10, 18}, {14, 4, 2, 16, 12, 18}, {14, 4, 18, 16, 8, 2}, {14, 8, 14, 4, 2, 18}, {14, 8, 14, 18, 2, 4}, {14, 8, 16, 4, 2, 18}, {14, 8, 16, 18, 4, 2}, {14, 10, 12, 18, 2, 4}, {14, 10, 16, 2, 4, 18}, {14, 12, 10, 2, 18, 4}, {14, 12, 16, 2, 4, 18}, {14, 12, 16, 2, 18, 4}, {14, 14, 8, 2, 4, 18}, {14, 14, 8, 2, 18, 4}, {14, 16, 8, 2, 4, 18}, {14, 16, 8, 4, 18, 2}, {14, 16, 10, 4, 2, 18}, {14, 16, 12, 4, 2, 18}, {14, 16, 12, 18, 2, 4}, {14, 18, 2, 8, 14, 4}, {14, 18, 2, 10, 12, 4}, {14, 18, 2, 16, 12, 4}, {14, 18, 4, 8, 16, 2}, {16, 2, 4, 8, 12, 18}, {16, 2, 4, 8, 14, 18}, {16, 2, 18, 12, 10, 4}, {16, 2, 18, 14, 8, 4}, {16, 4, 2, 12, 8, 18}, {16, 4, 2, 14, 8, 18}, {16, 4, 18, 12, 12, 2}, {16, 4, 18, 12, 14, 2}, {16, 4, 18, 14, 10, 2}, {16, 4, 18, 14, 12, 2}, {16, 8, 12, 2, 4, 18}, {16, 8, 14, 2, 4, 18}, {16, 8, 14, 18, 2, 4}, {16, 10, 12, 18, 2, 4}, {16, 10, 14, 18, 4, 2}, {16, 12, 8, 4, 2, 18}, {16, 12, 10, 2, 18, 4}, {16, 12, 12, 4, 18, 2}, {16, 12, 12, 18, 4, 2}, {16, 12, 14, 4, 18, 2}, {16, 12, 14, 18, 4, 2}, {16, 14, 8, 2, 18, 4}, {16, 14, 8, 4, 2, 18}, {16, 14, 10, 4, 18, 2}, {16, 14, 12, 4, 18, 2}, {16, 14, 12, 18, 4, 2}, {16, 18, 2, 8, 14, 4}, {16, 18, 2, 10, 12, 4}, {16, 18, 4, 10, 14, 2}, {16, 18, 4, 12, 12, 2}, {16, 18, 4, 12, 14, 2}, {16, 18, 4, 14, 12, 2}, {18, 2, 4, 8, 10, 18}, {18, 2, 4, 8, 12, 18}, {18, 2, 8, 4, 10, 18}, {18, 2, 8, 4, 12, 16}, {18, 2, 8, 4, 12, 18}, {18, 2, 8, 4, 14, 16}, {18, 2, 10, 4, 16, 14}, {18, 2, 12, 4, 16, 12}, {18, 2, 12, 4, 16, 14}, {18, 2, 14, 4, 8, 14}, {18, 2, 14, 4, 10, 12}, {18, 2, 14, 4, 16, 12}, {18, 2, 16, 4, 8, 14}, {18, 2, 16, 4, 10, 12}, {18, 4, 2, 10, 8, 18}, {18, 4, 2, 12, 8, 18}, {18, 4, 8, 2, 14, 14}, {18, 4, 8, 2, 16, 14}, {18, 4, 10, 2, 8, 18}, {18, 4, 10, 2, 14, 12}, {18, 4, 10, 2, 16, 12}, {18, 4, 12, 2, 8, 16}, {18, 4, 12, 2, 8, 18}, {18, 4, 14, 2, 8, 16}, {18, 4, 16, 2, 10, 14}, {18, 4, 16, 2, 12, 12}, {18, 4, 16, 2, 12, 14}, {18, 4, 16, 2, 14, 12}, {18, 8, 2, 10, 4, 18}, {18, 8, 2, 12, 4, 16}, {18, 8, 2, 12, 4, 18}, {18, 8, 2, 14, 4, 16}, {18, 8, 4, 14, 2, 14}, {18, 8, 4, 16, 2, 14}, {18, 8, 10, 2, 4, 18}, {18, 8, 12, 2, 4, 18}, {18, 10, 2, 16, 4, 14}, {18, 10, 4, 8, 2, 18}, {18, 10, 4, 14, 2, 12}, {18, 10, 4, 16, 2, 12}, {18, 10, 8, 4, 2, 18}, {18, 12, 2, 16, 4, 12}, {18, 12, 2, 16, 4, 14}, {18, 12, 4, 8, 2, 16}, {18, 12, 4, 8, 2, 18}, {18, 12, 8, 4, 2, 18}, {18, 14, 2, 8, 4, 14}, {18, 14, 2, 10, 4, 12}, {18, 14, 2, 16, 4, 12}, {18, 14, 4, 8, 2, 16}, {18, 16, 2, 8, 4, 14}, {18, 16, 2, 10, 4, 12}, {18, 16, 4, 10, 2, 14}, {18, 16, 4, 12, 2, 12}, {18, 16, 4, 12, 2, 14}, {18, 16, 4, 14, 2, 12}};\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(v1t9bIeq = {\(-x1\) - x2 - x3 - x4 - x5 - x6 \[LessEqual] \(-60\), \(-2\)\ x1 - x2 - x3 - x4 - x5 \[LessEqual] \(-50\), \(-x1\) - 2\ x2 - x3 - x4 - x6 \[LessEqual] \(-50\), \(-x1\) - x2 - 2\ x3 - x5 - x6 \[LessEqual] \(-50\), \(-x1\) - x2 - 2\ x4 - x5 - x6 \[LessEqual] \(-50\), \(-x1\) - x3 - x4 - 2\ x5 - x6 \[LessEqual] \(-50\), \(-x2\) - x3 - x4 - x5 - 2\ x6 \[LessEqual] \(-50\), \(-2\)\ x1 - x2 - x3 - x4 \[LessEqual] \(-32\), \(-2\)\ x1 - x2 - x3 - x5 \[LessEqual] \(-32\), \(-2\)\ x1 - x2 - x4 - x5 \[LessEqual] \(-32\), \(-2\)\ x1 - x3 - x4 - x5 \[LessEqual] \(-32\), \(-x1\) - 2\ x2 - x3 - x4 \[LessEqual] \(-32\), \(-x1\) - 2\ x2 - x3 - x6 \[LessEqual] \(-32\), \(-x1\) - 2\ x2 - x4 - x6 \[LessEqual] \(-32\), \(-x1\) - x2 - 2\ x3 - x5 \[LessEqual] \(-32\), \(-x1\) - x2 - 2\ x3 - x6 \[LessEqual] \(-32\), \(-x1\) - x2 - 2\ x4 - x5 \[LessEqual] \(-32\), \(-x1\) - x2 - 2\ x4 - x6 \[LessEqual] \(-32\), \(-x1\) - 2\ x3 - x5 - x6 \[LessEqual] \(-32\), \(-x1\) - x3 - x4 - 2\ x5 \[LessEqual] \(-32\), \(-x1\) - x3 - 2\ x5 - x6 \[LessEqual] \(-32\), \(-x1\) - 2\ x4 - x5 - x6 \[LessEqual] \(-32\), \(-x1\) - x4 - 2\ x5 - x6 \[LessEqual] \(-32\), \(-2\)\ x2 - x3 - x4 - x6 \[LessEqual] \(-32\), \(-x2\) - 2\ x3 - x5 - x6 \[LessEqual] \(-32\), \(-x2\) - x3 - x4 - 2\ x6 \[LessEqual] \(-32\), \(-x2\) - x3 - x5 - 2\ x6 \[LessEqual] \(-32\), \(-x2\) - 2\ x4 - x5 - x6 \[LessEqual] \(-32\), \(-x2\) - x4 - x5 - 2\ x6 \[LessEqual] \(-32\), \(-x3\) - x4 - 2\ x5 - x6 \[LessEqual] \(-32\), \(-x3\) - x4 - x5 - 2\ x6 \[LessEqual] \(-32\), \(-x1\) - x2 - x3 - x4 \[LessEqual] \(-28\), \(-x1\) - x2 - x3 - x5 \[LessEqual] \(-28\), \(-x1\) - x2 - x3 - x6 \[LessEqual] \(-28\), \(-x1\) - x2 - x4 - x5 \[LessEqual] \(-28\), \(-x1\) - x2 - x4 - x6 \[LessEqual] \(-28\), \(-x1\) - x3 - x4 - x5 \[LessEqual] \(-28\), \(-x1\) - x3 - x5 - x6 \[LessEqual] \(-28\), \(-x1\) - x4 - x5 - x6 \[LessEqual] \(-28\), \(-x2\) - x3 - x4 - x6 \[LessEqual] \(-28\), \(-x2\) - x3 - x5 - x6 \[LessEqual] \(-28\), \(-x2\) - x4 - x5 - x6 \[LessEqual] \(-28\), \(-x3\) - x4 - x5 - x6 \[LessEqual] \(-28\), \(-x1\) - x2 - x4 \[LessEqual] \(-24\), \(-x1\) - x3 - x5 \[LessEqual] \(-24\), \(-x2\) - x3 - x6 \[LessEqual] \(-24\), \(-x4\) - x5 - x6 \[LessEqual] \(-24\), \(-x1\) - x2 - x3 \[LessEqual] \(-18\), \(-x1\) - x4 - x5 \[LessEqual] \(-18\), \(-x2\) - x4 - x6 \[LessEqual] \(-18\), \(-x3\) - x5 - x6 \[LessEqual] \(-18\), \(-2\)\ x1 - x2 - x5 \[LessEqual] \(-16\), \(-2\)\ x1 - x3 - x4 \[LessEqual] \(-16\), \(-x1\) - 2\ x2 - x6 \[LessEqual] \(-16\), \(-x1\) - 2\ x3 - x6 \[LessEqual] \(-16\), \(-x1\) - 2\ x4 - x6 \[LessEqual] \(-16\), \(-x1\) - 2\ x5 - x6 \[LessEqual] \(-16\), \(-2\)\ x2 - x3 - x4 \[LessEqual] \(-16\), \(-x2\) - 2\ x3 - x5 \[LessEqual] \(-16\), \(-x2\) - 2\ x4 - x5 \[LessEqual] \(-16\), \(-x2\) - x5 - 2\ x6 \[LessEqual] \(-16\), \(-x3\) - x4 - 2\ x5 \[LessEqual] \(-16\), \(-x3\) - x4 - 2\ x6 \[LessEqual] \(-16\), \(-x1\) - x2 - x5 \[LessEqual] \(-14\), \(-x1\) - x2 - x6 \[LessEqual] \(-14\), \(-x1\) - x3 - x4 \[LessEqual] \(-14\), \(-x1\) - x3 - x6 \[LessEqual] \(-14\), \(-x1\) - x4 - x6 \[LessEqual] \(-14\), \(-x1\) - x5 - x6 \[LessEqual] \(-14\), \(-x2\) - x3 - x4 \[LessEqual] \(-14\), \(-x2\) - x3 - x5 \[LessEqual] \(-14\), \(-x2\) - x4 - x5 \[LessEqual] \(-14\), \(-x2\) - x5 - x6 \[LessEqual] \(-14\), \(-x3\) - x4 - x5 \[LessEqual] \(-14\), \(-x3\) - x4 - x6 \[LessEqual] \(-14\), \(-x1\) - x6 \[LessEqual] \(-8\), \(-x2\) - x5 \[LessEqual] \(-8\), \(-x3\) - x4 \[LessEqual] \(-8\), \(-x1\) \[LessEqual] 0, \(-x2\) \[LessEqual] 0, \(-x3\) \[LessEqual] 0, \(-x4\) \[LessEqual] 0, \(-x5\) \[LessEqual] 0, \(-x6\) \[LessEqual] 0, \(-x1\) - x2 - x3 + x6 \[LessEqual] 0, \(-x1\) - x2 - x3 + x5 \[LessEqual] 0, \(-x1\) - x2 - x3 + x4 \[LessEqual] 0, \(-x1\) - x4 - x5 + x6 \[LessEqual] 0, \(-x1\) + x3 - x4 - x5 \[LessEqual] 0, \(-x1\) + x2 - x4 - x5 \[LessEqual] 0, \(-x2\) - x4 + x5 - x6 \[LessEqual] 0, \(-x2\) + x3 - x4 - x6 \[LessEqual] 0, \(-x3\) + x4 - x5 - x6 \[LessEqual] 0, x2 - x3 - x5 - x6 \[LessEqual] 0, x1 - x2 - x4 - x6 \[LessEqual] 0, x1 - x3 - x5 - x6 \[LessEqual] 0, \(-x1\) - x2 + x4 - x5 \[LessEqual] 6, \(-x1\) - x2 + x4 - x6 \[LessEqual] 6, \(-x1\) - x2 + x3 - x5 \[LessEqual] 6, \(-x1\) - x2 + x3 - x6 \[LessEqual] 6, \(-x1\) - x3 - x4 + x5 \[LessEqual] 6, \(-x1\) - x3 + x5 - x6 \[LessEqual] 6, \(-x1\) - x4 + x5 - x6 \[LessEqual] 6, \(-x1\) + x4 - x5 - x6 \[LessEqual] 6, \(-x1\) + x3 - x5 - x6 \[LessEqual] 6, \(-x1\) + x2 - x3 - x4 \[LessEqual] 6, \(-x1\) + x2 - x3 - x6 \[LessEqual] 6, \(-x1\) + x2 - x4 - x6 \[LessEqual] 6, \(-x2\) - x3 - x4 + x6 \[LessEqual] 6, \(-x2\) - x3 - x5 + x6 \[LessEqual] 6, \(-x2\) - x4 - x5 + x6 \[LessEqual] 6, \(-x2\) + x4 - x5 - x6 \[LessEqual] 6, \(-x2\) + x3 - x5 - x6 \[LessEqual] 6, \(-x3\) - x4 - x5 + x6 \[LessEqual] 6, \(-x3\) - x4 + x5 - x6 \[LessEqual] 6, x2 - x3 - x4 - x6 \[LessEqual] 6, x1 - x2 - x3 - x4 \[LessEqual] 6, x1 - x2 - x3 - x5 \[LessEqual] 6, x1 - x2 - x4 - x5 \[LessEqual] 6, x1 - x3 - x4 - x5 \[LessEqual] 6, \(-x1\) - x2 + x4 \[LessEqual] 12, \(-x1\) - x3 + x5 \[LessEqual] 12, \(-x1\) + x3 - x5 \[LessEqual] 12, \(-x1\) + x2 - x4 \[LessEqual] 12, \(-x2\) - x3 + x6 \[LessEqual] 12, \(-x2\) + x3 - x6 \[LessEqual] 12, \(-x4\) - x5 + x6 \[LessEqual] 12, \(-x4\) + x5 - x6 \[LessEqual] 12, x4 - x5 - x6 \[LessEqual] 12, x2 - x3 - x6 \[LessEqual] 12, x1 - x2 - x4 \[LessEqual] 12, x1 - x3 - x5 \[LessEqual] 12, \(-x1\) + x6 \[LessEqual] 14, \(-x2\) + x5 \[LessEqual] 14, \(-x3\) + x4 \[LessEqual] 14, x3 - x4 \[LessEqual] 14, x2 - x5 \[LessEqual] 14, x1 - x6 \[LessEqual] 14, \(-x1\) + x5 \[LessEqual] 20, \(-x1\) + x4 \[LessEqual] 20, \(-x1\) + x3 \[LessEqual] 20, \(-x1\) + x2 \[LessEqual] 20, \(-x2\) + x6 \[LessEqual] 20, \(-x2\) + x4 \[LessEqual] 20, \(-x2\) + x3 \[LessEqual] 20, \(-x3\) + x6 \[LessEqual] 20, \(-x3\) + x5 \[LessEqual] 20, \(-x4\) + x6 \[LessEqual] 20, \(-x4\) + x5 \[LessEqual] 20, \(-x5\) + x6 \[LessEqual] 20, x5 - x6 \[LessEqual] 20, x4 - x5 \[LessEqual] 20, x4 - x6 \[LessEqual] 20, x3 - x5 \[LessEqual] 20, x3 - x6 \[LessEqual] 20, x2 - x3 \[LessEqual] 20, x2 - x4 \[LessEqual] 20, x2 - x6 \[LessEqual] 20, x1 - x2 \[LessEqual] 20, x1 - x3 \[LessEqual] 20, x1 - x4 \[LessEqual] 20, x1 - x5 \[LessEqual] 20, x6 \[LessEqual] 22, x5 \[LessEqual] 22, x4 \[LessEqual] 22, x3 \[LessEqual] 22, x2 \[LessEqual] 22, x1 \[LessEqual] 22, \(-x1\) + x5 + x6 \[LessEqual] 32, \(-x1\) + x4 + x6 \[LessEqual] 32, \(-x1\) + x3 + x6 \[LessEqual] 32, \(-x1\) + x2 + x6 \[LessEqual] 32, \(-x2\) + x5 + x6 \[LessEqual] 32, \(-x2\) + x4 + x5 \[LessEqual] 32, \(-x2\) + x3 + x5 \[LessEqual] 32, \(-x3\) + x4 + x6 \[LessEqual] 32, \(-x3\) + x4 + x5 \[LessEqual] 32, x3 - x4 + x6 \[LessEqual] 32, x3 - x4 + x5 \[LessEqual] 32, x2 - x3 + x4 \[LessEqual] 32, x2 - x5 + x6 \[LessEqual] 32, x2 + x4 - x5 \[LessEqual] 32, x2 + x3 - x4 \[LessEqual] 32, x2 + x3 - x5 \[LessEqual] 32, x1 - x2 + x5 \[LessEqual] 32, x1 - x3 + x4 \[LessEqual] 32, x1 + x5 - x6 \[LessEqual] 32, x1 + x4 - x6 \[LessEqual] 32, x1 + x3 - x4 \[LessEqual] 32, x1 + x3 - x6 \[LessEqual] 32, x1 + x2 - x5 \[LessEqual] 32, x1 + x2 - x6 \[LessEqual] 32, x5 + x6 \[LessEqual] 34, x4 + x6 \[LessEqual] 34, x4 + x5 \[LessEqual] 34, x3 + x6 \[LessEqual] 34, x3 + x5 \[LessEqual] 34, x2 + x6 \[LessEqual] 34, x2 + x4 \[LessEqual] 34, x2 + x3 \[LessEqual] 34, x1 + x5 \[LessEqual] 34, x1 + x4 \[LessEqual] 34, x1 + x3 \[LessEqual] 34, x1 + x2 \[LessEqual] 34, x3 + x4 \[LessEqual] 36, x2 + x5 \[LessEqual] 36, x1 + x6 \[LessEqual] 36, x3 + x5 + x6 \[LessEqual] 42, x2 + x4 + x6 \[LessEqual] 42, x1 + x4 + x5 \[LessEqual] 42, x1 + x2 + x3 \[LessEqual] 42, x4 + x5 + x6 \[LessEqual] 48, x3 + x4 + x6 \[LessEqual] 48, x3 + x4 + x5 \[LessEqual] 48, x2 + x5 + x6 \[LessEqual] 48, x2 + x4 + x5 \[LessEqual] 48, x2 + x3 + x6 \[LessEqual] 48, x2 + x3 + x5 \[LessEqual] 48, x2 + x3 + x4 \[LessEqual] 48, x1 + x5 + x6 \[LessEqual] 48, x1 + x4 + x6 \[LessEqual] 48, x1 + x3 + x6 \[LessEqual] 48, x1 + x3 + x5 \[LessEqual] 48, x1 + x3 + x4 \[LessEqual] 48, x1 + x2 + x6 \[LessEqual] 48, x1 + x2 + x5 \[LessEqual] 48, x1 + x2 + x4 \[LessEqual] 48, \(-x1\) + 2\ x5 + x6 \[LessEqual] 52, \(-x1\) + 2\ x4 + x6 \[LessEqual] 52, \(-x1\) + 2\ x3 + x6 \[LessEqual] 52, \(-x1\) + 2\ x2 + x6 \[LessEqual] 52, \(-x2\) + x5 + 2\ x6 \[LessEqual] 52, \(-x2\) + 2\ x4 + x5 \[LessEqual] 52, \(-x2\) + 2\ x3 + x5 \[LessEqual] 52, \(-x3\) + x4 + 2\ x6 \[LessEqual] 52, \(-x3\) + x4 + 2\ x5 \[LessEqual] 52, x3 - x4 + 2\ x6 \[LessEqual] 52, x3 - x4 + 2\ x5 \[LessEqual] 52, x2 - x5 + 2\ x6 \[LessEqual] 52, x2 + 2\ x4 - x5 \[LessEqual] 52, x2 + 2\ x3 - x5 \[LessEqual] 52, 2\ x2 - x3 + x4 \[LessEqual] 52, 2\ x2 + x3 - x4 \[LessEqual] 52, x1 + 2\ x5 - x6 \[LessEqual] 52, x1 + 2\ x4 - x6 \[LessEqual] 52, x1 + 2\ x3 - x6 \[LessEqual] 52, x1 + 2\ x2 - x6 \[LessEqual] 52, 2\ x1 - x2 + x5 \[LessEqual] 52, 2\ x1 - x3 + x4 \[LessEqual] 52, 2\ x1 + x3 - x4 \[LessEqual] 52, 2\ x1 + x2 - x5 \[LessEqual] 52, x2 + x3 + x4 + x5 \[LessEqual] 54, x1 + x3 + x4 + x6 \[LessEqual] 54, x1 + x2 + x5 + x6 \[LessEqual] 54, x4 + x5 + 2\ x6 \[LessEqual] 66, x4 + 2\ x5 + x6 \[LessEqual] 66, 2\ x4 + x5 + x6 \[LessEqual] 66, x3 + x4 + 2\ x6 \[LessEqual] 66, x3 + x4 + 2\ x5 \[LessEqual] 66, x2 + x5 + 2\ x6 \[LessEqual] 66, x2 + 2\ x4 + x5 \[LessEqual] 66, x2 + x3 + 2\ x6 \[LessEqual] 66, x2 + 2\ x3 + x6 \[LessEqual] 66, x2 + 2\ x3 + x5 \[LessEqual] 66, 2\ x2 + x3 + x6 \[LessEqual] 66, 2\ x2 + x3 + x4 \[LessEqual] 66, x1 + 2\ x5 + x6 \[LessEqual] 66, x1 + 2\ x4 + x6 \[LessEqual] 66, x1 + x3 + 2\ x5 \[LessEqual] 