Chocolate Games

How High School Students Discovered New Formulas Using Mathematica

Ryohei Miyadera, Shunsuke Nakamura, Yu Okada, Ryo Hanafusa, and Tomoki Ishikawa

This article presents the results of high school mathematics research projects. The authors are Dr. Miyadera and four high school students. Under the leadership of Dr. Miyadera, students have been doing mathematical research using Mathematica for more than 15 years, and they have discovered many formulas and theorems. They have given talks at conferences and published their results in mathematics magazines. In this article the authors present the results of the research on chocolate games, which are variants of the game of Nim. That high school students can discover new theorems and formulas with Mathematica is very important for mathematics education. The authors think that the best way to learn how to be creative is to make something new. The combination of Mathematica and the fresh minds of high school students can produce remarkable results.

Introduction

We study well-known chocolate games and new ones that we have invented. Most of the games presented here have simple formulas for the set of losing states, but many do not, and it is interesting that those have very beautiful graphs for the set of losing states.

Bitter Chocolate Games That Are Variants of Nim

The setup for Nim is a set of heaps that contain objects. For example, three heaps might contain three, four, and five objects. Two players alternate in taking any positive number of objects away from a single heap. The player who takes the last object loses.

Chocolate games generalize Nim to two dimensions. In this section we study well-known chocolate games and variations created by the authors. The chocolate games are simple to play, but they are interesting mathematically.

Definition 1

In a rectangular piece of chocolate made of squares, the brown parts are sweet and a single blue square is very bitter. Two players play alternately. To move, a player breaks the chocolate in a straight line along one of the grooves and eats the rectangular piece broken off. The player who takes the bitter square loses. The same game can be played with a rectangular box made of cubes.

There are other types of chocolate games; one of the most well-known is Chomp []. Again the chocolate is a rectangle made of squares, with the top-left square being very bitter. To move, a player removes a square and all the squares below it and to its right. Many people have studied this game and many interesting theories about it have been developed.

Each chocolate game treated in this article satisfies an inequality, so they are very different from Chomp, and for certain types of inequalities the mathematical structure of the winning strategy is very simple.

The Rectangular Chocolate Games

Can You Win This 2D Game?

Play the chocolate game in Figure  with “nim-sum” unchecked. Choose the values of x, y, z and then click “new game.” Each time you click a line (not a square), you break the chocolate into two pieces along that line and eat the piece without the bitter square []. The game coordinates x, y, z are the number of squares to the left, above, and to the right of the blue square, respectively.

Manipulate[
Module[{ab},
Column[{
Column[{
If[{x,y,z}=={0,0,0},
Text[Style[Row[{If[Mod[game1count,2]==0,"second","first"]," player won"}],Medium]],
Text[Style[Row[{If[Mod[game1count,2]==0,"first","second"]," player's turn"}],Medium]]],
EventHandler[
Framed@Graphics[game1graphics[x,y,z],
PlotRange->{{-8,9},{-1,9}},ImageSize->1.2{350,200},Background->Black],If[((Mod[game1count,2]==0&&firstplayer=="human")||(Mod[game1count,2]==1&&secondplayer=="human"))&&!(x==0&&y==0&&z==0),"MouseDown":>(ab=MousePosition["Graphics"];{x,y,z,game1count}=cutplayer[ab,x,y,z,game1count])]
],
Button["click for computer to move",If[((Mod[game1count,2]==0&&firstplayer=="computer")||(Mod[game1count,2]==1&&secondplayer=="computer"))&&!(x==0&&y==0&&z==0),{x,y,z,game1count}=cutcomputer[x,y,z,game1count]],BaseStyle->{"GenericButton",If[{x,y,z}≠{0,0,0}&&((Mod[game1count,2]==0&&firstplayer=="computer")||(Mod[game1count,2]==1&&secondplayer=="computer")),Bold,{Plain,Gray}]},ImageSize->{210,30}]
},Center],
Text@If[nimsum,Identity,Invisible]@
Column[
{
Style[Row[{x,"⊕",y,"⊕",z," = ",BitXor[x,y,z]}],Medium],Style[If[BitXor[x,y,z]==0,"losing state","winning state"]],
Grid[
Prepend[Transpose[{
{HoldForm[(2^2)],HoldForm[(2^1)],HoldForm[(2^0)]},
IntegerDigits[x,2,3],
IntegerDigits[y,2,3],
IntegerDigits[z,2,3],
IntegerDigits[BitXor[x,y,z],2,3]
}],
{"",Style["x",Italic],Style["y",Italic],Style["z",Italic],"nim\[Hyphen]sum"}],Frame->All]
},Alignment->Center
]
},Alignment->Center]
],

(* controls *)
Column[{
Control@{{nimsum,False,"nim\[Hyphen]sum"},{False,True}},
"",
Style["dimensions relative to bitter square",Bold],
"",
Grid[{
{Row[{Text@Style["x",Italic,10]," left"}],Control@{{x,7,""},0,7,1,ImageSize->Tiny,Appearance->"Labeled"}},
{Row[{Text@Style["y",Italic,10]," above"}],
Control@{{y,7,""},0,7,1,ImageSize->Tiny,Appearance->"Labeled"}},
{Row[{Text@Style["z",Italic,10]," right"}],Control@{{z,7,""},0,7,1,ImageSize->Tiny,Appearance->"Labeled"}}
}],
"",
Style["choice of players",Bold],
"",
Grid[{
{"first",Control@{{firstplayer,"human",""},{"human","computer"}}},
{"second",Control@{{secondplayer,"human",""},{"human","computer"}}}
}],
"",
"",
Button["new game",game1count=0,BaseStyle->{"GenericButton",10},ImageSize->{90,28}],
"",
Style["Click a line to make a move.",Bold]
},Alignment->Center],

ControlPlacement->Left,

Initialization:>{
game1count=0;

game1graphics[x_,y_,z_]:=
{
{Brown,Polygon[{{-x,0},{-x,1+y},{1+z,1+y},{1+z,0}}]},
{Blue,Polygon[{{0,0},{0,1},{1,1},{1,0}}]},
Table[{Black,Line[{{-k,0},{-k,1+y}}]},{k,0,x}],
Table[{Black,Line[{{-x,k},{1+z,k}}]},{k,0,y+1}],
Table[{Black,Line[{{1+k,0},{1+k,1+y}}]},{k,0,z}]
};

cutplayer[ab_,x_,y_,z_,count_]:=
Block[{a,b,X,Y,Z,g},
{a,b}=ab;
X=Y=Z=0;
g=0.2;
If[
-x≤a≤1+z&&0≤b≤1+y,
Do[If[-n-g<a<-n+g,X=x-n],{n,0,x-1}];
Do[If[1+n-g<b<1+n+g,Y=y-n],{n,0,y-1}];
Do[If[1+n-g<a<1+n+g,Z=z-n],{n,0,z}];
];
If[X+Y+Z≠0&&(X+Y==0||Y+Z==0||Z+X==0),
{x-X,y-Y,z-Z,count+1},
{x,y,z,count}
]
];

cutcomputer[x_,y_,z_,count_]:=
Block[{xyzc,randomway},
xyzc={x,y,z,count};
randomway=RandomInteger[{0,x+y+z-1}];
If[BitXor[x,y,z]≠0,
{
If[BitXor[x,y]<z,xyzc={x,y,BitXor[x,y],count+1}],
If[BitXor[y,z]<x,xyzc={BitXor[y,z],y,z,count+1}],
If[BitXor[z,x]<y,xyzc={x,BitXor[z,x],z,count+1}]
},
{
If[randomway≤x-1,xyzc={randomway,y,z,count+1}],
If[x≤randomway≤x+y-1,xyzc={x,randomway-x,z,count+1}],
If[x+y≤randomway,xyzc={x,y,randomway-x-y,count+1}]
}
];
xyzc
]
}
]

In chocolate games there are two kinds of states.

Definition 2

A winning state is a state from which we can force a win as long as we play correctly at every stage. A losing state is a state from which we lose no matter how well we play, if our opponent plays correctly.

The mathematical structure of chocolate game 1 is well-known, and there is a formula to calculate losing states.

Proposition 1

The state {x,y,z} is a losing state of chocolate game 1 if and only if x⊕y⊕z=0, where ⊕ is the bitwise exclusive-or operation (the same as BitXor in Mathematica).

For a proof, see [].

Once we know the formula for losing states, the strategy to win is clear. Suppose that you have a winning state. Then you can choose a move that gives your opponent a losing state. Any move by your opponent is a winning state for you, and you can always move to a losing state again. Finally, you reach {0,0,0} and win the game.

You can use this strategy in chocolate game 1 by selecting “nim-sum.” For each state {x,y,z} you see x⊕y⊕z, and you know if the state {x,y,z} is a losing state or a winning state.

Can You Win This 3D Game?

In the box chocolate game, the bitter (blue) cube is at the bottom of the 3D chocolate; to see it, drag to rotate.

Chocolate game 2 is a little more complicated than chocolate game 1, but the mathematical structure is almost the same.

In chocolate game 2, there are five controls. (You cannot cut the chocolate by clicking a face.)

Proposition 2

The state {v,w,x,y,z} is a losing state of chocolate game 2 if and only if v⊕w⊕ x⊕y⊕z=0.

For a proof, see [].

Manipulate[
Graphics3D[{
Table[{Opacity[.5],Brown,Cuboid[{a,b,c}]},{a,-w,x},{b,-v,y},{c,0,z}],Blue,Cuboid[{0,0,0}]},
Axes->True,PlotRange->{{-5,6},{-5,6},{0,6}},ImageSize->2{250,180}
],
Row[{
Column[{
Style["cut",Bold],
Grid[{
{"",Control@{{y,2,Text@Style["y",Italic,10]},0,5,1,Setter},""},
{
Control@{{w,5,Text@Style["w",Italic,10]},0,5,1,Setter},
Control@{{z,5,Text@Style["z",Italic,10]},0,5,1,Setter},
Control@{{x,5,Text@Style["x",Italic,10]},0,5,1,Setter}
},
{"",Control@{{v,4,Text@Style["v",Italic,10]},0,5,1,Setter},""}
}]
},Alignment->Center],
Graphics3D[{
Arrow[{{0,.5,.5},{-5,.5,.5}}],Text[Style["w",Italic,18],Mean[{{0,.5,.5},{-5,.5,.5}}],{0,1}],
Arrow[{{.5,0,.5},{.5,-5,.5}}],Text[Style["v",Italic,18],Mean[{{.5,0,.5},{.5,-5,.5}}],{-2,0}],
Arrow[{{1,.5,.5},{5,.5,.5}}],Text[Style["x",Italic,18],Mean[{{1,.5,.5},{5,.5,.5}}],{0,1}],
Arrow[{{.5,1,.5},{.5,5,.5}}],Text[Style["y",Italic,18],Mean[{{.5,1,.5},{.5,5,.5}}],{-2.5,0}],
Arrow[{{.5,.5,1},{.5,.5,5}}],
Text[Style["z",Italic,18],{.5,.5,5},{-1.5,0}],
Blue,Cuboid[{0,0,0}]
},Boxed->False,ViewAngle->15Degree,PlotRange->{{-5,6},{-5,5},{0,5}},Axes->False,Ticks->False,ImageSize->.65{250,150},ImagePadding->.1{{10,10},{10,10}},Background->GrayLevel[.959]]
}]
]

Can You Win These New Chocolate Games?

Here are some new chocolate games.

Chocolate Games That Satisfy the Inequality 2y≤z

In chocolate game 3, you can cut the chocolate in three ways: to the left or right of the blue piece, or above it. The coordinates x, y, and z are the maximum number of times you can cut the chocolate in those directions.

The geometry is such that clicking lines with low values of z also deletes y lines, so that the coordinates always satisfy 2y≤z; that is, y≤⌊z/2⌋.

Manipulate[
Module[
{ab},
If[y>Floor[z/2],y=Floor[z/2]];

Column[
{
If[{x,y,z}=={0,0,0},
Text[Style[Row[{If[Mod[game3count,2]==0,"second","first"]," player won"}],Medium]],
Text[Style[Row[{If[Mod[game3count,2]==0,"first","second"]," player's turn"}],Medium]]],
EventHandler[Framed@
Graphics[game3graphics[x,y,z,(* k = *)2 ],
PlotRange->{{-8,9},{-1,8}},ImageSize->1.2{350,200},Background->Black
],
"MouseDown":>(ab=MousePosition["Graphics"];{x,y,z}=cut3[ab,x,y,z,2])
],
Text@If[nimsum,Identity,Invisible]@
Column[{
Style[Row[{x," ⊕ ",y," ⊕ ",z," = ",BitXor[x,y,z]}],Medium],Style[If[BitXor[x,y,z]==0,"losing state","winning state"]],
Grid[
Prepend[Transpose[{
{HoldForm[(2^2)],HoldForm[(2^1)],HoldForm[(2^0)]},
IntegerDigits[x,2,3],
IntegerDigits[Min[y,Floor[z/2]],2,3],
IntegerDigits[z,2,3],
IntegerDigits[BitXor[x,y,z],2,3]}],{"","x","y","z","nim\[Hyphen]sum"}],Frame->All]},Alignment->Center]
},Alignment->Center]
],

(* controls *)
Column[
{
Control@{{nimsum,False,"nim\[Hyphen]sum"},{False,True}},
"",
Style["game coordinates",Bold],
"",
Control@{{x,7,Text@Style["x",Italic,10]},0,7,1,ImageSize->Tiny,Appearance->"Labeled"},
Control@{{y,2,Text@Style["y",Italic,10]},0,Floor[z/2],1,ImageSize->Tiny,Appearance->"Labeled"},
Control@{{z,7,Text@Style["z",Italic,10]},0,7,1,ImageSize->Tiny,Appearance->"Labeled"},
"",
Button[
"new game",
game3count=0,
BaseStyle->{"GenericButton",10},ImageSize->{90,28}
],
"",
Style["Click a line to make a move.",Bold],
"",
"",
Text@Style[Row[{"With ",Style["k",Italic]," = 2, the coordinates\n(",Style["x",Italic],", ",Style["y",Italic],", ",Style["z",Italic],") = (",Dynamic@x,", ",Dynamic@y,", ",Dynamic@z,") satisfy\n",Style["y",Italic]," ≤ ⌊",Style["z",Italic]," / ",Style["k",Italic],"⌋, (",
Dynamic@y," ≤ ",Dynamic@Floor[z/2]," = ⌊",Dynamic@z," / ",2,"⌋)."}],11]
},Alignment->Center
],

ControlPlacement->Left,

Initialization:>(
game3count=0;

game3graphics[x_,y_,z_,k_]:=
{
{Brown,
Polygon[{
{-x,0},{-x,0},
{(-x+1+z)/2-Max[z-(k-1)-k y,0]/2,(x+1+z)/2-Max[z-(k-1)-k y,0]/2},
{(-x+1+z)/2+Max[z-(k-1)-k y,0]/2,(x+1+z)/2-Max[z-(k-1)-k y,0]/2},
{1+z,0}
}]},
{Blue,Polygon[{{0,0},{-x/2,x/2},{(-x+1)/2,(x+1)/2},{1,0}}]},
Table[{Black,Line[{{-t,0},{-x/2-t/2,(x-t)/2}}]},{t,0,x}],
Table[{Black,Line[{{(-x+1+(k-1))/2+t k/2,(x+1+k-1)/2+t k/2},{(1+z-(x+1)/2-(k-1)/2)-t k/2,(x+1+k-1)/2+t k/2}}]},{t,0,y-Boole[y k≤z]}],
Table[{Black,Line[{{1+t,0},{(-x+1+t)/2+Max[(t-y k-(k-1)),0]/2,(x+1+t)/2-Max[(t-y k-(k-1)),0]/2}}]},{t,0,z}]
};

cut3[ab_,x_,y_,z_,k_]:=
Block[
{xyz,a,b,X,Y,Z,g},
xyz={x,y,z};
{a,b}=ab;
X=Y=Z=0;
g=0.2;
If[
0≤b&&b+a>-x&&b-a<x&&b<(x+1+z)/2-Max[z-(k-1)-k y,0]/2&&1+z>b+a,
Do[If[-n-g<b+a<-n+g,X=x-n],{n,0,x-1}];
Do[If[(x+1)/2+(k-1+n k)/2-g<b<(x+1)/2+(k-1+n k)/2+g,Y=y-n],{n,0,y-1}];
Do[If[1+n-g<b+a<1+n+g,Z=z-n],{n,0,z-1}];
xyz={x-X,Min[Floor[(z-Z)/k],y-Y],z-Z}
];
If[
X+Y+Z≠0&&(X+Y==0||Y+Z==0||Z+X==0),
game3count++
];
xyz
]
)
]

Proposition 3

For k=2, {x,y,z} is a losing state of chocolate game 3 if and only if x⊕y⊕z=0.

In fact this proposition is valid for chocolate games with the inequality k y≤z for even k. Although Proposition 3 is very similar to Proposition 1, their proofs are very different. For proofs, see [] and [].

Chocolate Games That Satisfy the Inequality k y≤z

Chocolate game 4 is the same as chocolate game 3, but you can vary k. In this game k y≤z; that is, y≤⌊z/k⌋ for any state.

Manipulate[
Module[
{ab},
If[y>Floor[z/k],y=Floor[z/k]];

Column[
{
If[{x,y,z}=={0,0,0},
Text[Style[Row[{If[Mod[game3count,2]==0,"second","first"]," player won"}],Medium]],
Text[Style[Row[{If[Mod[game3count,2]==0,"first","second"]," player's turn"}],Medium]]],
EventHandler[Framed@
Graphics[game3graphics[x,y,z,(* k = *)k],
PlotRange->{{-8,9},{-1,8}},ImageSize->1.2{350,200},Background->Black
],
"MouseDown":>(ab=MousePosition["Graphics"];{x,y,z}=cut3[ab,x,y,z,k])
]},Alignment->Center]
],
(* controls *)
Column[
{Style["game coordinates",Bold],
"",
Control@{{x,7,Text@Style["x",Italic,10]},0,7,1,ImageSize->Tiny,Appearance->"Labeled"},
Control@{{y,2,Text@Style["y",Italic,10]},0,Floor[z/k],1,ImageSize->Tiny,Appearance->"Labeled"},
Control@{{z,7,Text@Style["z",Italic,10]},0,7,1,ImageSize->Tiny,Appearance->"Labeled"},
Control@{{k,2,Text@Style["k",Italic,10]},1,4,1,ImageSize->Tiny,Appearance->"Labeled"},
"",
Button[
"new game",
game3count=0,
BaseStyle->{"GenericButton",10},ImageSize->{90,28}
],
"",
Style["Click a line to make a move.",Bold],
"",
""
},Alignment->Center
],

ControlPlacement->Left,

Initialization:>(
game3count=0;

game3graphics[x_,y_,z_,k_]:=
{
{Brown,
Polygon[{
{-x,0},{-x,0},
{(-x+1+z)/2-Max[z-(k-1)-k y,0]/2,(x+1+z)/2-Max[z-(k-1)-k y,0]/2},
{(-x+1+z)/2+Max[z-(k-1)-k y,0]/2,(x+1+z)/2-Max[z-(k-1)-k y,0]/2},
{1+z,0}
}]},
{Blue,Polygon[{{0,0},{-x/2,x/2},{(-x+1)/2,(x+1)/2},{1,0}}]},
Table[{Black,Line[{{-t,0},{-x/2-t/2,(x-t)/2}}]},{t,0,x}],
Table[{Black,Line[{{(-x+1+(k-1))/2+t k/2,(x+1+k-1)/2+t k/2},{(1+z-(x+1)/2-(k-1)/2)-t k/2,(x+1+k-1)/2+t k/2}}]},{t,0,y-Boole[y k≤z]}],
Table[{Black,Line[{{1+t,0},{(-x+1+t)/2+Max[(t-y k-(k-1)),0]/2,(x+1+t)/2-Max[(t-y k-(k-1)),0]/2}}]},{t,0,z}]
};

cut3[ab_,x_,y_,z_,k_]:=
Block[
{xyz,a,b,X,Y,Z,g},
xyz={x,y,z};
{a,b}=ab;
X=Y=Z=0;
g=0.2;
If[
0≤b&&b+a>-x&&b-a<x&&b<(x+1+z)/2-Max[z-(k-1)-k y,0]/2&&1+z>b+a,
Do[If[-n-g<b+a<-n+g,X=x-n],{n,0,x-1}];
Do[If[(x+1)/2+(k-1+n k)/2-g<b<(x+1)/2+(k-1+n k)/2+g,Y=y-n],{n,0,y-1}];
Do[If[1+n-g<b+a<1+n+g,Z=z-n],{n,0,z-1}];
xyz={x-X,Min[Floor[(z-Z)/k],y-Y],z-Z}
];
If[
X+Y+Z≠0&&(X+Y==0||Y+Z==0||Z+X==0),
game3count++
];
xyz
]
)
]

The authors are the first researchers who studied chocolate games whose coordinates {x,y,z} satisfy inequalities.

For certain types of inequalities, the mathematical structure of the set of losing states is very similar to that of the well-known games of Nim and rectangular chocolate, but for most inequalities the mathematical structure of the set of losing states is very different.

Chocolate Games That Satisfy the Inequality y≤z

The authors could not find any simple formula for the losing states of triangular chocolate games whose coordinates {x,y,z} satisfy the inequality y≤z. They present a conjecture for the formulas of losing states in Section 3 of []. It seems that chocolate games whose coordinates satisfy k y≤z for odd k do not have simple formulas for the set of losing states, because the set of losing states has very complicated graphs. In Figure  you can see graphs made by the set of losing states; for even k the graph is a Sierpinski gasket and for odd k the graph is complicated. As for the graphs made by losing states, see Figure .

Chocolate Games That Satisfy the Inequality y≤(x+z)/k

Manipulate[
Module[
{ab},
If[yy>Floor[(xx+zz)/k],yy=Floor[(xx+zz)/k]];
Column[{
If[{xx,yy,zz}=={0,0,0},
Text[Style[Row[{If[Mod[game5count2,2]==0,"second","first"]," player won"}],Medium]],
Text[Style[Row[{Dynamic@ab}],11]];
Text[Style[Row[{If[Mod[game5count2,2]==0,"first","second"]," player's turn"}],Medium]]],
EventHandler[Framed[game5graphics2[xx,yy,zz,k,sst]],{"MouseClicked":>(ab=MousePosition["Graphics"];
{xx,yy,zz,game5count2,sst}=cut52[ab,xx,yy,zz,k,game5count2])}]
},Alignment->Center]
],

Column[{
Style["game coordinates",Bold],
"",
Control@{{xx,7,Text@Style["x",Italic,10]},0,7,1,ImageSize->Tiny,Appearance->"Labeled"},
Control@{{zz,7,Text@Style["z",Italic,10]},0,7,1,ImageSize->Tiny,Appearance->"Labeled"},
Control@{{yy,Floor[(xx+zz)/k],Text@Style["y",Italic,10]},0,Floor[(xx+zz)/k],1,ImageSize->Tiny,Appearance->"Labeled"},
Control@{{k,1,Text@Style["k",Italic,10]},1,4,1,ImageSize->Tiny,Appearance->"Labeled"},
"",
Button[
"new game",
game5count2=0,
BaseStyle->{"GenericButton",10},ImageSize->{90,28}
],
"",
Style["Click a line to make a move.",Bold]
},Alignment->Center
],
ControlPlacement->Left,
Initialization:>(
game5count2=0;
game5graphics2[x_,y_,z_,k_,st_]:=
Graphics[{
{
Brown,Polygon[{
{-x-0.5,0},{z+0.5,0},