66, x1 + 2\ x3 + x6 \[LessEqual] 66, x1 + 2\ x3 + x5 \[LessEqual] 66, x1 + x2 + 2\ x4 \[LessEqual] 66, x1 + 2\ x2 + x6 \[LessEqual] 66, x1 + 2\ x2 + x4 \[LessEqual] 66, 2\ x1 + x3 + x5 \[LessEqual] 66, 2\ x1 + x3 + x4 \[LessEqual] 66, 2\ x1 + x2 + x5 \[LessEqual] 66, 2\ x1 + x2 + x4 \[LessEqual] 66, x3 + 2\ x4 + x6 \[LessEqual] 68, x3 + 2\ x4 + x5 \[LessEqual] 68, 2\ x3 + x4 + x6 \[LessEqual] 68, 2\ x3 + x4 + x5 \[LessEqual] 68, x2 + 2\ x5 + x6 \[LessEqual] 68, x2 + x4 + 2\ x5 \[LessEqual] 68, x2 + x3 + 2\ x5 \[LessEqual] 68, x2 + x3 + 2\ x4 \[LessEqual] 68, x2 + 2\ x3 + x4 \[LessEqual] 68, 2\ x2 + x5 + x6 \[LessEqual] 68, 2\ x2 + x4 + x5 \[LessEqual] 68, 2\ x2 + x3 + x5 \[LessEqual] 68, x1 + x5 + 2\ x6 \[LessEqual] 68, x1 + x4 + 2\ x6 \[LessEqual] 68, x1 + x3 + 2\ x6 \[LessEqual] 68, x1 + x3 + 2\ x4 \[LessEqual] 68, x1 + 2\ x3 + x4 \[LessEqual] 68, x1 + x2 + 2\ x6 \[LessEqual] 68, x1 + x2 + 2\ x5 \[LessEqual] 68, x1 + 2\ x2 + x5 \[LessEqual] 68, 2\ x1 + x5 + x6 \[LessEqual] 68, 2\ x1 + x4 + x6 \[LessEqual] 68, 2\ x1 + x3 + x6 \[LessEqual] 68, 2\ x1 + x2 + x6 \[LessEqual] 68, x3 + 2\ x4 + x5 + x6 \[LessEqual] 78, x2 + x4 + 2\ x5 + x6 \[LessEqual] 78, x2 + 2\ x3 + x4 + x6 \[LessEqual] 78, 2\ x2 + x3 + x5 + x6 \[LessEqual] 78, x1 + x4 + x5 + 2\ x6 \[LessEqual] 78, x1 + 2\ x3 + x4 + x5 \[LessEqual] 78, x1 + x2 + x3 + 2\ x6 \[LessEqual] 78, x1 + x2 + x3 + 2\ x5 \[LessEqual] 78, x1 + x2 + x3 + 2\ x4 \[LessEqual] 78, x1 + 2\ x2 + x4 + x5 \[LessEqual] 78, 2\ x1 + x3 + x5 + x6 \[LessEqual] 78, 2\ x1 + x2 + x4 + x6 \[LessEqual] 78, x1 + x2 + x3 + x4 + x5 + x6 \[LessEqual] 78, x2 + x3 + x4 + x5 + 2\ x6 \[LessEqual] 82, x1 + x3 + x4 + 2\ x5 + x6 \[LessEqual] 82, x1 + x2 + 2\ x4 + x5 + x6 \[LessEqual] 82, x1 + x2 + 2\ x3 + x5 + x6 \[LessEqual] 82, x1 + 2\ x2 + x3 + x4 + x6 \[LessEqual] 82, 2\ x1 + x2 + x3 + x4 + x5 \[LessEqual] 82, x1 + x2 + x3 + x4 + x5 + 2\ x6 \[LessEqual] 92, x1 + x2 + x3 + x4 + 2\ x5 + x6 \[LessEqual] 92, x1 + x2 + x3 + 2\ x4 + x5 + x6 \[LessEqual] 92, x1 + x2 + 2\ x3 + x4 + x5 + x6 \[LessEqual] 92, x1 + 2\ x2 + x3 + x4 + x5 + x6 \[LessEqual] 92, 2\ x1 + x2 + x3 + x4 + x5 + x6 \[LessEqual] 92, x1 + x2 + x3 + x4 + 2\ x5 + 2\ x6 \[LessEqual] 106, x1 + x2 + x3 + 2\ x4 + x5 + 2\ x6 \[LessEqual] 106, x1 + x2 + x3 + 2\ x4 + 2\ x5 + x6 \[LessEqual] 106, x1 + x2 + 2\ x3 + x4 + x5 + 2\ x6 \[LessEqual] 106, x1 + x2 + 2\ x3 + x4 + 2\ x5 + x6 \[LessEqual] 106, x1 + x2 + 2\ x3 + 2\ x4 + x5 + x6 \[LessEqual] 106, x1 + 2\ x2 + x3 + x4 + x5 + 2\ x6 \[LessEqual] 106, x1 + 2\ x2 + x3 + x4 + 2\ x5 + x6 \[LessEqual] 106, x1 + 2\ x2 + x3 + 2\ x4 + x5 + x6 \[LessEqual] 106, x1 + 2\ x2 + 2\ x3 + x4 + x5 + x6 \[LessEqual] 106, 2\ x1 + x2 + x3 + x4 + x5 + 2\ x6 \[LessEqual] 106, 2\ x1 + x2 + x3 + x4 + 2\ x5 + x6 \[LessEqual] 106, 2\ x1 + x2 + x3 + 2\ x4 + x5 + x6 \[LessEqual] 106, 2\ x1 + x2 + 2\ x3 + x4 + x5 + x6 \[LessEqual] 106, 2\ x1 + 2\ x2 + x3 + x4 + x5 + x6 \[LessEqual] 106, x2 + x3 + x4 + 3\ x5 + 2\ x6 \[LessEqual] 118, x2 + x3 + 3\ x4 + x5 + 2\ x6 \[LessEqual] 118, x2 + 3\ x3 + x4 + x5 + 2\ x6 \[LessEqual] 118, 3\ x2 + x3 + x4 + x5 + 2\ x6 \[LessEqual] 118, x1 + x3 + x4 + 2\ x5 + 3\ x6 \[LessEqual] 118, x1 + x3 + 3\ x4 + 2\ x5 + x6 \[LessEqual] 118, x1 + 3\ x3 + x4 + 2\ x5 + x6 \[LessEqual] 118, x1 + x2 + 2\ x4 + x5 + 3\ x6 \[LessEqual] 118, x1 + x2 + 2\ x4 + 3\ x5 + x6 \[LessEqual] 118, x1 + x2 + 2\ x3 + x5 + 3\ x6 \[LessEqual] 118, x1 + x2 + 2\ x3 + 3\ x5 + x6 \[LessEqual] 118, x1 + 2\ x2 + x3 + x4 + 3\ x6 \[LessEqual] 118, x1 + 2\ x2 + x3 + 3\ x4 + x6 \[LessEqual] 118, x1 + 2\ x2 + 3\ x3 + x4 + x6 \[LessEqual] 118, x1 + 3\ x2 + 2\ x4 + x5 + x6 \[LessEqual] 118, x1 + 3\ x2 + 2\ x3 + x5 + x6 \[LessEqual] 118, 2\ x1 + x2 + x3 + x4 + 3\ x5 \[LessEqual] 118, 2\ x1 + x2 + x3 + 3\ x4 + x5 \[LessEqual] 118, 2\ x1 + x2 + 3\ x3 + x4 + x5 \[LessEqual] 118, 2\ x1 + 3\ x2 + x3 + x4 + x5 \[LessEqual] 118, 3\ x1 + x3 + x4 + 2\ x5 + x6 \[LessEqual] 118, 3\ x1 + x2 + 2\ x4 + x5 + x6 \[LessEqual] 118, 3\ x1 + x2 + 2\ x3 + x5 + x6 \[LessEqual] 118, 3\ x1 + 2\ x2 + x3 + x4 + x6 \[LessEqual] 118, x1 + x2 + x3 + 2\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 120, x1 + 2\ x2 + 2\ x3 + x4 + x5 + 2\ x6 \[LessEqual] 120, 2\ x1 + x2 + 2\ x3 + x4 + 2\ x5 + x6 \[LessEqual] 120, 2\ x1 + 2\ x2 + x3 + 2\ x4 + x5 + x6 \[LessEqual] 120, x1 + x2 + x3 + x4 + 2\ x5 + 3\ x6 \[LessEqual] 124, x1 + x2 + x3 + x4 + 3\ x5 + 2\ x6 \[LessEqual] 124, x1 + x2 + x3 + 2\ x4 + x5 + 3\ x6 \[LessEqual] 124, x1 + x2 + x3 + 2\ x4 + 3\ x5 + x6 \[LessEqual] 124, x1 + x2 + x3 + 3\ x4 + x5 + 2\ x6 \[LessEqual] 124, x1 + x2 + x3 + 3\ x4 + 2\ x5 + x6 \[LessEqual] 124, x1 + x2 + 2\ x3 + x4 + x5 + 3\ x6 \[LessEqual] 124, x1 + x2 + 2\ x3 + x4 + 3\ x5 + x6 \[LessEqual] 124, x1 + x2 + 3\ x3 + x4 + x5 + 2\ x6 \[LessEqual] 124, x1 + x2 + 3\ x3 + x4 + 2\ x5 + x6 \[LessEqual] 124, x1 + 2\ x2 + x3 + x4 + x5 + 3\ x6 \[LessEqual] 124, x1 + 2\ x2 + x3 + 3\ x4 + x5 + x6 \[LessEqual] 124, x1 + 2\ x2 + 3\ x3 + x4 + x5 + x6 \[LessEqual] 124, x1 + 3\ x2 + x3 + x4 + x5 + 2\ x6 \[LessEqual] 124, x1 + 3\ x2 + x3 + 2\ x4 + x5 + x6 \[LessEqual] 124, x1 + 3\ x2 + 2\ x3 + x4 + x5 + x6 \[LessEqual] 124, 2\ x1 + x2 + x3 + x4 + 3\ x5 + x6 \[LessEqual] 124, 2\ x1 + x2 + x3 + 3\ x4 + x5 + x6 \[LessEqual] 124, 2\ x1 + x2 + 3\ x3 + x4 + x5 + x6 \[LessEqual] 124, 2\ x1 + 3\ x2 + x3 + x4 + x5 + x6 \[LessEqual] 124, 3\ x1 + x2 + x3 + x4 + 2\ x5 + x6 \[LessEqual] 124, 3\ x1 + x2 + x3 + 2\ x4 + x5 + x6 \[LessEqual] 124, 3\ x1 + x2 + 2\ x3 + x4 + x5 + x6 \[LessEqual] 124, 3\ x1 + 2\ x2 + x3 + x4 + x5 + x6 \[LessEqual] 124, x1 + x2 + 2\ x3 + 2\ x4 + x5 + 3\ x6 \[LessEqual] 134, x1 + x2 + 2\ x3 + 2\ x4 + 3\ x5 + x6 \[LessEqual] 134, x1 + 2\ x2 + x3 + x4 + 2\ x5 + 3\ x6 \[LessEqual] 134, x1 + 2\ x2 + x3 + 3\ x4 + 2\ x5 + x6 \[LessEqual] 134, x1 + 2\ x2 + 3\ x3 + x4 + 2\ x5 + x6 \[LessEqual] 134, x1 + 3\ x2 + 2\ x3 + 2\ x4 + x5 + x6 \[LessEqual] 134, 2\ x1 + x2 + x3 + x4 + 3\ x5 + 2\ x6 \[LessEqual] 134, 2\ x1 + x2 + x3 + 3\ x4 + x5 + 2\ x6 \[LessEqual] 134, 2\ x1 + x2 + 3\ x3 + x4 + x5 + 2\ x6 \[LessEqual] 134, 2\ x1 + 3\ x2 + x3 + x4 + x5 + 2\ x6 \[LessEqual] 