If[
y==Floor[(x+z)/k],
{0.5+z-(x+z+1)/2,(x+z+1)/2},
{0.5+z-k (y+1)/2,(k+k y)/2}
],
If[
y==Floor[(x+z)/k],
{-(x+0.5)+(x+z+1)/2,(x+z+1)/2},
{-(x+0.5)+k (y+1)/2,(k+k y)/2}]
}]
},
{Blue,Polygon[{{-0.5,0},{0.5,0},{0,0.5}}]},
Table[
Line[{
{-0.5-n,0},
If[
Floor[(n+z)/k]≤y,
{-0.5-n+(n+z+1)/2,(n+z+1)/2},
{-0.5-n+(n+z+1)/2-((n+z+1)-(y+1) k)/2,(n+z+1)/2-((n+z+1)-(y+1) k)/2}
]
}],{n,0,x}],
Table[
Line[{
{n+0.5,0},
If[
Floor[(n+x)/k]≤y,
{0.5+n-(n+x+1)/2,(n+x+1)/2},{0.5+n-(n+x+1)/2+((n+x+1)-(y+1) k)/2,(n+x+1)/2-((n+x+1)-(y+1) k)/2}
]
}],{n,0,z}],
Table[
Line[{
{-0.5-x+Min[n k,x+z+1]/2,Min[n k,x+z+1]/2},{z+0.5-Min[n k,x+z+1]/2,Min[n k,x+z+1]/2}
}],{n,0,y+1}]
},PlotRange->{{-8,8},{0,8}},ImageSize->1.2{350,200},Background->Black];

cut52[ab_,x_,y_,z_,k_,count_]:=
Block[
{f,a,b,xyzc},
f=True;
{a,b}=ab;
xyzc={x,y,z,count,ab};
If[b≤0||b≥Min[(y+1) k,x+z+1]/2||a+b≥z+ (1/k)||b-a≥x+ (1/2),f=False];
Do[If[Abs[-0.5-n-(a-b)]≤0.33&&f,xyzc={n,Min[Floor[(n+z)/k],y],z,count+1,ab};f=False,],{n,0,x-1}];
Do[If[Abs[0.5+n-(a+b)]≤0.33&&f,xyzc={x,Min[Floor[(x+n)/k],y],n,count+1,ab};f=False,],{n,0,z-1}];
Do[If[Abs[(n+1)k/2-b]≤(0.33k)&&f,xyzc={x,n,z,count+1,ab};f=False],{n,0,y-1}];
xyzc
]
)
]

Conjecture 1

For a triangular chocolate game satisfying y≤(x+z) / k, {x,y,z} is a losing state if and only if x⊕y⊕y=0 when k=3 (mod 4), and {x+1,y,z+1} is a losing state if and only if x⊕y⊕y=0 when k=1 (mod 4).

This conjecture is Proposition 4 when k=1 and is proved for k=3 in [].

For other types of chocolate games that the authors studied, see [], [], [], and [].

Chocolate Games That Satisfy the Inequality y≤x+z

Manipulate[
(* The code is the same as for Figure 5 except for the nim-sum part and k=1. *)
Module[
{ab,k=1},
If[y>Floor[(x+z)/k],y=Floor[(x+z)/k]];


Column[{
If[{x,y,z}=={0,0,0},
Text[Style[Row[{If[Mod[game5count,2]==0,"second","first"]," player won"}],Medium]],
Text[Style[Row[{If[Mod[game5count,2]==0,"first","second"]," player's turn"}],Medium]]],
EventHandler[Framed@Graphics[game5graphics[x,y,z,k],PlotRange->{{-11,11},{-1,11}},ImageSize->1.2{350,200},Background->Black]
,"MouseClicked":>(ab=MousePosition["Graphics"];{x,y,z}=cut5[ab,x,y,z,1])]
,
Text@If[nimsum,Identity,Invisible]@
Column[
{
Style[Row[{"(",x," + 1) ⊕ ",y," ⊕ (",z," + 1) = ",BitXor[x,y,z]}],Medium],Style[If[BitXor[x,y,z]==0,"losing state","winning state"]],
Grid[
Prepend[Transpose[{
{HoldForm[(2^3)],HoldForm[(2^2)],HoldForm[(2^1)],HoldForm[(2^0)]},
IntegerDigits[x+1,2,4],
IntegerDigits[y,2,4],
IntegerDigits[z+1,2,4],
IntegerDigits[BitXor[x+1,y,z+1],2,4]
}],
{"",Row[{Style["x",Italic]," + 1"}],Style["y",Italic],Row[{Style["z",Italic]," + 1"}],"nim\[Hyphen]sum"}],Frame->All]
},Alignment->Center
]
},Alignment->Center]
],

Column[{
Control@{{nimsum,False,"nim\[Hyphen]sum"},{False,True}},
"",
Style["game coordinates",Bold],
"",
Grid[{
{Row[{Text@Style["x",Italic,10]," left"}],Control@{{x,7,""},0,7,1,ImageSize->Tiny,Appearance->"Labeled"}},
{Row[{Text@Style["y",Italic,10]," above"}],
Control@{{y,7,""},0,14,1,ImageSize->Tiny,Appearance->"Labeled"}},
{Row[{Text@Style["z",Italic,10]," right"}],Control@{{z,7,""},0,7,1,ImageSize->Tiny,Appearance->"Labeled"}}
}],
"",
Button[
"new game",
game5count=0,
BaseStyle->{"GenericButton",10},ImageSize->{90,28}
],
"",
Style["Click a line to make a move.",Bold]
},Alignment->Center],

ControlPlacement->Left,

Initialization:>(
game5count=0;
game5graphics[x_,y_,z_,k_]:=
{
{
Brown,Polygon[{
{-x-0.5,0},{z+0.5,0},

If[
y==Floor[(x+z)/k],
{0.5+z-(x+z+1)/2,(x+z+1)/2},
{0.5+z-k (y+1)/2,(k+k y)/2}
],
If[
y==Floor[(x+z)/k],
{-(x+0.5)+(x+z+1)/2,(x+z+1)/2},
{-(x+0.5)+k (y+1)/2,(k+k y)/2}]
}]
},
{Blue,Polygon[{{-0.5,0},{0.5,0},{0,0.5}}]},
Table[
Line[{
{-0.5-n,0},
If[
Floor[(n+z)/k]≤y,
{-0.5-n+(n+z+1)/2,(n+z+1)/2},
{-0.5-n+(n+z+1)/2-((n+z+1)-(y+1) k)/2,(n+z+1)/2-((n+z+1)-(y+1) k)/2}
]
}],{n,0,x}],
Table[
Line[{
{n+0.5,0},
If[
Floor[(n+x)/k]≤y,
{0.5+n-(n+x+1)/2,(n+x+1)/2},{0.5+n-(n+x+1)/2+((n+x+1)-(y+1) k)/2,(n+x+1)/2-((n+x+1)-(y+1) k)/2}
]
}],{n,0,z}],
Table[
Line[{
{-0.5-x+Min[n k,x+z+1]/2,Min[n k,x+z+1]/2},{z+0.5-Min[n k,x+z+1]/2,Min[n k,x+z+1]/2}
}],{n,0,y+1}]
};

cut5[ab_,x_,y_,z_,k_]:=
Block[
{f,a,b,xyzc},
f=True;
{a,b}=ab;
xyzc={x,y,z};
If[b≤0||b≥Min[(y+1) k,x+z+1]/2||a+b≥z+0.5||b-a≥x+0.5,f=False];
Do[If[Abs[-0.5-n-(a-b)]<0.2&&f,xyzc={n,Min[Floor[(n+z)/k],y],z};f=False],{n,0,x-1}];
Do[If[Abs[0.5+n-(a+b)]≤0.2&&f,xyzc={x,Min[Floor[(x+n)/k],y],n};f=False],{n,0,z-1}];
Do[If[Abs[(n+1) k/2-b]<0.2&&f,xyzc={x,n,z};f=False],{n,0,y-1}];
game5count++;
xyzc
]
)
]

Proposition 4

For the triangular chocolate game that satisfies the inequality y≤x+z, {x+1,y,z+1} is a losing state if and only if x⊕y⊕y=0.

For a proof, see [].

Chocolate Games That Satisfy the Inequalities 2x≤y and 2y≤z

Manipulate[
If[x>Min[Floor[y/2],Floor[z/4]],x=Min[Floor[y/2],Floor[z/4]]];
If[y>Floor[z/2],y=Floor[z/2]];
Framed@game7graphics[w,x,y,z],

Column[{
"",
Style["game coordinates",Bold],
"",
Control@{{w,6,Text@Style["w",Italic,10]},0,6,1,ImageSize->Tiny,Appearance->"Labeled"},
"",
Control@{{x,4,Text@Style["x",Italic,10]},0,4,1,ImageSize->Tiny,Appearance->"Labeled"},
Control@{{y,8,Text@Style["y",Italic,10]},0,8,1,ImageSize->Tiny,Appearance->"Labeled"},
Control@{{z,16,Text@Style["z",Italic,10]},0,16,1,ImageSize->Tiny,Appearance->"Labeled"},
"",
Text@Style[Row[{"The ",Style["x",Italic]," and ",Style["y",Italic]," coordinates are automatically\nadjusted to keep 2 ",Style["x",Italic]," ≤ ",Style["y",Italic]," and 2 ",Style["y",Italic]," ≤ ",Style["z",Italic],"."}],10],
"",
Framed@Graphics3D[
{
Arrow[{{0,0,0},{1,0,0}}],
Arrow[{{0,0,0},{0,1,0}}],
Arrow[{{0,0,0},{0,0,1}}],
Arrow[{{0,0,0},{0,0,-.5}}],
Text[Style["x",Italic],{1.2,0,0}],
Text[Style["y",Italic],{0,1.3,0}],
Text[Style["z",Italic],{0,0,1.2}],
Text[Style["w",Italic],{0,0,-.7}]
},Boxed->False,ImageSize->.7{100,100},ImagePadding->5,PlotRange->{{0,1},{0,1},{-1,1}},Background->GrayLevel[.959]]
},Alignment->Center],

ControlPlacement->Left,
Initialization:>(
game7graphics[w_,x_,y_,z_]:=Block[
{bb,bb2,ss,aa,bb0},
ss=4;
aa=Flatten[Table[{a,b,c},{a,0,ss},{b,0,2ss},{c,0,4ss}],2];
bb0=Select[aa,2#[[1]]≤#[[2]]&&2#[[2]]≤#[[3]]&];
bb02=Table[{0,0,-n},{n,1,6}];
bb=Select[bb0,#[[1]]≤x&&#[[2]]≤y&&#[[3]]≤z&];
bb2=Select[bb02,Abs[#[[3]]]≤w&];
Graphics3D[{
Table[{Brown,Cuboid[bb2[[h]]]},{h,1,Length[bb2]}],
Table[{Brown,Cuboid[bb[[h]]]},{h,1,Length[bb]}],
{Blue,Cuboid[{0,0,0}]}
},Boxed->False,PlotRange->{{0,4},{0,8},{-6,18}},ImageSize->2{100,200},Background->Black]
];
)
]

Conjecture 2

For the chocolate game that satisfies the inequalities 2x≤y and 2y≤z, the state {w,x,y,z} is a losing state of this chocolate game if and only if w⊕x⊕y⊕z=0.

The authors have proved but not published this proposition.

Grundy Numbers and Chocolate Games

Here the authors present a Mathematica program to calculate losing states of the chocolate game whose coordinates satisfy the inequality k y≤z. First define the function move({x,y,z}) for each state {x,y,z} of the chocolate and the function mex(A), where A is a set of positive integers.

Definition 3

The function move({x,y,z}) is the union of the four sets {{u,y,z};u<x}, {{x,v,z};v<y}, {{x,v,w};w<z}, and {{x,min({y,⌊w / k⌋),w};w<z}, where x, v, w are non-negative integers.

Definition 4

The function mex(A) is the smallest non-negative integer that is not an element of the set A (the “minimum excluded ordinal”).

Example 1

mex({0,2,3,4})=1 and mex({0,1,3,4})=2.

This defines the Grundy number G({x,y,z}) recursively.

Definition 5

Let G({0,0,0})=0 and G({x,y,z})=mex(G({u,v,w});{u,v,w}∈move({x,y,z})).

Proposition 5

The state {x,y,z} is a losing state of the chocolate game if and only if G({x,y,z})=0.

This is a well-known fact in the field of combinatorial games.

Restricting the Number of Rows and Columns You Can Remove

This game has two coordinates {x,y} with the inequality k y≤x; x and y are the height and width of the chocolate when we ignore the blue part.

See Figure ; here h is the upper bound of the number of the rows and columns you can remove. Below the game is the table of Grundy numbers {G({x,y}),x=0,1,…,y=0,1,…}.

Manipulate[
If[k y≥x,y=Floor[x/k]];
Module[{ab},
Pane[
Column[{
If[{x,y}=={0,0},
Text[Style[Row[{If[Mod[game8count,2]==0,"second","first"]," player won"}],Medium]],
Text[Style[Row[{If[Mod[game8count,2]==0,"first","second"]," player's turn"}],Medium]]],
EventHandler[Framed[game8graphics[x,y,k]],
{"MouseClicked":>(ab=MousePosition["Graphics"];{x,y,game8count}=cut8[ab,x,y,h,k,game8count])}],
"",
Text@grundylist[x,y,h,k]
},Alignment->Center],ImageSize->{250,520}]
],

Column[{
Style["game coordinates",Bold],
"",
Control@{{x,5,Text@Style["x",Italic,10]},0,10,1,ImageSize->Tiny,Appearance->"Labeled"},
Control@{{y,8,Text@Style["y",Italic,10]},0,20,1,ImageSize->Tiny,Appearance->"Labeled"},
"",
Control@{{h,3,Text@Style["h",Italic,10]},0,10,1,ImageSize->Tiny,Appearance->"Labeled"},
Control@{{k,2,Text@Style["k",Italic,10]},1,5,1,ImageSize->Tiny,Appearance->"Labeled"},
"",
Button[
"new game",
game8count=0,
BaseStyle->{"GenericButton",10},ImageSize->{90,28}
],
"",
Style["Click a line to make a move.",Bold]
},Alignment->Center
],

ControlPlacement->Left,

Initialization:>
(
game8count=0;

game8graphics[x_,y_,k_]:=
Graphics[{
Table[{EdgeForm[Thin],Brown,Rectangle[{n,-m}]},{m,0,x},{n,0,Min[Floor[m/k],y]}],
EdgeForm[Thin],Blue,Rectangle[{0,0}]
},Background->Black,PlotRange->{{-2,12},{-12,2}},ImageSize->1.2{200,200}];

cut8[ab_,x_,y_,h_,k_,count_]:=
Block[
{f,temp,xyc},
{a,b}=ab;
f=True;
xyc={x,y,count};
If[a≤0||b≤-x||a≥y+1,f=False];
Do[If[Abs[b+i]≤0.2&&f,temp={i,y,count};f=False],{i,Max[x-h,0],x}];
Do[If[Abs[a-i-1]≤0.2&&f,temp={x,i,count};f=False],{i,Max[y-h,0],y}];
If[xyc≠temp,temp+{0,0,1},xyc]
];

mex[L_]:=Min[Complement[Range[0,Length[L]],L]];

move[{m_,n_},h_,k_]:=Union[
Table[{i,Min[Floor[i/k ],n]},{i,Max[0,m-h],m-1}],
Table[{m,j},{j,Max[0,n-h],n-1}]
];

Gr[pos_,h_,k_]:=Gr[pos,h,k]=mex[Map[Gr[#,h,k]&,move[pos,h,k]]];

grundylistAux[{m_,n_},h_,k_]:=
If[
{m,n}=={-1,-1},"",
If[
n==-1,m,
If[
m==-1,n,
If[
m≥k n,Gr[{m,n},h,k],
""
]
]
]
];

grundylist[x_,y_,h_,k_]:=
Block[
{p,q},
p=
Select[
Select[
Flatten[Outer[List,Range[0,x],Range[0,y]],1],
1/k#[[1]]≥#[[2]]&
],
Gr[#,h,k]==0&
];
q=Select[
Flatten[Outer[List,Range[2,x+2],Range[2+Min[x,y]]],1],(#[[1]]-2)<k (#[[2]]-2)&
];
Row[{
Style["x",Italic],
Spacer[5],
Column[{
Style["y",Italic],
Grid[
Table[grundylistAux[{m,n},h,k],{m,-1,x},{n,-1,y}],Frame->All,Background->
{
None,None,
Join[
Table[q[[s]]->GrayLevel[0.1],{s,Length[q]}],
Table[
{p[[s,1]]+2,p[[s,2]]+2}->Blue,{s,Length[p]}]
]
}
]
},Alignment->Center]
}]

]

)
]

Conjecture 3

Let h, k be natural numbers such that h<k.

G ({t,k t})=h+1, for any natural number t.

If k y<z, then G ({y,z})=mod (z – y,h+1).

Mathematica Programs for Chocolate Games

Mathematica Programs to Calculate Losing States

By Proposition 5, {x,y,z} is a losing state if and only if the Grundy number G({x,y,z})=0.

Calculating Losing States with Grundy Numbers

Here is a Mathematica program to calculate losing states using Grundy numbers. Here k=4. This Mathematica program comes from []. The definition for mex is as in the code for Figure . The definitions for move3 and Gr3 are modifications of move and Gr from that code, so we change their names slightly.

mex[L_]:=Min[Complement[Range[0,Length[L]],L]]

move3[{m_,n_,p_},k_]:=
Union[
Table[{a,n,p},{a,0,m-1}],Table[{m,b,p},{b,0,n-1}],Table[{m,Min[c/k,n],c},{c,0,p-1}]
]

Gr3[pos_,k_]:=Gr3[pos,k]=mex[Map[Gr3[#,k]&,move3[pos,k]]]

These are the candidate states for a particular case.

allstates[k_,s_]:=allstates[k,s]=
Select[
Flatten[Table[{a,b,c},{a,0,s},{b,0,s},{c,0,s}],2],
1/k #[[3]]≥#[[2]] &]

allstates[4,20]

Length@allstates[4,20]

This calculates the losing states using Grundy numbers.

losing=Select[allstates[4,20],Gr3[#,4]==0 &]

Indeed these are losing states.

BitXor@@@losing

There are no other losing states.

MemberQ[BitXor@@@Complement[allstates[4,20],losing],0]

Calculating Losing States Using Grundy-Like Numbers

Here the authors define the Grundy-like numbers (Subscript[G, 2])({x,y,z}), which are efficient to calculate.

Definition 6

For any state {x,y,z}, let (Subscript[G, 2])({x,y,z})=(a,b,c), where (a,b,c) is defined by the following rules.

If x=0, then let a=0. If y=0, then let b=0. If z=0, then let c=0.

Suppose that x≥1 and (Subscript[G, 2])({x–1,y,z})=(p,q,r).

Let a=0, if (p,q,r)=(0,0,0).

Let a=p, if (p,q,r)≠(0,0,0).

Suppose that y≥1 and (Subscript[G, 2])({x,y–1,z})=(p,q,r).

Let b=1, if (p,q,r)=(0,0,0).

Let b=q, if (p,q,r)≠(0,0,0).

Suppose that z≥1 and (Subscript[G, 2])({x,min( z–1,y),z–1})=(p,q,r).

Let c=1, if (p,q,r)=(0,0,0).

Let c=r, if (p,q,r)≠(0,0,0).

Proposition 6

The state {x,y,z} is a losing state of the chocolate game if and only if (Subscript[G, 2])({x,y,z})=0.

For a proof of this proposition see Theorem 4.2 of [].

This defines the corresponding Mathematica function G2.

G2[{x_,y_,z_},k_]:=G2[{x,y,z},k]=Module[
{w},
w=Min[Floor[1/k (z-1)],y];
{
If[x > 0,If[Norm[G2[{x-1,y,z},k]]==0,1,G2[{x-1,y,z},k][[1]]],0],If[y > 0,If[Norm[G2[{x,y-1,z},k]]==0,1,G2[{x,y-1,z},k][[2]]],0],
If[z > 0,If[Norm[G2[{x,w,z-1},k]]==0,1,G2[{x,w,z-1},k][[3]]],0]
}
]

This calculates the losing states using Grundy-like numbers.

losing2=Select[allstates[4,20],G2[#,4]=={0,0,0} &]

They are exactly all the losing states.

Apply[And,0==#&/@BitXor@@@losing2]&&Not[MemberQ[BitXor@@@Complement[allstates[4,20],losing2],0]]

Graphs of the Set of Losing States

Here are some graphs of the set of losing states of chocolate games. (For more, see [].)

2D and 3D Graphs of the Set of Losing States of the Triangular Chocolate Game with k y≤z

By Proposition 2 there is a simple formula for the set of losing states of the chocolate games satisfying k y≤z, where k is even. In Figure  the graph is a Sierpinski gasket for even k.

When k is odd, the graph is very different from a Sierpinski gasket. Since the graph is quite complicated, it seems likely that there is no simple formula for the set of losing states. As for the relation between the graphs of losing states and the Sierpinski gasket, see [] (in Japanese).