134, 3\ x1 + x2 + 2\ x3 + 2\ x4 + x5 + x6 \[LessEqual] 134, 3\ x1 + 2\ x2 + x3 + x4 + 2\ x5 + x6 \[LessEqual] 134, x1 + x2 + x3 + 2\ x4 + 2\ x5 + 4\ x6 \[LessEqual] 156, x1 + x2 + x3 + 2\ x4 + 4\ x5 + 2\ x6 \[LessEqual] 156, x1 + x2 + x3 + 4\ x4 + 2\ x5 + 2\ x6 \[LessEqual] 156, x1 + 2\ x2 + 2\ x3 + x4 + x5 + 4\ x6 \[LessEqual] 156, x1 + 2\ x2 + 4\ x3 + x4 + x5 + 2\ x6 \[LessEqual] 156, x1 + 4\ x2 + 2\ x3 + x4 + x5 + 2\ x6 \[LessEqual] 156, 2\ x1 + x2 + 2\ x3 + x4 + 4\ x5 + x6 \[LessEqual] 156, 2\ x1 + x2 + 4\ x3 + x4 + 2\ x5 + x6 \[LessEqual] 156, 2\ x1 + 2\ x2 + x3 + 4\ x4 + x5 + x6 \[LessEqual] 156, 2\ x1 + 4\ x2 + x3 + 2\ x4 + x5 + x6 \[LessEqual] 156, 4\ x1 + x2 + 2\ x3 + x4 + 2\ x5 + x6 \[LessEqual] 156, 4\ x1 + 2\ x2 + x3 + 2\ x4 + x5 + x6 \[LessEqual] 156, x1 + x2 + 2\ x3 + 4\ x4 + x5 + 3\ x6 \[LessEqual] 170, x1 + x2 + 2\ x3 + 4\ x4 + 3\ x5 + x6 \[LessEqual] 170, x1 + x2 + 4\ x3 + 2\ x4 + x5 + 3\ x6 \[LessEqual] 170, x1 + x2 + 4\ x3 + 2\ x4 + 3\ x5 + x6 \[LessEqual] 170, x1 + 2\ x2 + x3 + x4 + 4\ x5 + 3\ x6 \[LessEqual] 170, x1 + 2\ x2 + x3 + 3\ x4 + 4\ x5 + x6 \[LessEqual] 170, x1 + 2\ x2 + 3\ x3 + x4 + 4\ x5 + x6 \[LessEqual] 170, x1 + 3\ x2 + 2\ x3 + 4\ x4 + x5 + x6 \[LessEqual] 170, x1 + 3\ x2 + 4\ x3 + 2\ x4 + x5 + x6 \[LessEqual] 170, x1 + 4\ x2 + x3 + x4 + 2\ x5 + 3\ x6 \[LessEqual] 170, x1 + 4\ x2 + x3 + 3\ x4 + 2\ x5 + x6 \[LessEqual] 170, x1 + 4\ x2 + 3\ x3 + x4 + 2\ x5 + x6 \[LessEqual] 170, 2\ x1 + x2 + x3 + x4 + 3\ x5 + 4\ x6 \[LessEqual] 170, 2\ x1 + x2 + x3 + 3\ x4 + x5 + 4\ x6 \[LessEqual] 170, 2\ x1 + x2 + 3\ x3 + x4 + x5 + 4\ x6 \[LessEqual] 170, 2\ x1 + 3\ x2 + x3 + x4 + x5 + 4\ x6 \[LessEqual] 170, 3\ x1 + x2 + 2\ x3 + 4\ x4 + x5 + x6 \[LessEqual] 170, 3\ x1 + x2 + 4\ x3 + 2\ x4 + x5 + x6 \[LessEqual] 170, 3\ x1 + 2\ x2 + x3 + x4 + 4\ x5 + x6 \[LessEqual] 170, 3\ x1 + 4\ x2 + x3 + x4 + 2\ x5 + x6 \[LessEqual] 170, 4\ x1 + x2 + x3 + x4 + 3\ x5 + 2\ x6 \[LessEqual] 170, 4\ x1 + x2 + x3 + 3\ x4 + x5 + 2\ x6 \[LessEqual] 170, 4\ x1 + x2 + 3\ x3 + x4 + x5 + 2\ x6 \[LessEqual] 170, 4\ x1 + 3\ x2 + x3 + x4 + x5 + 2\ x6 \[LessEqual] 170};\)\)}], "Input", CellOpen->False, FontSize->14], Cell["The cells below define the equations used in section 5.1.", "Text", FontSize->14], Cell[BoxData[{ \(\(General[spell1::off];\)\), "\[IndentingNewLine]", \(\(VarNames[n_] := Flatten[Table[{z[j] \[Rule] ToExpression[StringJoin["\", ToString[j]]], G[j] \[Rule] ToExpression[StringJoin["\", ToString[j]]]}, {j, 1, n}]];\)\), "\[IndentingNewLine]", \(\(VarNames2 := Flatten[Table[ s[i, j] \[Rule] ToExpression[ StringJoin["\", ToString[i], ToString[j]]], {i, 1, 3}, {j, i + 1, 4}]];\)\), "\[IndentingNewLine]", \(\(s[i_, i_] := 0;\)\), "\[IndentingNewLine]", \(\(s[i_, j_] := s[j, i] /; j < i;\)\), "\[IndentingNewLine]", \(\(S[i_, i_] := \ 0;\)\), "\[IndentingNewLine]", \(\(S[i_, j_]\ := 1/s[i, j] - 1/1;\)\), "\[IndentingNewLine]", \(\(Z[i_, j_] := 0 /; i \[Equal] j;\)\), "\[IndentingNewLine]", \(\(Z[i_, j_] := 1 /; i \[NotEqual] j;\)\), "\[IndentingNewLine]", \(\(Sigma[i_, j_, n_]\ := \ 2*\((G[i] + G[j])\) S[i, j] + Plus @@ Table[ G[h]*Z[i, h]*Z[j, h]*\((S[i, h] + S[j, h])\), {h, 1, n}];\)\), "\[IndentingNewLine]", \(\(P[i_, j_, n_]\ := s[i, j]*Sigma[i, j, n] + Plus @@ Table[ G[h]*Z[i, h]* Z[j, h]*\((s[i, h] - s[j, h])\)*\((S[i, h] - S[j, h])\), {h, 1, n}];\)\), "\[IndentingNewLine]", \(\(CCeqs[ n_]\ := \ \(\(Table[P[i, j, n], {j, 2, n}, {i, 1, j - 1}] // Flatten\) // Factor\) // Numerator;\)\), "\[IndentingNewLine]", \(\(ACEquations\ = \(CCeqs[4] /. VarNames[4]\) /. VarNames2;\)\), "\[IndentingNewLine]", \(\(dz1\ = \ \(\((1/s12 - 1)\)*\((1/s34 - 1)\) - \((1/s14 - 1)\) \((1/s23 - 1)\) // Factor\) // Numerator;\)\), "\[IndentingNewLine]", \(\(dz2\ = \ \(\((1/s12 - 1)\)*\((1/s34 - 1)\) - \((1/s13 - 1)\) \((1/s24 - 1)\) // Factor\) // Numerator;\)\), "\[IndentingNewLine]", \(\(dz3\ = \ \(\((1/s13 - 1)\)*\((1/s24 - 1)\) - \((1/s14 - 1)\) \((1/s23 - 1)\) // Factor\) // Numerator;\)\), "\n", \(\(NineEquations\ = \ ACEquations~Join~{dz1, dz2, dz3};\)\), "\[IndentingNewLine]", \(GetExponents[mon_, vars_]\ := \ Map[Exponent[mon, #] &, vars]\), "\n", \(GetAllExponents[poly_, vars_] := \[IndentingNewLine]Table[ GetExponents[poly[\([i]\)], vars], {i, 1, Length[poly]}] // Union\), "\[IndentingNewLine]", \(\(vars4\ = \ {s12, s13, s14, s23, s24, s34};\)\), "\[IndentingNewLine]", \(\(NineEquationsExponents\ = \ Map[GetAllExponents[#, vars4] &, NineEquations];\)\)}], "Input"], Cell["\<\ The following functions are used to extract the nontrivial facets of the \ Minkowski sum polytope. \ \>", "Text", FontSize->16], Cell[BoxData[{ \(\(Subst[v_]\ := \ {x1 \[Rule] v[\([1]\)], \ x2 \[Rule] v[\([2]\)], \ x3 \[Rule] v[\([3]\)], x4 \[Rule] v[\([4]\)], x5 \[Rule] v[\([5]\)], x6 \[Rule] v[\([6]\)]};\)\), "\[IndentingNewLine]", \(\(lhs[LessEqual[a_, b_]]\ := \ a;\)\), "\[IndentingNewLine]", \(\(rhs[LessEqual[a_, b_]]\ := \ b;\)\), "\[IndentingNewLine]", \(\(\(FindMax[linform_, vertlist_]\ := \ Max[\ Map[linform /. Subst[#] &, vertlist]];\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(GetMaximalExponents[ineq_, vertlist_] := \[IndentingNewLine]With[{linform = lhs[ineq], maxval\ = \ FindMax[lhs[ineq], vertlist]}, \ Select[vertlist, \((\((linform /. Subst[#])\)\ \[Equal] maxval)\) &]];\)\[IndentingNewLine]\[IndentingNewLine]\ \ (*returns\ 1\ if\ the\ inequality\ determines\ a\ reduced\ polynomial\ with\ \ more\ than\ one\ term\ *) \), "\[IndentingNewLine]", \(\(Nontrivial[ineq_, vertlist_] := \ If[Length[GetMaximalExponents[ineq, vertlist]] > 1, 1, 0];\)\[IndentingNewLine]\[IndentingNewLine] (*\ returns\ 1\ if\ ineq\ is\ nontrivial\ all\ of\ the\ reduced\ \ polynomials\ whose\ exponents\ are\ in\ vllist\ \((list\ of\ exponent\ lists)\ \)\ *) \), "\[IndentingNewLine]", \(\(AllNontrivial[ineq_, vllist_]\ := \[IndentingNewLine]If[ Min[Map[Nontrivial[ineq, #] &, vllist]] > 0, True, False];\)\)}], "Input"], Cell[TextData[{ StyleBox["There are 35 nontrivial facets of the Minkowski sum polytope. \ Here are their defining inequalities, sorted according to the value of a \ linear function on their inward