Manipulate[
If[
ns=="2D",
ListPlot[Map[{#[[2]],#[[1]]-#[[3]]}&,Select[datayz9[[k]],#[[1]]≤s&&#[[2]]≤s&&#[[3]]≤s&]],Background->Black,PlotStyle->Yellow,ImageSize->1.6{350,200}],
ListPointPlot3D[Map[{#[[1]],#[[2]],#[[3]]}&,Select[datayz9[[k]],#[[1]]≤s&&#[[2]]≤s&&#[[3]]≤s&]],Axes->False,Background->Black,ColorFunction->"Rainbow",PlotStyle->PointSize[0.01],ImageSize->1.6{350,200}]],
Row[{
Control@{{ns,"2D",""},{"2D","3D"},ControlType->Setter},
Spacer[30],
Control@{{k,1},1,5,1,Setter},
Spacer[30],
Control@{{s,50},1,75,1,ImageSize->Small,Appearance->"Labeled"}
}],
Initialization:>
(
datayz9={{{0,0,0},{1,0,1},{1,1,2},{1,2,3},{1,3,4},{1,4,5},{1,5,6},{1,6,7},{1,7,8},{1,8,9},{1,9,10},{1,10,11},{1,11,12},{1,12,13},{1,13,14},{1,14,15},{1,15,16},{1,16,17},{1,17,18},{1,18,19},{1,19,20},{1,20,21},{1,21,22},{1,22,23},{1,23,24},{1,24,25},{1,25,26},{1,26,27},{1,27,28},{1,28,29},{1,29,30},{1,30,31},{1,31,32},{1,32,33},{1,33,34},{1,34,35},{1,35,36},{1,36,37},{1,37,38},{1,38,39},{1,39,40},{1,40,41},{1,41,42},{1,42,43},{1,43,44},{1,44,45},{1,45,46},{1,46,47},{1,47,48},{1,48,49},{1,49,50},{1,50,51},{1,51,52},{1,52,53},{1,53,54},{1,54,55},{1,55,56},{1,56,57},{1,57,58},{1,58,59},{1,59,60},{1,60,61},{1,61,62},{1,62,63},{1,63,64},{1,64,65},{1,65,66},{1,66,67},{1,67,68},{1,68,69},{1,69,70},{1,70,71},{1,71,72},{1,72,73},{1,73,74},{1,74,75},{1,75,76},{2,0,2},{2,1,1},{3,0,3},{3,1,4},{3,2,2},{4,0,4},{4,1,3},{4,2,5},{4,3,6},{4,4,7},{4,5,8},{4,6,9},{4,7,10},{4,8,11},{4,9,12},{4,10,13},{4,11,14},{4,12,15},{4,13,16},{4,14,17},{4,15,18},{4,16,19},{4,17,20},{4,18,21},{4,19,22},{4,20,23},{4,21,24},{4,22,25},{4,23,26},{4,24,27},{4,25,28},{4,26,29},{4,27,30},{4,28,31},{4,29,32},{4,30,33},{4,31,34},{4,32,35},{4,33,36},{4,34,37},{4,35,38},{4,36,39},{4,37,40},{4,38,41},{4,39,42},{4,40,43},{4,41,44},{4,42,45},{4,43,46},{4,44,47},{4,45,48},{4,46,49},{4,47,50},{4,48,51},{4,49,52},{4,50,53},{4,51,54},{4,52,55},{4,53,56},{4,54,57},{4,55,58},{4,56,59},{4,57,60},{4,58,61},{4,59,62},{4,60,63},{4,61,64},{4,62,65},{4,63,66},{4,64,67},{4,65,68},{4,66,69},{4,67,70},{4,68,71},{4,69,72},{4,70,73},{4,71,74},{4,72,75},{4,73,76},{4,74,77},{4,75,78},{5,0,5},{5,1,6},{5,2,4},{5,3,3},{6,0,6},{6,1,5},{6,2,7},{6,3,8},{6,4,4},{7,0,7},{7,1,8},{7,2,6},{7,3,5},{7,4,9},{7,5,10},{7,6,11},{7,7,12},{7,8,13},{7,9,14},{7,10,15},{7,11,16},{7,12,17},{7,13,18},{7,14,19},{7,15,20},{7,16,21},{7,17,22},{7,18,23},{7,19,24},{7,20,25},{7,21,26},{7,22,27},{7,23,28},{7,24,29},{7,25,30},{7,26,31},{7,27,32},{7,28,33},{7,29,34},{7,30,35},{7,31,36},{7,32,37},{7,33,38},{7,34,39},{7,35,40},{7,36,41},{7,37,42},{7,38,43},{7,39,44},{7,40,45},{7,41,46},{7,42,47},{7,43,48},{7,44,49},{7,45,50},{7,46,51},{7,47,52},{7,48,53},{7,49,54},{7,50,55},{7,51,56},{7,52,57},{7,53,58},{7,54,59},{7,55,60},{7,56,61},{7,57,62},{7,58,63},{7,59,64},{7,60,65},{7,61,66},{7,62,67},{7,63,68},{7,64,69},{7,65,70},{7,66,71},{7,67,72},{7,68,73},{7,69,74},{7,70,75},{7,71,76},{7,72,77},{7,73,78},{7,74,79},{7,75,80},{8,0,8},{8,1,7},{8,2,9},{8,3,10},{8,4,6},{8,5,5},{9,0,9},{9,1,10},{9,2,8},{9,3,7},{9,4,11},{9,5,12},{9,6,6},{10,0,10},{10,1,9},{10,2,11},{10,3,12},{10,4,8},{10,5,7},{10,6,13},{10,7,14},{10,8,15},{10,9,16},{10,10,17},{10,11,18},{10,12,19},{10,13,20},{10,14,21},{10,15,22},{10,16,23},{10,17,24},{10,18,25},{10,19,26},{10,20,27},{10,21,28},{10,22,29},{10,23,30},{10,24,31},{10,25,32},{10,26,33},{10,27,34},{10,28,35},{10,29,36},{10,30,37},{10,31,38},{10,32,39},{10,33,40},{10,34,41},{10,35,42},{10,36,43},{10,37,44},{10,38,45},{10,39,46},{10,40,47},{10,41,48},{10,42,49},{10,43,50},{10,44,51},{10,45,52},{10,46,53},{10,47,54},{10,48,55},{10,49,56},{10,50,57},{10,51,58},{10,52,59},{10,53,60},{10,54,61},{10,55,62},{10,56,63},{10,57,64},{10,58,65},{10,59,66},{10,60,67},{10,61,68},{10,62,69},{10,63,70},{10,64,71},{10,65,72},{10,66,73},{10,67,74},{10,68,75},{10,69,76},{10,70,77},{10,71,78},{10,72,79},{10,73,80},{10,74,81},{10,75,82},{11,0,11},{11,1,12},{11,2,10},{11,3,9},{11,4,13},{11,5,14},{11,6,8},{11,7,7},{12,0,12},{12,1,11},{12,2,13},{12,3,14},{12,4,10},{12,5,9},{12,6,15},{12,7,16},{12,8,8},{13,0,13},{13,1,14},{13,2,12},{13,3,11},{13,4,15},{13,5,16},{13,6,10},{13,7,9},{13,8,17},{13,9,18},{13,10,19},{13,11,20},{13,12,21},{13,13,22},{13,14,23},{13,15,24},{13,16,25},{13,17,26},{13,18,27},{13,19,28},{13,20,29},{13,21,30},{13,22,31},{13,23,32},{13,24,33},{13,25,34},{13,26,35},{13,27,36},{13,28,37},{13,29,38},{13,30,39},{13,31,40},{13,32,41},{13,33,42},{13,34,43},{13,35,44},{13,36,45},{13,37,46},{13,38,47},{13,39,48},{13,40,49},{13,41,50},{13,42,51},{13,43,52},{13,44,53},{13,45,54},{13,46,55},{13,47,56},{13,48,57},{13,49,58},{13,50,59},{13,51,60},{13,52,61},{13,53,62},{13,54,63},{13,55,64},{13,56,65},{13,57,66},{13,58,67},{13,59,68},{13,60,69},{13,61,70},{13,62,71},{13,63,72},{13,64,73},{13,65,74},{13,66,75},{13,67,76},{13,68,77},{13,69,78},{13,70,79},{13,71,80},{13,72,81},{13,73,82},{13,74,83},{13,75,84},{14,0,14},{14,1,13},{14,2,15},{14,3,16},{14,4,12},{14,5,11},{14,6,17},{14,7,18},{14,8,10},{14,9,9},{15,0,15},{15,1,16},{15,2,14},{15,3,13},{15,4,17},{15,5,18},{15,6,12},{15,7,11},{15,8,19},{15,9,20},{15,10,10},{16,0,16},{16,1,15},{16,2,17},{16,3,18},{16,4,14},{16,5,13},{16,6,19},{16,7,20},{16,8,12},{16,9,11},{16,10,21},{16,11,22},{16,12,23},{16,13,24},{16,14,25},{16,15,26},{16,16,27},{16,17,28},{16,18,29},{16,19,30},{16,20,31},{16,21,32},{16,22,33},{16,23,34},{16,24,35},{16,25,36},{16,26,37},{16,27,38},{16,28,39},{16,29,40},{16,30,41},{16,31,42},{16,32,43},{16,33,44},{16,34,45},{16,35,46},{16,36,47},{16,37,48},{16,38,49},{16,39,50},{16,40,51},{16,41,52},{16,42,53},{16,43,54},{16,44,55},{16,45,56},{16,46,57},{16,47,58},{16,48,59},{16,49,60},{16,50,61},{16,51,62},{16,52,63},{16,53,64},{16,54,65},{16,55,66},{16,56,67},{16,57,68},{16,58,69},{16,59,70},{16,60,71},{16,61,72},{16,62,73},{16,63,74},{16,64,75},{16,65,76},{16,66,77},{16,67,78},{16,68,79},{16,69,80},{16,70,81},{16,71,82},{16,72,83},{16,73,84},{16,74,85},{16,75,86},{17,0,17},{17,1,18},{17,2,16},{17,3,15},{17,4,19},{17,5,20},{17,6,14},{17,7,13},{17,8,21},{17,9,22},{17,10,12},{17,11,11},{18,0,18},{18,1,17},{18,2,19},{18,3,20},{18,4,16},{18,5,15},{18,6,21},{18,7,22},{18,8,14},{18,9,13},{18,10,23},{18,11,24},{18,12,12},{19,0,19},{19,1,20},{19,2,18},{19,3,17},{19,4,21},{19,5,22},{19,6,16},{19,7,15},{19,8,23},{19,9,24},{19,10,14},{19,11,13},{19,12,25},{19,13,26},{19,14,27},{19,15,28},{19,16,29},{19,17,30},{19,18,31},{19,19,32},{19,20,33},{19,21,34},{19,22,35},{19,23,36},{19,24,37},{19,25,38},{19,26,39},{19,27,40},{19,28,41},{19,29,42},{19,30,43},{19,31,44},{19,32,45},{19,33,46},{19,34,47},{19,35,48},{19,36,49},{19,37,50},{19,38,51},{19,39,52},{19,40,53},{19,41,54},{19,42,55},{19,43,56},{19,44,57},{19,45,58},{19,46,59},{19,47,60},{19,48,61},{19,49,62},{19,50,63},{19,51,64},{19,52,65},{19,53,66},{19,54,67},{19,55,68},{19,56,69},{19,57,70},{19,58,71},{19,59,72},{19,60,73},{19,61,74},{19,62,75},{19,63,76},{19,64,77},{19,65,78},{19,66,79},{19,67,80},{19,68,81},{19,69,82},{19,70,83},{19,71,84},{19,72,85},{19,73,86},{19,74,87},{19,75,88},{20,0,20},{20,1,19},{20,2,21},{20,3,22},{20,4,18},{20,5,17},{20,6,23},{20,7,24},{20,8,16},{20,9,15},{20,10,25},{20,11,26},{20,12,14},{20,13,13},{21,0,21},{21,1,22},{21,2,20},{21,3,19},{21,4,23},{21,5,24},{21,6,18},{21,7,17},{21,8,25},{21,9,26},{21,10,16},{21,11,15},{21,12,27},{21,13,28},{21,14,14},{22,0,22},{22,1,21},{22,2,23},{22,3,24},{22,4,20},{22,5,19},{22,6,25},{22,7,26},{22,8,18},{22,9,17},{22,10,27},{22,11,28},{22,12,16},{22,13,15},{22,14,29},{22,15,30},{22,16,31},{22,17,32},{22,18,33},{22,19,34},{22,20,35},{22,21,36},{22,22,37},{22,23,38},{22,24,39},{22,25,40},{22,26,41},{22,27,42},{22,28,43},{22,29,44},{22,30,45},{22,31,46},{22,32,47},{22,33,48},{22,34,49},{22,35,50},{22,36,51},{22,37,52},{22,38,53},{22,39,54},{22,40,55},{22,41,56},{22,42,57},{22,43,58},{22,44,59},{22,45,60},{22,46,61},{22,47,62},{22,48,63},{22,49,64},{22,50,65},{22,51,66},{22,52,67},{22,53,68},{22,54,69},{22,55,70},{22,56,71},{22,57,72},{22,58,73},{22,59,74},{22,60,75},{22,61,76},{22,62,77},{22,63,78},{22,64,79},{22,65,80},{22,66,81},{22,67,82},{22,68,83},{22,69,84},{22,70,85},{22,71,86},{22,72,87},{22,73,88},{22,74,89},{22,75,90},{23,0,23},{23,1,24},{23,2,22},{23,3,21},{23,4,25},{23,5,26},{23,6,20},{23,7,19},{23,8,27},{23,9,28},{23,10,18},{23,11,17},{23,12,29},{23,13,30},{23,14,16},{23,15,15},{24,0,24},{24,1,23},{24,2,25},{24,3,26},{24,4,22},{24,5,21},{24,6,27},{24,7,28},{24,8,20},{24,9,19},{24,10,29},{24,11,30},{24,12,18},{24,13,17},{24,14,31},{24,15,32},{24,16,16},{25,0,25},{25,1,26},{25,2,24},{25,3,23},{25,4,27},{25,5,28},{25,6,22},{25,7,21},{25,8,29},{25,9,30},{25,10,20},{25,11,19},{25,12,31},{25,13,32},{25,14,18},{25,15,17},{25,16,33},{25,17,34},{25,18,35},{25,19,36},{25,20,37},{25,21,38},{25,22,39},{25,23,40},{25,24,41},{25,25,42},{25,26,43},{25,27,44},{25,28,45},{25,29,46},{25,30,47},{25,31,48},{25,32,49},{25,33,50},{25,34,51},{25,35,52},{25,36,53},{25,37,54},{25,38,55},{25,39,56},{25,40,57},{25,41,58},{25,42,59},{25,43,60},{25,44,61},{25,45,62},{25,46,63},{25,47,64},{25,48,65},{25,49,66},{25,50,67},{25,51,68},{25,52,69},{25,53,70},{25,54,71},{25,55,72},{25,56,73},{25,57,74},{25,58,75},{25,59,76},{25,60,77},{25,61,78},{25,62,79},{25,63,80},{25,64,81},{25,65,82},{25,66,83},{25,67,84},{25,68,85},{25,69,86},{25,70,87},{25,71,88},{25,72,89},{25,73,90},{25,74,91},{25,75,92},{26,0,26},{26,1,25},{26,2,27},{26,3,28},{26,4,24},{26,5,23},{26,6,29},{26,7,30},{26,8,22},{26,9,21},{26,10,31},{26,11,32},{26,12,20},{26,13,19},{26,14,33},{26,15,34},{26,16,18},{26,17,17},{27,0,27},{27,1,28},{27,2,26},{27,3,25},{27,4,29},{27,5,30},{27,6,24},{27,7,23},{27,8,31},{27,9,32},{27,10,22},{27,11,21},{27,12,33},{27,13,34},{27,14,20},{27,15,19},{27,16,35},{27,17,36},{27,18,18},{28,0,28},{28,1,27},{28,2,29},{28,3,30},{28,4,26},{28,5,25},{28,6,31},{28,7,32},{28,8,24},{28,9,23},{28,10,33},{28,11,34},{28,12,22},{28,13,21},{28,14,35},{28,15,36},{28,16,20},{28,17,19},{28,18,37},{28,19,38},{28,20,39},{28,21,40},{28,22,41},{28,23,42},{28,24,43},{28,25,44},{28,26,45},{28,27,46},{28,28,47},{28,29,48},{28,30,49},{28,31,50},{28,32,51},{28,33,52},{28,34,53},{28,35,54},{28,36,55},{28,37,56},{28,38,57},{28,39,58},{28,40,59},{28,41,60},{28,42,61},{28,43,62},{28,44,63},{28,45,64},{28,46,65},{28,47,66},{28,48,67},{28,49,68},{28,50,69},{28,51,70},{28,52,71},{28,53,72},{28,54,73},{28,55,74},{28,56,75},{28,57,76},{28,58,77},{28,59,78},{28,60,79},{28,61,80},{28,62,81},{28,63,82},{28,64,83},{28,65,84},{28,66,85},{28,67,86},{28,68,87},{28,69,88},{28,70,89},{28,71,90},{28,72,91},{28,73,92},{28,74,93},{28,75,94},{29,0,29},{29,1,30},{29,2,28},{29,3,27},{29,4,31},{29,5,32},{29,6,26},{29,7,25},{29,8,33},{29,9,34},{29,10,24},{29,11,23},{29,12,35},{29,13,36},{29,14,22},{29,15,21},{29,16,37},{29,17,38},{29,18,20},{29,19,19},{30,0,30},{30,1,29},{30,2,31},{30,3,32},{30,4,28},{30,5,27},{30,6,33},{30,7,34},{30,8,26},{30,9,25},{30,10,35},{30,11,36},{30,12,24},{30,13,23},{30,14,37},{30,15,38},{30,16,22},{30,17,21},{30,18,39},{30,19,40},{30,20,20},{31,0,31},{31,1,32},{31,2,30},{31,3,29},{31,4,33},{31,5,34},{31,6,28},{31,7,27},{31,8,35},{31,9,36},{31,10,26},{31,11,25},{31,12,37},{31,13,38},{31,14,24},{31,15,23},{31,16,39},{31,17,40},{31,18,22},{31,19,21},{31,20,41},{31,21,42},{31,22,43},{31,23,44},{31,24,45},{31,25,46},{31,26,47},{31,27,48},{31,28,49},{31,29,50},{31,30,51},{31,31,52},{31,32,53},{31,33,54},{31,34,55},{31,35,56},{31,36,57},{31,37,58},{31,38,59},{31,39,60},{31,40,61},{31,41,62},{31,42,63},{31,43,64},{31,44,65},{31,45,66},{31,46,67},{31,47,68},{31,48,69},{31,49,70},{31,50,71},{31,51,72},{31,52,73},{31,53,74},{31,54,75},{31,55,76},{31,56,77},{31,57,78},{31,58,79},{31,59,80},{31,60,81},{31,61,82},{31,62,83},{31,63,84},{31,64,85},{31,65,86},{31,66,87},{31,67,88},{31,68,89},{31,69,90},{31,70,91},{31,71,92},{31,72,93},{31,73,94},{31,74,95},{31,75,96},{32,0,32},{32,1,31},{32,2,33},{32,3,34},{32,4,30},{32,5,29},{32,6,35},{32,7,36},{32,8,28},{32,9,27},{32,10,37},{32,11,38},{32,12,26},{32,13,25},{32,14,39},{32,15,40},{32,16,24},{32,17,23},{32,18,41},{32,19,42},{32,20,22},{32,21,21},{33,0,33},{33,1,34},{33,2,32},{33,3,31},{33,4,35},{33,5,36},{33,6,30},{33,7,29},{33,8,37},{33,9,38},{33,10,28},{33,11,27},{33,12,39},{33,13,40},{33,14,26},{33,15,25},{33,16,41},{33,17,42},{33,18,24},{33,19,23},{33,20,43},{33,21,44},{33,22,22},{34,0,34},{34,1,33},{34,2,35},{34,3,36},{34,4,32},{34,5,31},{34,6,37},{34,7,38},{34,8,30},{34,9,29},{34,10,39},{34,11,40},{34,12,28},{34,13,27},{34,14,41},{34,15,42},{34,16,26},{34,17,25},{34,18,43},{34,19,44},{34,20,24},{34,21,23},{34,22,45},{34,23,46},{34,24,47},{34,25,48},{34,26,49},{34,27,50},{34,28,51},{34,29,52},{34,30,53},{34,31,54},{34,32,55},{34,33,56},{34,34,57},{34,35,58},{34,36,59},{34,37,60},{34,38,61},{34,39,62},{34,40,63},{34,41,64},{34,42,65},{34,43,66},{34,44,67},{34,45,68},{34,46,69},{34,47,70},{34,48,71},{34,49,72},{34,50,73},{34,51,74},{34,52,75},{34,53,76},{34,54,77},{34,55,78},{34,56,79},{34,57,80},{34,58,81},{34,59,82},{34,60,83},{34,61,84},{34,62,85},{34,63,86},{34,64,87},{34,65,88},{34,66,89},{34,67,90},{34,68,91},{34,69,92},{34,70,93},{34,71,94},{34,72,95},{34,73,96},{34,74,97},{34,75,98},{35,0,35},{35,1,36},{35,2,34},{35,3,33},{35,4,37},{35,5,38},{35,6,32},{35,7,31},{35,8,39},{35,9,40},{35,10,30},{35,11,29},{35,12,41},{35,13,42},{35,14,28},{35,15,27},{35,16,43},{35,17,44},{35,18,26},{35,19,25},{35,20,45},{35,21,46},{35,22,24},{35,23,23},{36,0,36},{36,1,35},{36,2,37},{36,3,38},{36,4,34},{36,5,33},{36,6,39},{36,7,40},{36,8,32},{36,9,31},{36,10,41},{36,11,42},{36,12,30},{36,13,29},{36,14,43},{36,15,44},{36,16,28},{36,17,27},{36,18,45},{36,19,46},{36,20,26},{36,21,25},{36,22,47},{36,23,48},{36,24,24},{37,0,37},{37,1,38},{37,2,36},{37,3,35},{37,4,39},{37,5,40},{37,6,34},{37,7,33},{37,8,41},{37,9,42},{37,10,32},{37,11,31},{37,12,43},{37,13,44},{37,14,30},{37,15,29},{37,16,45},{37,17,46},{37,18,28},{37,19,27},{37,20,47},{37,21,48},{37,22,26},{37,23,25},{37,24,49},{37,25,50},{37,26,51},{37,27,52},{37,28,53},{37,29,54},{37,30,55},{37,31,56},{37,32,57},{37,33,58},{37,34,59},{37,35,60},{37,36,61},{37,37,62},{37,38,63},{37,39,64},{37,40,65},{37,41,66},{37,42,67},{37,43,68},{37,44,69},{37,45,70},{37,46,71},{37,47,72},{37,48,73},{37,49,74},{37,50,75},{37,51,76},{37,52,77},{37,53,78},{37,54,79},{37,55,80},{37,56,81},{37,57,82},{37,58,83},{37,59,84},{37,60,85},{37,61,86},{37,62,87},{37,63,88},{37,64,89},{37,65,90},{37,66,91},{37,67,92},{37,68,93},{37,69,94},{37,70,95},{37,71,96},{37,72,97},{37,73,98},{37,74,99},{37,75,100},{38,0,38},{38,1,37},{38,2,39},{38,3,40},{38,4,36},{38,5,35},{38,6,41},{38,7,42},{38,8,34},{38,9,33},{38,10,43},{38,11,44},{38,12,32},{38,13,31},{38,14,45},{38,15,46},{38,16,30},{38,17,29},{38,18,47},{38,19,48},{38,20,28},{38,21,27},{38,22,49},{38,23,50},{38,24,26},{38,25,25},{39,0,39},{39,1,40},{39,2,38},{39,3,37},{39,4,41},{39,5,42},{39,6,36},{39,7,35},{39,8,43},{39,9,44},{39,10,34},{39,11,33},{39,12,45},{39,13,46},{39,14,32},{39,15,31},{39,16,47},{39,17,48},{39,18,30},{39,19,29},{39,20,49},{39,21,50},{39,22,28},{39,23,27},{39,24,51},{39,25,52},{39,26,26},{40,0,40},{40,1,39},{40,2,41},{40,3,42},{40,4,38},{40,5,37},{40,6,43},{40,7,44},{40,8,36},{40,9,35},{40,10,45},{40,11,46},{40,12,34},{40,13,33},{40,14,47},{40,15,48},{40,16,32},{40,17,31},{40,18,49},{40,19,50},{40,20,30},{40,21,29},{40,22,51},{40,23,52},{40,24,28},{40,25,27},{40,26,53},{40,27,54},{40,28,55},{40,29,56},{40,30,57},{40,31,58},{40,32,59},{40,33,60},{40,34,61},{40,35,62},{40,36,63},{40,37,64},{40,38,65},{40,39,66},{40,40,67},{40,41,68},{40,42,69},{40,43,70},{40,44,71},{40,45,72},{40,46,73},{40,47,74},{40,48,75},{40,49,76},{40,50,77},{40,51,78},{40,52,79},{40,53,80},{40,54,81},{40,55,82},{40,56,83},{40,57,84},{40,58,85},{40,59,86},{40,60,87},{40,61,88},{40,62,89},{40,63,90},{40,64,91},{40,65,92},{40,66,93},{40,67,94},{40,68,95},{40,69,96},{40,70,97},{40,71,98},{40,72,99},{40,73,100},{40,74,101},{40,75,102},{41,0,41},{41,1,42},{41,2,40},{41,3,39},{41,4,43},{41,5,44},{41,6,38},{41,7,37},{41,8,45},{41,9,46},{41,10,36},{41,11,35},{41,12,47},{41,13,48},{41,14,34},{41,15,33},{41,16,49},{41,17,50},{41,18,32},{41,19,31},{41,20,51},{41,21,52},{41,22,30},{41,23,29},{41,24,53},{41,25,54},{41,26,28},{41,27,27},{42,0,42},{42,1,41},{42,2,43},{42,3,44},{42,4,40},{42,5,39},{42,6,45},{42,7,46},{42,8,38},{42,9,37},{42,10,47},{42,11,48},{42,12,36},{42,13,35},{42,14,49},{42,15,50},{42,16,34},{42,17,33},{42,18,51},{42,19,52},{42,20,32},{42,21,31},{42,22,53},{42,23,54},{42,24,30},{42,25,29},{42,26,55},{42,27,56},{42,28,28},{43,0,43},{43,1,44},{43,2,42},{43,3,41},{43,4,