normal vectors ", FontSize->16], StyleBox["a", FontFamily->"Symbol", FontSize->16], StyleBox[".", FontSize->16] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(nontrivialfacets\ = \ Select[v1t9bIeq, AllNontrivial[#, NineEquationsExponents] &];\)\), "\[IndentingNewLine]", \(Length[%]\[IndentingNewLine]\), "\[IndentingNewLine]", \(GetAlpha[ LessEqual[a_, b_]] := \ \(-Coefficient[ a, {x1, x2, x3, x4, x5, x6}]\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(\(nontrivialfacets\ = \ Sort[nontrivialfacets, \(({1, 1, 1, 1, 1, 1} . GetAlpha[#1] > {1, 1, 1, 1, 1, 1} . GetAlpha[#2])\) &];\)\[IndentingNewLine]\), "\ \[IndentingNewLine]", \(\({Table[i, {i, 1, Length[nontrivialfacets]}], nontrivialfacets} // Transpose\) // MatrixForm\)}], "Input"], Cell[BoxData[ \(35\)], "Output"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", \(\(-x2\) - x3 - x4 - x5 - 2\ x6 \[LessEqual] \(-50\)\)}, {"2", \(\(-x1\) - x3 - x4 - 2\ x5 - x6 \[LessEqual] \(-50\)\)}, {"3", \(\(-x1\) - x2 - 2\ x4 - x5 - x6 \[LessEqual] \(-50\)\)}, {"4", \(\(-x1\) - x2 - 2\ x3 - x5 - x6 \[LessEqual] \(-50\)\)}, {"5", \(\(-x1\) - 2\ x2 - x3 - x4 - x6 \[LessEqual] \(-50\)\)}, {"6", \(\(-2\)\ x1 - x2 - x3 - x4 - x5 \[LessEqual] \(-50\)\)}, {"7", \(\(-x1\) - x2 - x3 - x4 - x5 - x6 \[LessEqual] \(-60\)\)}, {"8", \(\(-x3\) - x5 - x6 \[LessEqual] \(-18\)\)}, {"9", \(\(-x2\) - x4 - x6 \[LessEqual] \(-18\)\)}, {"10", \(\(-x1\) - x4 - x5 \[LessEqual] \(-18\)\)}, {"11", \(\(-x1\) - x2 - x3 \[LessEqual] \(-18\)\)}, {"12", \(\(-x4\) - x5 - x6 \[LessEqual] \(-24\)\)}, {"13", \(\(-x2\) - x3 - x6 \[LessEqual] \(-24\)\)}, {"14", \(\(-x1\) - x3 - x5 \[LessEqual] \(-24\)\)}, {"15", \(\(-x1\) - x2 - x4 \[LessEqual] \(-24\)\)}, {"16", \(\(-x6\) \[LessEqual] 0\)}, {"17", \(\(-x5\) \[LessEqual] 0\)}, {"18", \(\(-x4\) \[LessEqual] 0\)}, {"19", \(\(-x3\) \[LessEqual] 0\)}, {"20", \(\(-x2\) \[LessEqual] 0\)}, {"21", \(\(-x1\) \[LessEqual] 0\)}, {"22", \(x1 + x6 \[LessEqual] 36\)}, {"23", \(x2 + x5 \[LessEqual] 36\)}, {"24", \(x3 + x4 \[LessEqual] 36\)}, {"25", \(x1 + x2 + x4 \[LessEqual] 48\)}, {"26", \(x1 + x3 + x5 \[LessEqual] 48\)}, {"27", \(x2 + x3 + x6 \[LessEqual] 48\)}, {"28", \(x4 + x5 + x6 \[LessEqual] 48\)}, {"29", \(x1 + x2 + x3 \[LessEqual] 42\)}, {"30", \(x1 + x4 + x5 \[LessEqual] 42\)}, {"31", \(x2 + x4 + x6 \[LessEqual] 42\)}, {"32", \(x3 + x5 + x6 \[LessEqual] 42\)}, {"33", \(x1 + x2 + x5 + x6 \[LessEqual] 54\)}, {"34", \(x1 + x3 + x4 + x6 \[LessEqual] 54\)}, {"35", \(x2 + x3 + x4 + x5 \[LessEqual] 54\)} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Open ]], Cell["\<\ Besides the facets of the Minkowski sum polytope, we need to detect \ nontrivial faces of lower dimension. We will use these functions to work our \ way down from the facets.\ \>", "Text", FontSize->16], Cell[BoxData[{ \(\(FindFacet[ineq_, vlist_] := Select[vlist, \((\((lhs[ineq] /. Subst[#])\) === rhs[ineq])\) &];\)\), "\[IndentingNewLine]", \(\(FacetsIncident[indlist_, ineqlist_, vlist_]\ := \ With[{f = Map[FindFacet[#, vlist] &, Part[ineqlist, indlist]]}, \[IndentingNewLine]If[ Length[Intersection @@ f] > 0, True, False]];\)\), "\[IndentingNewLine]", \(\(AddLEInequalities[indlist_, ineqlist_] := Module[{ins, rights, \ lefts}, \[IndentingNewLine]ins\ = \ Part[ineqlist, indlist]; \[IndentingNewLine]rights\ = \ Map[rhs, ins]; \[IndentingNewLine]lefts\ = \ Map[lhs, ins]; \[IndentingNewLine]LessEqual[Plus @@ lefts, Plus @@ rights]];\)\), "\[IndentingNewLine]", \(\(NontrivialFace[indlist_, ineqlist_, explist_]\ := \ With[{in = AddLEInequalities[indlist, ineqlist]}, \[IndentingNewLine]AllNontrivial[in, explist]];\)\)}], "Input"], Cell["\<\ The symmetry of our equations under the action S_4, the permutation group, \ can be exploited to reduce the amount of analysis required. The following \ functions are for that purpose. \ \>", "Text", FontSize->16], Cell[BoxData[{ \(\(Off[General::spell1];\)\), "\[IndentingNewLine]", \(\(sigma4\ = \ Permutations[{1, 2, 3, 4}];\)\), "\[IndentingNewLine]", \(\(k[i_, i_] := 0;\)\), "\n", \(\(k[i_, j_] := k[j, i] /; j < i;\)\), "\n", \(\(kvars\ = \ {k[1, 2], k[1, 3], k[1, 4], k[2, 3], k[2, 4], k[3, 4]};\)\), "\[IndentingNewLine]", \(\(kineqs\ = \ nontrivialfacets /. {x1 \[Rule] k[1, 2], x2 \[Rule] k[1, 3], x3 \[Rule] k[1, 4], x4 \[Rule] k[2, 3], x5 \[Rule] k[2, 4], x6 \[Rule] k[3, 4]};\)\), "\[IndentingNewLine]", \(\(Permute[perm_, k[i_, j_]] := \ k[perm[\([i]\)], perm[\([j]\)]];\)\), "\[IndentingNewLine]", \(\(Permute[perm_, LessEqual[a_, b_]] := \ With[{coeffs = \ Coefficient[a, kvars]}, \[IndentingNewLine]LessEqual[ coeffs . Map[Permute[perm, #] &, kvars], b]];\)\), "\n", \(\(PermutedIndex[perm_, ineqlist_, ind_]\ := \ With[{pineq\ = \ Permute[perm, ineqlist[\([ind]\)]]}, \[IndentingNewLine]\(Position[ ineqlist, pineq]\)[\([1, 1]\)]\[IndentingNewLine]];\)\), "\n", \(\(PermutedIndexList[perm_, ineqlist_, indlist_]\ := \ Sort[Map[PermutedIndex[perm, ineqlist, #] &, indlist]];\)\), "\[IndentingNewLine]", \(\(IndexListOrbit[pgroup_, ineqlist_, indlist_] := \ Union[Map[PermutedIndexList[#, ineqlist, indlist] &, pgroup]];\)\), "\[IndentingNewLine]", \(\(MinimalOrbitRep[pgroup_, ineqlist_, indlist_] := \ First[IndexListOrbit[pgroup, ineqlist, indlist]];\)\), "\[IndentingNewLine]", \(\(ExtendIndexList[ineqlist_, {}]\ := \ Table[{i}, {i, 1, Length[ineqlist]}];\)\), "\[IndentingNewLine]", \(\(ExtendIndexList[ineqlist_, indlist_]\ := \ Table[indlist~Join~{i}, {i, Last[indlist] + 1, Length[ineqlist]}];\)\), "\[IndentingNewLine]", \(\(ExtendedMinimalOrbitReps[pgroup_, ineqlist_, indlist_]\ := \ Module[{i, ext, minrep, oreps = {}}, \[IndentingNewLine]ext\ = \ ExtendIndexList[ineqlist, indlist]; \[IndentingNewLine]For[i = 1, i \[LessEqual] Length[ext], \(i++\), \[IndentingNewLine]minrep = MinimalOrbitRep[pgroup, ineqlist, ext[\([i]\)]]; \[IndentingNewLine]AppendTo[oreps, minrep];\[IndentingNewLine]]; \[IndentingNewLine]oreps // Union];\)\), "\[IndentingNewLine]", \(\(ExtendedMinimalOrbitRepsList[pgroup_, ineqlist_, indlistlist_]\ := \ \[IndentingNewLine]\(Map[ ExtendedMinimalOrbitReps[pgroup, ineqlist, #] &, indlistlist] // Flatten[#, 