45},{43,5,46},{43,6,40},{43,7,39},{43,8,47},{43,9,48},{43,10,38},{43,11,37},{43,12,49},{43,13,50},{43,14,36},{43,15,35},{43,16,51},{43,17,52},{43,18,34},{43,19,33},{43,20,53},{43,21,54},{43,22,32},{43,23,31},{43,24,55},{43,25,56},{43,26,30},{43,27,29},{43,28,57},{43,29,58},{43,30,59},{43,31,60},{43,32,61},{43,33,62},{43,34,63},{43,35,64},{43,36,65},{43,37,66},{43,38,67},{43,39,68},{43,40,69},{43,41,70},{43,42,71},{43,43,72},{43,44,73},{43,45,74},{43,46,75},{43,47,76},{43,48,77},{43,49,78},{43,50,79},{43,51,80},{43,52,81},{43,53,82},{43,54,83},{43,55,84},{43,56,85},{43,57,86},{43,58,87},{43,59,88},{43,60,89},{43,61,90},{43,62,91},{43,63,92},{43,64,93},{43,65,94},{43,66,95},{43,67,96},{43,68,97},{43,69,98},{43,70,99},{43,71,100},{43,72,101},{43,73,102},{43,74,103},{43,75,104},{44,0,44},{44,1,43},{44,2,45},{44,3,46},{44,4,42},{44,5,41},{44,6,47},{44,7,48},{44,8,40},{44,9,39},{44,10,49},{44,11,50},{44,12,38},{44,13,37},{44,14,51},{44,15,52},{44,16,36},{44,17,35},{44,18,53},{44,19,54},{44,20,34},{44,21,33},{44,22,55},{44,23,56},{44,24,32},{44,25,31},{44,26,57},{44,27,58},{44,28,30},{44,29,29},{45,0,45},{45,1,46},{45,2,44},{45,3,43},{45,4,47},{45,5,48},{45,6,42},{45,7,41},{45,8,49},{45,9,50},{45,10,40},{45,11,39},{45,12,51},{45,13,52},{45,14,38},{45,15,37},{45,16,53},{45,17,54},{45,18,36},{45,19,35},{45,20,55},{45,21,56},{45,22,34},{45,23,33},{45,24,57},{45,25,58},{45,26,32},{45,27,31},{45,28,59},{45,29,60},{45,30,30},{46,0,46},{46,1,45},{46,2,47},{46,3,48},{46,4,44},{46,5,43},{46,6,49},{46,7,50},{46,8,42},{46,9,41},{46,10,51},{46,11,52},{46,12,40},{46,13,39},{46,14,53},{46,15,54},{46,16,38},{46,17,37},{46,18,55},{46,19,56},{46,20,36},{46,21,35},{46,22,57},{46,23,58},{46,24,34},{46,25,33},{46,26,59},{46,27,60},{46,28,32},{46,29,31},{46,30,61},{46,31,62},{46,32,63},{46,33,64},{46,34,65},{46,35,66},{46,36,67},{46,37,68},{46,38,69},{46,39,70},{46,40,71},{46,41,72},{46,42,73},{46,43,74},{46,44,75},{46,45,76},{46,46,77},{46,47,78},{46,48,79},{46,49,80},{46,50,81},{46,51,82},{46,52,83},{46,53,84},{46,54,85},{46,55,86},{46,56,87},{46,57,88},{46,58,89},{46,59,90},{46,60,91},{46,61,92},{46,62,93},{46,63,94},{46,64,95},{46,65,96},{46,66,97},{46,67,98},{46,68,99},{46,69,100},{46,70,101},{46,71,102},{46,72,103},{46,73,104},{46,74,105},{46,75,106},{47,0,47},{47,1,48},{47,2,46},{47,3,45},{47,4,49},{47,5,50},{47,6,44},{47,7,43},{47,8,51},{47,9,52},{47,10,42},{47,11,41},{47,12,53},{47,13,54},{47,14,40},{47,15,39},{47,16,55},{47,17,56},{47,18,38},{47,19,37},{47,20,57},{47,21,58},{47,22,36},{47,23,35},{47,24,59},{47,25,60},{47,26,34},{47,27,33},{47,28,61},{47,29,62},{47,30,32},{47,31,31},{48,0,48},{48,1,47},{48,2,49},{48,3,50},{48,4,46},{48,5,45},{48,6,51},{48,7,52},{48,8,44},{48,9,43},{48,10,53},{48,11,54},{48,12,42},{48,13,41},{48,14,55},{48,15,56},{48,16,40},{48,17,39},{48,18,57},{48,19,58},{48,20,38},{48,21,37},{48,22,59},{48,23,60},{48,24,36},{48,25,35},{48,26,61},{48,27,62},{48,28,34},{48,29,33},{48,30,63},{48,31,64},{48,32,32},{49,0,49},{49,1,50},{49,2,48},{49,3,47},{49,4,51},{49,5,52},{49,6,46},{49,7,45},{49,8,53},{49,9,54},{49,10,44},{49,11,43},{49,12,55},{49,13,56},{49,14,42},{49,15,41},{49,16,57},{49,17,58},{49,18,40},{49,19,39},{49,20,59},{49,21,60},{49,22,38},{49,23,37},{49,24,61},{49,25,62},{49,26,36},{49,27,35},{49,28,63},{49,29,64},{49,30,34},{49,31,33},{49,32,65},{49,33,66},{49,34,67},{49,35,68},{49,36,69},{49,37,70},{49,38,71},{49,39,72},{49,40,73},{49,41,74},{49,42,75},{49,43,76},{49,44,77},{49,45,78},{49,46,79},{49,47,80},{49,48,81},{49,49,82},{49,50,83},{49,51,84},{49,52,85},{49,53,86},{49,54,87},{49,55,88},{49,56,89},{49,57,90},{49,58,91},{49,59,92},{49,60,93},{49,61,94},{49,62,95},{49,63,96},{49,64,97},{49,65,98},{49,66,99},{49,67,100},{49,68,101},{49,69,102},{49,70,103},{49,71,104},{49,72,105},{49,73,106},{49,74,107},{49,75,108},{50,0,50},{50,1,49},{50,2,51},{50,3,52},{50,4,48},{50,5,47},{50,6,53},{50,7,54},{50,8,46},{50,9,45},{50,10,55},{50,11,56},{50,12,44},{50,13,43},{50,14,57},{50,15,58},{50,16,42},{50,17,41},{50,18,59},{50,19,60},{50,20,40},{50,21,39},{50,22,61},{50,23,62},{50,24,38},{50,25,37},{50,26,63},{50,27,64},{50,28,36},{50,29,35},{50,30,65},{50,31,66},{50,32,34},{50,33,33},{51,0,51},{51,1,52},{51,2,50},{51,3,49},{51,4,53},{51,5,54},{51,6,48},{51,7,47},{51,8,55},{51,9,56},{51,10,46},{51,11,45},{51,12,57},{51,13,58},{51,14,44},{51,15,43},{51,16,59},{51,17,60},{51,18,42},{51,19,41},{51,20,61},{51,21,62},{51,22,40},{51,23,39},{51,24,63},{51,25,64},{51,26,38},{51,27,37},{51,28,65},{51,29,66},{51,30,36},{51,31,35},{51,32,67},{51,33,68},{51,34,34},{52,0,52},{52,1,51},{52,2,53},{52,3,54},{52,4,50},{52,5,49},{52,6,55},{52,7,56},{52,8,48},{52,9,47},{52,10,57},{52,11,58},{52,12,46},{52,13,45},{52,14,59},{52,15,60},{52,16,44},{52,17,43},{52,18,61},{52,19,62},{52,20,42},{52,21,41},{52,22,63},{52,23,64},{52,24,40},{52,25,39},{52,26,65},{52,27,66},{52,28,38},{52,29,37},{52,30,67},{52,31,68},{52,32,36},{52,33,35},{52,34,69},{52,35,70},{52,36,71},{52,37,72},{52,38,73},{52,39,74},{52,40,75},{52,41,76},{52,42,77},{52,43,78},{52,44,79},{52,45,80},{52,46,81},{52,47,82},{52,48,83},{52,49,84},{52,50,85},{52,51,86},{52,52,87},{52,53,88},{52,54,89},{52,55,90},{52,56,91},{52,57,92},{52,58,93},{52,59,94},{52,60,95},{52,61,96},{52,62,97},{52,63,98},{52,64,99},{52,65,100},{52,66,101},{52,67,102},{52,68,103},{52,69,104},{52,70,105},{52,71,106},{52,72,107},{52,73,108},{52,74,109},{52,75,110},{53,0,53},{53,1,54},{53,2,52},{53,3,51},{53,4,55},{53,5,56},{53,6,50},{53,7,49},{53,8,57},{53,9,58},{53,10,48},{53,11,47},{53,12,59},{53,13,60},{53,14,46},{53,15,45},{53,16,61},{53,17,62},{53,18,44},{53,19,43},{53,20,63},{53,21,64},{53,22,42},{53,23,41},{53,24,65},{53,25,66},{53,26,40},{53,27,39},{53,28,67},{53,29,68},{53,30,38},{53,31,37},{53,32,69},{53,33,70},{53,34,36},{53,35,35},{54,0,54},{54,1,53},{54,2,55},{54,3,56},{54,4,52},{54,5,51},{54,6,57},{54,7,58},{54,8,50},{54,9,49},{54,10,59},{54,11,60},{54,12,48},{54,13,47},{54,14,61},{54,15,62},{54,16,46},{54,17,45},{54,18,63},{54,19,64},{54,20,44},{54,21,43},{54,22,65},{54,23,66},{54,24,42},{54,25,41},{54,26,67},{54,27,68},{54,28,40},{54,29,39},{54,30,69},{54,31,70},{54,32,38},{54,33,37},{54,34,71},{54,35,72},{54,36,36},{55,0,55},{55,1,56},{55,2,54},{55,3,53},{55,4,57},{55,5,58},{55,6,52},{55,7,51},{55,8,59},{55,9,60},{55,10,50},{55,11,49},{55,12,61},{55,13,62},{55,14,48},{55,15,47},{55,16,63},{55,17,64},{55,18,46},{55,19,45},{55,20,65},{55,21,66},{55,22,44},{55,23,43},{55,24,67},{55,25,68},{55,26,42},{55,27,41},{55,28,69},{55,29,70},{55,30,40},{55,31,39},{55,32,71},{55,33,72},{55,34,38},{55,35,37},{55,36,73},{55,37,74},{55,38,75},{55,39,76},{55,40,77},{55,41,78},{55,42,79},{55,43,80},{55,44,81},{55,45,82},{55,46,83},{55,47,84},{55,48,85},{55,49,86},{55,50,87},{55,51,88},{55,52,89},{55,53,90},{55,54,91},{55,55,92},{55,56,93},{55,57,94},{55,58,95},{55,59,96},{55,60,97},{55,61,98},{55,62,99},{55,63,100},{55,64,101},{55,65,102},{55,66,103},{55,67,104},{55,68,105},{55,69,106},{55,70,107},{55,71,108},{55,72,109},{55,73,110},{55,74,111},{55,75,112},{56,0,56},{56,1,55},{56,2,57},{56,3,58},{56,4,54},{56,5,53},{56,6,59},{56,7,60},{56,8,52},{56,9,51},{56,10,61},{56,11,62},{56,12,50},{56,13,49},{56,14,63},{56,15,64},{56,16,48},{56,17,47},{56,18,65},{56,19,66},{56,20,46},{56,21,45},{56,22,67},{56,23,68},{56,24,44},{56,25,43},{56,26,69},{56,27,70},{56,28,42},{56,29,41},{56,30,71},{56,31,72},{56,32,40},{56,33,39},{56,34,73},{56,35,74},{56,36,38},{56,37,37},{57,0,57},{57,1,58},{57,2,56},{57,3,55},{57,4,59},{57,5,60},{57,6,54},{57,7,53},{57,8,61},{57,9,62},{57,10,52},{57,11,51},{57,12,63},{57,13,64},{57,14,50},{57,15,49},{57,16,65},{57,17,66},{57,18,48},{57,19,47},{57,20,67},{57,21,68},{57,22,46},{57,23,45},{57,24,69},{57,25,70},{57,26,44},{57,27,43},{57,28,71},{57,29,72},{57,30,42},{57,31,41},{57,32,73},{57,33,74},{57,34,40},{57,35,39},{57,36,75},{57,37,76},{57,38,38},{58,0,58},{58,1,57},{58,2,59},{58,3,60},{58,4,56},{58,5,55},{58,6,61},{58,7,62},{58,8,54},{58,9,53},{58,10,63},{58,11,64},{58,12,52},{58,13,51},{58,14,65},{58,15,66},{58,16,50},{58,17,49},{58,18,67},{58,19,68},{58,20,48},{58,21,47},{58,22,69},{58,23,70},{58,24,46},{58,25,45},{58,26,71},{58,27,72},{58,28,44},{58,29,43},{58,30,73},{58,31,74},{58,32,42},{58,33,41},{58,34,75},{58,35,76},{58,36,40