1] &\) // Union;\)\)}], "Input"], Cell["\<\ Using the above functions, we first find the nontrivial facet representatives \ under the action of the permutation group. These are listed in table 1 of \ the paper and numbered 1-9. \ \>", "Text", FontSize->16], Cell[CellGroupData[{ Cell[BoxData[ \(faces1\ \ = \ ExtendedMinimalOrbitRepsList[sigma4, kineqs, {{}}]\)], "Input"], Cell[BoxData[ \({{1}, {7}, {8}, {12}, {16}, {22}, {25}, {29}, {33}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(nontrivialfacetreps = Sort[Map[nontrivialfacets[\([#]\)] &, Flatten[faces1]], \(({1, 1, 1, 1, 1, 1} . GetAlpha[#1] > {1, 1, 1, 1, 1, 1} . GetAlpha[#2])\) &]\)], "Input"], Cell[BoxData[ \({\(-x1\) - x2 - x3 - x4 - x5 - x6 \[LessEqual] \(-60\), \(-x2\) - x3 - x4 - x5 - 2\ x6 \[LessEqual] \(-50\), \(-x4\) - x5 - x6 \[LessEqual] \(-24\), \(-x3\) - x5 - x6 \[LessEqual] \(-18\), \(-x6\) \[LessEqual] 0, x1 + x6 \[LessEqual] 36, x1 + x2 + x3 \[LessEqual] 42, x1 + x2 + x4 \[LessEqual] 48, x1 + x2 + x5 + x6 \[LessEqual] 54}\)], "Output"] }, Open ]], Cell["\<\ Now we work our way down in dimension, finding lower-dimension faces of the \ Minkowski sum polytope that correspond to nontrivial reduced equations. \ \>", "Text", FontSize->16], Cell[BoxData[{ \(\(faces2\ \ = \ ExtendedMinimalOrbitRepsList[sigma4, kineqs, faces1];\)\), "\[IndentingNewLine]", \(faces2\ = \ Select[faces2, \((NontrivialFace[#, nontrivialfacets, NineEquationsExponents]\ && FacetsIncident[#, nontrivialfacets, v1t9bH])\) &]\)}], "Input"], Cell[BoxData[{ \(\(faces3\ \ = \ ExtendedMinimalOrbitRepsList[sigma4, kineqs, faces2];\)\), "\[IndentingNewLine]", \(faces3\ = \ Select[faces3, \((NontrivialFace[#, nontrivialfacets, NineEquationsExponents]\ && FacetsIncident[#, nontrivialfacets, v1t9bH])\) &]\)}], "Input"], Cell[BoxData[{ \(\(faces4\ \ = \ ExtendedMinimalOrbitRepsList[sigma4, kineqs, faces3];\)\), "\[IndentingNewLine]", \(faces4\ = \ Select[faces4, \((NontrivialFace[#, nontrivialfacets, NineEquationsExponents]\ && FacetsIncident[#, nontrivialfacets, v1t9bH])\) &]\)}], "Input"], Cell[TextData[{ StyleBox["We only need to test faces which have at least one inward normal \ ", FontSize->16], StyleBox["a", FontFamily->"Symbol", FontSize->16], StyleBox[" in the half-space \n", FontSize->16], StyleBox["-a1 - ... - a6 >= 0. ", FontFamily->"Symbol", FontSize->16], StyleBox["In the list of nontrivial facets, only facets 22 - 35 have such a \ normal. Here are all the indices of the nontrivial faces which intersect at \ least one of these facets and therefore have an inward normal in the \ half-space. We will have to examine their reduced equations below.", FontSize->16] }], "Text"], Cell[BoxData[ \(\(nontrivialfacetrepsIndex = {{22}, {25}, {29}, {33}, {8, 25}, {12, 29}, {12, 33}, {16, 35}, {22, 33}, {12, 16, 35}};\)\)], "Input"], Cell["\<\ In addition to identifying the nontrivial faces of the polytopes, we must \ also compute the corresponding reduced equations. The following functions \ perform these computations. \ \>", "Text", FontSize->16], Cell[BoxData[{ \(\(ReducePoly[p_, ineq_]\ := Module[{q, linform, maxval, explist}, \[IndentingNewLine]q = Expand[p]; \[IndentingNewLine]linform\ = \ lhs[ineq]; \[IndentingNewLine]explist\ = \ GetAllExponents[q, vars4]; \[IndentingNewLine]maxval\ = \ FindMax[linform, explist]; \[IndentingNewLine]Select[ q, \((\((linform /. Subst[GetExponents[#, vars4]])\) \[Equal] maxval)\) &]\[IndentingNewLine]];\)\), \ "\[IndentingNewLine]", \(\(ReducedSystem[LessEqual[lhs_, rhs_], eqlist_]\ := \ Map[ReducePoly[#, LessEqual[lhs, rhs]] &, eqlist];\)\), "\n", \(\(ReducedSystem[indlist_, ineqlist_, eqlist_]\ := \ ReducedSystem[AddLEInequalities[indlist, ineqlist], eqlist];\)\), "\[IndentingNewLine]", \(\(RemoveFactor[poly_, var_]\ := Module[{i, pow, p}, \[IndentingNewLine]p\ = \ Expand[poly]; \[IndentingNewLine]pow = \ Min[Table[ Exponent[p[\([i]\)], var], {i, 1, Length[p]}]]; \[IndentingNewLine]If[ pow > 0 && pow < Infinity, \((poly/var^pow)\) // Factor, poly]];\)\), "\[IndentingNewLine]", \(\(CleanUp[poly_, vars_]\ := \ \[IndentingNewLine]Fold[RemoveFactor, poly, vars\ ];\)\)}], "Input"], Cell["\<\ Any reduced system is homogeneous with respect to some weight vector. In \ searching for nonzero solutions, we can use this homogeneity to require an \ additional condition, that the polynomial nzeq defined below is zero: \ \>", "Text", FontSize->16], Cell[BoxData[ \(\(nzeq\ = \ s12*s13*s14*s23*s24*s34 - 1;\)\)], "Input"], Cell["\<\ The ReductionElimination function eliminates the s_{ij} variables from a \ given set of reduced equations, to obtain polynomial conditions in the G_i \ that would have to hold for a corresponding solution curve to exist. \ \>", "Text", FontSize->16], Cell[BoxData[ \(ReductionElimination[indlist_, ineqlist_, eqlist_] := Module[{redeqs, gb}, \[IndentingNewLine]redeqs = \ ReducedSystem[indlist, ineqlist, eqlist] // Factor; \[IndentingNewLine]redeqs\ = Map[CleanUp[#, vars4] &, redeqs]; \[IndentingNewLine]gb = GroebnerBasis[redeqs, Union[{G1, G2, G3, G4}, vars4], MonomialOrder \[Rule] DegreeReverseLexicographic]; \[IndentingNewLine]gb = GroebnerBasis[gb~Join~{nzeq}, Union[{G1, G2, G3, G4}, vars4], MonomialOrder \[Rule] DegreeReverseLexicographic]; \[IndentingNewLine]gb = GroebnerBasis[gb, {G1, G2, G3, G4}, vars4]; \[IndentingNewLine]gb = GroebnerBasis[gb~Join~{G1*G2*G3*G4*w - 1}, {G1, G2, G3, G4}, {w}]; Factor[GroebnerBasis[ gb~Join~{\((G1 + G2 + G3 + G4)\)*w - 1}, {G1, G2, G3, G4}, {w}]]\[IndentingNewLine]]\)], "Input"], Cell["\<\ \tThe following computations may take some time. For convenience we include \ the results so the reader can skip the evaluation. \tThe results show two sets of problematic vorticities. The first, when \ polynomials of the form G1 G2-G3 G4 = 0 are satisfied, can be dealt with by \ considering higher order Puiseux expansions. These calculations follow \ below. In the second case, we are restricted to vorticities of the form \ k(-1,1,1,1), for which we can compute an explicit Groebner basis. \ \>", "Text", FontSize->16], Cell[CellGroupData[{ Cell[BoxData[ \(Map[ ReductionElimination[#, nontrivialfacets, NineEquations] &, {{22}, {25}, {29}, {33}}]\)], "Input"], Cell[BoxData[ \({{G1\ G2 - G3\ G4}, {1}, {G2\^2 - G2\ G3 + G3\^2 - G2\ G4 - G3\ G4 + G4\^2, 3\ G1 + G2 + G3 + G4}, {1}}\)], "Output"] }, Open ]], Cell["\<\ The computation below shows that for lower-dimensional faces, problems can \ only occur if a subsum of two or three of the G_i vanishes. \ \>", "Text", FontSize->16], Cell[BoxData[ \(Map[ ReductionElimination[#, nontrivialfacets, NineEquations] &, {{8, 25}, {12, 29}, {12, 33}, {16, 35}, {22, 33}, {12, 16, 35}}]\)], "Input"], Cell["\<\ The remainder of this section is devoted to showing that extending the \ Puiseux series further results in a contradiction. First we analyze the \ reduced system of facet 22 (which is called number 6 in table 1 and in \ section 5.1.1 of the paper) to find the leading terms in the Puiseux \ expansion. Fortunately, there is a unique solution up to the expected \ homogeneity. \ \>", "Text", FontSize->16], Cell[BoxData[{ \(\(red\ = \ ReducedSystem[{22}, nontrivialfacets, NineEquations] // Factor;\)\), "\[IndentingNewLine]", \(\(red\ = Map[CleanUp[#, vars4] &, red];\)\), "\[IndentingNewLine]", \(Factor[red]\[IndentingNewLine]\), "\[IndentingNewLine]", \(SimplifiedRed22 = Complement[ Factor[red /. {s24 \[Rule] 1 - s13, s23 \[Rule] 1 - s14}], {0}]\[IndentingNewLine]\), "\[IndentingNewLine]", \(Factor[ GroebnerBasis[ Join[SimplifiedRed22, {G1\ G2 - G3\ G4, G1*G2*G3*G4*s34*w - 1}], {s12, s13, s14, s34, G1, G2, G3, G4}, {w}]]\)}], "Input"], Cell["\<\ Note that if some pairs of vorticities add to zero, such as G1+G3=0, then \ there are no nonzero solutions to the reduced equations for nonzero \ vorticities. This justifies the substitutions used below in solving the \ reduced system. \ \>", "Text", FontSize->16], Cell[BoxData[{ \(Solve[\(-G1\) + G1\ s14 + G3\ s14 \[Equal] 0, s14]\), "\[IndentingNewLine]", \(Solve[\(-G1\) + G1\ s13 + G4\ s13 \[Equal] 0, s13]\[IndentingNewLine]\), "\[IndentingNewLine]", \(Numerator[ Factor[\(red /. {s24 \[Rule] 1 - s13, s23 \[Rule] 1 - s14, s34 \[Rule] \(-s12\)}\) /. {s14 \[Rule] G1\/\(G1 + G3\), s13 \[Rule] G1\/\(G1 + G4\)}]]\)}], "Input"], Cell[TextData[StyleBox["Here are the values of the leading coefficients. s34 \ = s12 but the value is arbitrary and could be normalized.", FontSize->16]], "Text"], Cell[BoxData[ \(\(vars4 /. {s24 \[Rule] 1 - s13, s23 \[Rule] 1 - s14, s34 \[Rule] \(-s12\)}\) /. {s14 \[Rule] G1\/\(G1 + G3\), s13 \[Rule] G1\/\(G1 + G4\)}\)], "Input"], Cell["\<\ Next, we make a change of variable so that the leading terms of the Puiseux \ series are constants. In an abuse of notation, our new variables have the \ same name as the old (s_{ij}). As a check on our calculations, we verify \ that upon substituting our new variables into the equations the constant \ terms are zero. \ \>", "Text", FontSize->16], Cell[BoxData[{ \(NewNineEquations = Numerator[ Factor[\(\((NineEquations/t)\) /. {s12 \[Rule] s12\ t^\((\(-\ 1\))\), s34 \[Rule] s34\ t^\((\(-\ 1\))\)}\) /. {G4 \[Rule] G1*G2/G3}]]\[IndentingNewLine]\), "\[IndentingNewLine]", \(\(red0 = Factor[Simplify[ NewNineEquations /. {t \[Rule] 0}]];\)\), "\[IndentingNewLine]", \(red0\ = Factor[Map[CleanUp[#, vars4] &, red0]]\[IndentingNewLine]\), "\[IndentingNewLine]", \(sub1 = {s24 \[Rule] 1 - G1\/\(G1 + G4\), s23 \[Rule] 1 - G1\/\(G1 + G3\), s34 \[Rule] \(-s12\), s14 \[Rule] G1\/\(G1 + G3\), s13 \[Rule] G1\/\(G1 + G4\)}\), "\[IndentingNewLine]", \(Factor[\(red0 /. sub1\) /. G4 \[Rule] G1*G2/G3]\)}], "Input"], Cell["\<\ Next we show that the reduced system has full rank. It follows that the \ Puiseux series in these variables is actually a power series. \ \>", "Text", FontSize->16], Cell[BoxData[{ \(grad[f_]\ := \ {D[f, s13], D[f, s14], D[f, s23], D[f, s24], D[f, s34]}\), "\[IndentingNewLine]", \(\(DF0\ = \ \(Map[grad, red0] /. sub1\) /. {G4 \[Rule] G1*G2/G3} // Factor;\)\), "\[IndentingNewLine]", \(DF0 // MatrixForm\[IndentingNewLine]\), "\[IndentingNewLine]", \(\(Union[Factor[Minors[DF0, 5]]]\)[\([60]\)]\)}], "Input"], Cell["\<\ Finally we show that the series cannot be continued consistently to the first \ order in t: \ \>", "Text", FontSize->16], Cell[BoxData[{ \(NewNineEquationsO1 = NewNineEquations /. {s12 \[Rule] s12 + t*u12, s13 \[Rule] s13 + t*u13, s14 \[Rule] s14 + t*u14, s23 \[Rule] s23 + t*u23, s24 \[Rule] s24 + t*u24, s34 \[Rule] s34 + t*u34}\[IndentingNewLine]\), "\[IndentingNewLine]", \(Ft1\ = Numerator[\ \(Coefficient[NewNineEquationsO1, t] /. sub1\) /. {G4 \[Rule] G1*G2/G3} // Factor]\[IndentingNewLine]\), "\[IndentingNewLine]", \(Factor[ GroebnerBasis[ Union[Ft1, {s12*G1*G2*G3*w - 1}], {w, s12, u12, u13, u14, u23, u24, u34, G1, G2, G3}]]\)}], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["\<\ Strictly Planar Relative Equilibria with zero total circulation\ \>", "Section", FontSize->24], Cell["\<\ Finally, we verify the calculations from section 5.2, which show that there \ are at most 14 strictly planar relative equilibria when the total circulation \ (G1+G2+G3+G4) is zero. As usual, we begin by setting up the equations. s34 \ is normalized to be 1. \ \>", "Text", FontSize->14], Cell[BoxData[{ \(\(s[i_, i_] := 0;\)\), "\[IndentingNewLine]", \(\(s[i_, j_] := s[j, i] /; j < i;\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(S[i_] := \(Sum[G[j]\ s[i, j], {j, 1, 4}] /. VarNames[4]\) /. VarNames2\[IndentingNewLine]\), "\[IndentingNewLine]", \(SEquations1 = Table[S[i] - S[i + 1], {i, 1, 3}] /. {s34 \[Rule] 1}\[IndentingNewLine]\), "\[IndentingNewLine]", \(\(SLagrange = {s12^\((\(-1\))\) + s34^\((\(-1\))\), s13^\((\(-1\))\) + s24^\((\(-1\))\), s14^\((\(-1\))\) + s23^\((\(-1\))\)};\)\), "\[IndentingNewLine]", \(SEquations2 = Numerator[ Factor[Table[ SLagrange[\([Mod[i, 3] + 1]\)] - SLagrange[\([Mod[i + 1, 3] + 1]\)], {i, 1, 3}] /. {s34 \[Rule] 1}]]\)}], "Input", FontSize->14], Cell[TextData[StyleBox["Next we eliminate three of the variables.", FontSize->16]], "Text"], Cell[BoxData[{ \(SolvingFors12s13s23 = \(Solve[ SEquations1 \[Equal] {0, 0, 0}, {s12, s13, s23}]\)[\([1]\)]\[IndentingNewLine]\), "\[IndentingNewLine]", \(SEquations2AfterSubstitution = Numerator[Factor[SEquations2 /. SolvingFors12s13s23]]\)}], "Input"], Cell[TextData[StyleBox["There are only two variables left, s14 and s24. \ Computing resultants yields a complicated degree 7 polynomial in s14.", FontSize->16]], "Text"], Cell[BoxData[{ \(PairwiseResultants = {Factor[ Resultant[SEquations2AfterSubstitution[\([1]\)], SEquations2AfterSubstitution[\([2]\)], s24]], Factor[Resultant[SEquations2AfterSubstitution[\([2]\)], SEquations2AfterSubstitution[\([3]\)], s24]]}\[IndentingNewLine]\), "\[IndentingNewLine]", \(\(p7 = PairwiseResultants[\([2]\)]/\((\(-16\)\ G1\^2\ G2\^5\ G3\ \((G1 + G2 - G3 - G4)\)\ G4)\);\)\)}], "Input"], Cell[BoxData[{ \(\(p7Coefficients = Table[Coefficient[p7, s14, i], {i, 0, 7}];\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(Factor[ GroebnerBasis[ Union[p7Coefficients, {G1\ + \ G2\ + \ G3\ + \ G4, \ G1\ G2\ G3\ G4\ - 1}], {G1, G2, G3, G4}, MonomialOrder \[Rule] DegreeReverseLexicographic]]\)}], "Input"], Cell[BoxData[ \(SpecialCaseEquations = Union[SEquations1, SEquations2] /. {G1 \[Rule] 1, G2 \[Rule] \(-1\), G3 \[Rule] 1, G4 \[Rule] \(-1\), s34 \[Rule] 1}\)], "Input"], Cell[BoxData[ \(GroebnerBasis[ SpecialCaseEquations, {s12, s13, s14, s23, s24}]\)], "Input"], Cell["\<\ Adding in our normalization s34=1, we find explicitly the solutions to the \ special case: \ \>", "Text", FontSize->16], Cell[BoxData[ \(Solve[{\(-2\) + 8\ s24 - 11\ s24\^2 + 6\ s24\^3 - s24\^4, \(-7\) + s23 + 16\ s24 - 11\ s24\^2 + 2\ s24\^3, \(-7\) + s14 + 16\ s24 - 11\ s24\^2 + 2\ s24\^3, \(-16\) + s13 + 33\ s24 - 22\ s24\^2 + 4\ s24\^3, \(-1\) + s12, 1 - s34} \[Equal] {0, 0, 0, 0, 0, 0}, {s12, s13, s14, s23, s24, s34}]\)], "Input"] }, Closed]] }, Open ]] }, FrontEndVersion->"5.2 for Macintosh", ScreenRectangle->{{0, 978}, {0, 746}}, WindowToolbars->{}, WindowSize->{853, 622}, WindowMargins->{{10, Automatic}, {Automatic, 9}}, ShowSelection->True ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1776, 53, 110, 5, 340, "Title"], Cell[CellGroupData[{ Cell[1911, 62, 47, 1, 78, "Section"], Cell[1961, 65, 488, 10, 134, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[2486, 80, 65, 1, 78, "Section"], Cell[2554, 83, 177, 2, 54, "Text"], Cell[2734, 87, 963, 20, 267, "Input"], Cell[3700, 109, 124, 2, 34, "Text"], Cell[3827, 113, 69, 1, 27, "Input"], Cell[3899, 116, 143, 2, 34, "Text"], Cell[4045, 120, 620, 13, 139, "Input"], Cell[4668, 135, 358, 7, 107, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[5063, 147, 64, 1, 48, "Section"], Cell[5130, 150, 207, 7, 94, "Text"], Cell[5340, 159, 1002, 22, 172, "Input"], Cell[6345, 183, 107, 2, 34, "Text"], Cell[6455, 187, 137, 3, 28, "Input"], Cell[6595, 192, 158, 2, 34, "Text"], Cell[6756, 196, 349, 8, 69, "Input"], Cell[7108, 206, 173, 2, 34, "Text"], Cell[7284, 210, 327, 7, 82, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[7648, 222, 64, 1, 48, "Section"], Cell[7715, 225, 234, 7, 94, "Text"], Cell[7952, 234, 570, 13, 91, "Input"], Cell[8525, 249, 210, 8, 35, "Text"], Cell[8738, 259, 476, 10, 123, "Input"], Cell[9217, 271, 110, 2, 34, "Text"], Cell[9330, 275, 124, 3, 31, "Input"], Cell[9457, 280, 102, 1, 34, "Text"], Cell[9562, 283, 353, 7, 75, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[9952, 295, 109, 3, 48, "Section"], Cell[10064, 300, 89, 1, 34, "Text"], Cell[10156, 303, 164, 2, 34, "Text"], Cell[10323, 307, 153349, 2075, 19, "Input", CellOpen->False], Cell[163675, 2384, 89, 1, 34, "Text"], Cell[163767, 2387, 2797, 57, 459, "Input"], Cell[166567, 2446, 140, 6, 74, "Text"], Cell[166710, 2454, 1499, 25, 267, "Input"], Cell[168212, 2481, 343, 10, 55, "Text"], Cell[CellGroupData[{ Cell[168580, 2495, 751, 16, 171, "Input"], Cell[169334, 2513, 36, 1, 27, "Output"], Cell[169373, 2516, 2358, 43, 581, "Output"] }, Open ]], Cell[171746, 2562, 215, 5, 54, "Text"], Cell[171964, 2569, 1067, 20, 203, "Input"], Cell[173034, 2591, 227, 7, 94, "Text"], Cell[173264, 2600, 2730, 46, 539, "Input"], Cell[175997, 2648, 226, 7, 94, "Text"], Cell[CellGroupData[{ Cell[176248, 2659, 105, 2, 27, "Input"], Cell[176356, 2663, 85, 1, 27, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[176478, 2669, 241, 5, 43, "Input"], Cell[176722, 2676, 420, 7, 43, "Output"] }, Open ]], Cell[177157, 2686, 191, 6, 94, "Text"], Cell[177351, 2694, 345, 7, 91, "Input"], Cell[177699, 2703, 345, 7, 91, "Input"], Cell[178047, 2712, 345, 7, 91, "Input"], Cell[178395, 2721, 644, 17, 96, "Text"], Cell[179042, 2740, 165, 2, 43, "Input"], Cell[179210, 2744, 222, 7, 94, "Text"], Cell[179435, 2753, 1347, 24, 283, "Input"], Cell[180785, 2779, 264, 7, 94, "Text"], Cell[181052, 2788, 76, 1, 27, "Input"], Cell[181131, 2791, 262, 7, 94, "Text"], Cell[181396, 2800, 963, 16, 187, "Input"], Cell[182362, 2818, 540, 10, 154, "Text"], Cell[CellGroupData[{ Cell[182927, 2832, 140, 3, 27, "Input"], Cell[183070, 2837, 148, 2, 29, "Output"] }, Open ]], Cell[183233, 2842, 178, 6, 94, "Text"], Cell[183414, 2850, 190, 4, 43, "Input"], Cell[183607, 2856, 420, 10, 134, "Text"], Cell[184030, 2868, 668, 15, 139, "Input"], Cell[184701, 2885, 278, 8, 94, "Text"], Cell[184982, 2895, 427, 8, 92, "Input"], Cell[185412, 2905, 166, 2, 34, "Text"], Cell[185581, 2909, 192, 3, 42, "Input"], Cell[185776, 2914, 363, 9, 114, "Text"], Cell[186142, 2925, 798, 16, 158, "Input"], Cell[186943, 2943, 180, 6, 94, "Text"], Cell[187126, 2951, 384, 6, 91, "Input"], Cell[187513, 2959, 133, 6, 74, "Text"], Cell[187649, 2967, 654, 14, 139, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[188340, 2986, 106, 3, 48, "Section"], Cell[188449, 2991, 301, 8, 94, "Text"], Cell[188753, 3001, 857, 18, 226, "Input"], Cell[189613, 3021, 93, 1, 34, "Text"], Cell[189709, 3024, 292, 5, 59, "Input"], Cell[190004, 3031, 171, 2, 34, "Text"], Cell[190178, 3035, 498, 9, 127, "Input"], Cell[190679, 3046, 380, 8, 75, "Input"], Cell[191062, 3056, 190, 3, 27, "Input"], Cell[191255, 3061, 102, 2, 27, "Input"], Cell[191360, 3065, 132, 6, 74, "Text"], Cell[191495, 3073, 372, 5, 70, "Input"] }, Closed]] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)