},{58,37,39},{58,38,77},{58,39,78},{58,40,79},{58,41,80},{58,42,81},{58,43,82},{58,44,83},{58,45,84},{58,46,85},{58,47,86},{58,48,87},{58,49,88},{58,50,89},{58,51,90},{58,52,91},{58,53,92},{58,54,93},{58,55,94},{58,56,95},{58,57,96},{58,58,97},{58,59,98},{58,60,99},{58,61,100},{58,62,101},{58,63,102},{58,64,103},{58,65,104},{58,66,105},{58,67,106},{58,68,107},{58,69,108},{58,70,109},{58,71,110},{58,72,111},{58,73,112},{58,74,113},{58,75,114},{59,0,59},{59,1,60},{59,2,58},{59,3,57},{59,4,61},{59,5,62},{59,6,56},{59,7,55},{59,8,63},{59,9,64},{59,10,54},{59,11,53},{59,12,65},{59,13,66},{59,14,52},{59,15,51},{59,16,67},{59,17,68},{59,18,50},{59,19,49},{59,20,69},{59,21,70},{59,22,48},{59,23,47},{59,24,71},{59,25,72},{59,26,46},{59,27,45},{59,28,73},{59,29,74},{59,30,44},{59,31,43},{59,32,75},{59,33,76},{59,34,42},{59,35,41},{59,36,77},{59,37,78},{59,38,40},{59,39,39},{60,0,60},{60,1,59},{60,2,61},{60,3,62},{60,4,58},{60,5,57},{60,6,63},{60,7,64},{60,8,56},{60,9,55},{60,10,65},{60,11,66},{60,12,54},{60,13,53},{60,14,67},{60,15,68},{60,16,52},{60,17,51},{60,18,69},{60,19,70},{60,20,50},{60,21,49},{60,22,71},{60,23,72},{60,24,48},{60,25,47},{60,26,73},{60,27,74},{60,28,46},{60,29,45},{60,30,75},{60,31,76},{60,32,44},{60,33,43},{60,34,77},{60,35,78},{60,36,42},{60,37,41},{60,38,79},{60,39,80},{60,40,40},{61,0,61},{61,1,62},{61,2,60},{61,3,59},{61,4,63},{61,5,64},{61,6,58},{61,7,57},{61,8,65},{61,9,66},{61,10,56},{61,11,55},{61,12,67},{61,13,68},{61,14,54},{61,15,53},{61,16,69},{61,17,70},{61,18,52},{61,19,51},{61,20,71},{61,21,72},{61,22,50},{61,23,49},{61,24,73},{61,25,74},{61,26,48},{61,27,47},{61,28,75},{61,29,76},{61,30,46},{61,31,45},{61,32,77},{61,33,78},{61,34,44},{61,35,43},{61,36,79},{61,37,80},{61,38,42},{61,39,41},{61,40,81},{61,41,82},{61,42,83},{61,43,84},{61,44,85},{61,45,86},{61,46,87},{61,47,88},{61,48,89},{61,49,90},{61,50,91},{61,51,92},{61,52,93},{61,53,94},{61,54,95},{61,55,96},{61,56,97},{61,57,98},{61,58,99},{61,59,100},{61,60,101},{61,61,102},{61,62,103},{61,63,104},{61,64,105},{61,65,106},{61,66,107},{61,67,108},{61,68,109},{61,69,110},{61,70,111},{61,71,112},{61,72,113},{61,73,114},{61,74,115},{61,75,116},{62,0,62},{62,1,61},{62,2,63},{62,3,64},{62,4,60},{62,5,59},{62,6,65},{62,7,66},{62,8,58},{62,9,57},{62,10,67},{62,11,68},{62,12,56},{62,13,55},{62,14,69},{62,15,70},{62,16,54},{62,17,53},{62,18,71},{62,19,72},{62,20,52},{62,21,51},{62,22,73},{62,23,74},{62,24,50},{62,25,49},{62,26,75},{62,27,76},{62,28,48},{62,29,47},{62,30,77},{62,31,78},{62,32,46},{62,33,45},{62,34,79},{62,35,80},{62,36,44},{62,37,43},{62,38,81},{62,39,82},{62,40,42},{62,41,41},{63,0,63},{63,1,64},{63,2,62},{63,3,61},{63,4,65},{63,5,66},{63,6,60},{63,7,59},{63,8,67},{63,9,68},{63,10,58},{63,11,57},{63,12,69},{63,13,70},{63,14,56},{63,15,55},{63,16,71},{63,17,72},{63,18,54},{63,19,53},{63,20,73},{63,21,74},{63,22,52},{63,23,51},{63,24,75},{63,25,76},{63,26,50},{63,27,49},{63,28,77},{63,29,78},{63,30,48},{63,31,47},{63,32,79},{63,33,80},{63,34,46},{63,35,45},{63,36,81},{63,37,82},{63,38,44},{63,39,43},{63,40,83},{63,41,84},{63,42,42},{64,0,64},{64,1,63},{64,2,65},{64,3,66},{64,4,62},{64,5,61},{64,6,67},{64,7,68},{64,8,60},{64,9,59},{64,10,69},{64,11,70},{64,12,58},{64,13,57},{64,14,71},{64,15,72},{64,16,56},{64,17,55},{64,18,73},{64,19,74},{64,20,54},{64,21,53},{64,22,75},{64,23,76},{64,24,52},{64,25,51},{64,26,77},{64,27,78},{64,28,50},{64,29,49},{64,30,79},{64,31,80},{64,32,48},{64,33,47},{64,34,81},{64,35,82},{64,36,46},{64,37,45},{64,38,83},{64,39,84},{64,40,44},{64,41,43},{64,42,85},{64,43,86},{64,44,87},{64,45,88},{64,46,89},{64,47,90},{64,48,91},{64,49,92},{64,50,93},{64,51,94},{64,52,95},{64,53,96},{64,54,97},{64,55,98},{64,56,99},{64,57,100},{64,58,101},{64,59,102},{64,60,103},{64,61,104},{64,62,105},{64,63,106},{64,64,107},{64,65,108},{64,66,109},{64,67,110},{64,68,111},{64,69,112},{64,70,113},{64,71,114},{64,72,115},{64,73,116},{64,74,117},{64,75,118},{65,0,65},{65,1,66},{65,2,64},{65,3,63},{65,4,67},{65,5,68},{65,6,62},{65,7,61},{65,8,69},{65,9,70},{65,10,60},{65,11,59},{65,12,71},{65,13,72},{65,14,58},{65,15,57},{65,16,73},{65,17,74},{65,18,56},{65,19,55},{65,20,75},{65,21,76},{65,22,54},{65,23,53},{65,24,77},{65,25,78},{65,26,52},{65,27,51},{65,28,79},{65,29,80},{65,30,50},{65,31,49},{65,32,81},{65,33,82},{65,34,48},{65,35,47},{65,36,83},{65,37,84},{65,38,46},{65,39,45},{65,40,85},{65,41,86},{65,42,44},{65,43,43},{66,0,66},{66,1,65},{66,2,67},{66,3,68},{66,4,64},{66,5,63},{66,6,69},{66,7,70},{66,8,62},{66,9,61},{66,10,71},{66,11,72},{66,12,60},{66,13,59},{66,14,73},{66,15,74},{66,16,58},{66,17,57},{66,18,75},{66,19,76},{66,20,56},{66,21,55},{66,22,77},{66,23,78},{66,24,54},{66,25,53},{66,26,79},{66,27,80},{66,28,52},{66,29,51},{66,30,81},{66,31,82},{66,32,50},{66,33,49},{66,34,83},{66,35,84},{66,36,48},{66,37,47},{66,38,85},{66,39,86},{66,40,46},{66,41,45},{66,42,87},{66,43,88},{66,44,44},{67,0,67},{67,1,68},{67,2,66},{67,3,65},{67,4,69},{67,5,70},{67,6,64},{67,7,63},{67,8,71},{67,9,72},{67,10,62},{67,11,61},{67,12,73},{67,13,74},{67,14,60},{67,15,59},{67,16,75},{67,17,76},{67,18,58},{67,19,57},{67,20,77},{67,21,78},{67,22,56},{67,23,55},{67,24,79},{67,25,80},{67,26,54},{67,27,53},{67,28,81},{67,29,82},{67,30,52},{67,31,51},{67,32,83},{67,33,84},{67,34,50},{67,35,49},{67,36,85},{67,37,86},{67,38,48},{67,39,47},{67,40,87},{67,41,88},{67,42,46},{67,43,45},{67,44,89},{67,45,90},{67,46,91},{67,47,92},{67,48,93},{67,49,94},{67,50,95},{67,51,96},{67,52,97},{67,53,98},{67,54,99},{67,55,100},{67,56,101},{67,57,102},{67,58,103},{67,59,104},{67,60,105},{67,61,106},{67,62,107},{67,63,108},{67,64,109},{67,65,110},{67,66,111},{67,67,112},{67,68,113},{67,69,114},{67,70,115},{67,71,116},{67,72,117},{67,73,118},{67,74,119},{67,75,120},{68,0,68},{68,1,67},{68,2,69},{68,3,70},{68,4,66},{68,5,65},{68,6,71},{68,7,72},{68,8,64},{68,9,63},{68,10,73},{68,11,74},{68,12,62},{68,13,61},{68,14,75},{68,15,76},{68,16,60},{68,17,59},{68,18,77},{68,19,78},{68,20,58},{68,21,57},{68,22,79},{68,23,80},{68,24,56},{68,25,55},{68,26,81},{68,27,82},{68,28,54},{68,29,53},{68,30,83},{68,31,84},{68,32,52},{68,33,51},{68,34,85},{68,35,86},{68,36,50},{68,37,49},{68,38,87},{68,39,88},{68,40,48},{68,41,47},{68,42,89},{68,43,90},{68,44,46},{68,45,45},{69,0,69},{69,1,70},{69,2,68},{69,3,67},{69,4,71},{69,5,72},{69,6,66},{69,7,65},{69,8,73},{69,9,74},{69,10,64},{69,11,63},{69,12,75},{69,13,76},{69,14,62},{69,15,61},{69,16,77},{69,17,78},{69,18,60},{69,19,59},{69,20,79},{69,21,80},{69,22,58},{69,23,57},{69,24,81},{69,25,82},{69,26,56},{69,27,55},{69,28,83},{69,29,84},{69,30,54},{69,31,53},{69,32,85},{69,33,86},{69,34,52},{69,35,51},{69,36,87},{69,37,88},{69,38,50},{69,39,49},{69,40,89},{69,41,90},{69,42,48},{69,43,47},{69,44,91},{69,45,92},{69,46,46},{70,0,70},{70,1,69},{70,2,71},{70,3,72},{70,4,68},{70,5,67},{70,6,73},{70,7,74},{70,8,66},{70,9,65},{70,10,75},{70,11,76},{70,12,64},{70,13,63},{70,14,77},{70,15,78},{70,16,62},{70,17,61},{70,18,79},{70,19,80},{70,20,60},{70,21,59},{70,22,81},{70,23,82},{70,24,58},{70,25,57},{70,26,83},{70,27,84},{70,28,56},{70,29,55},{70,30,85},{70,31,86},{70,32,54},{70,33,53},{70,34,87},{70,35,88},{70,36,52},{70,37,51},{70,38,89},{70,39,90},{70,40,50},{70,41,49},{70,42,91},{70,43,92},{70,44,48},{70,45,47},{70,46,93},{70,47,94},{70,48,95},{70,49,96},{70,50,97},{70,51,98},{70,52,99},{70,53,100},{70,54,101},{70,55,102},{70,56,103},{70,57,104},{70,58,105},{70,59,106},{70,60,107},{70,61,108},{70,62,109},{70,63,110},{70,64,111},{70,65,112},{70,66,113},{70,67,114},{70,68,115},{70,69,116},{70,70,117},{70,71,118},{70,72,119},{70,73,120},{70,74,121},{70,75,122},{71,0,71},{71,1,72},{71,2,70},{71,3,69},{71,4,73},{71,5,74},{71,6,68},{71,7,67},{71,8,75},{71,9,76},{71,10,66},{71,11,65},{71,12,77},{71,13,78},{71,14,64},{71,15,63},{71,16,79},{71,17,80},{71,18,62},{71,19,61},{71,20,81},{71,21,82},{71,22,60},{71,23,59},{71,24,83},{71,25,84},{71,26,58},{71,27,57},{71,28,85},{71,29,86},{71,30,56},{71,31,55},{71,32,87},{71,33,88},{71,34,54},{71,35,53},{71,36,89},{71,37,90},{71,38,52},{71,39,51},{71,40,91},{71,41,92},{71,42,50},{71,43,49},{71,44,93},{71,45,94},{71,46,48},{71,47,47},{72,0,72},{72,1,71},{72,2,73},{72,3,74},{72,4,70},{72,5,69},{72,6,75},{72,7,76},{72,8,68},{72,9,67},{72,10,77},{72,11,78},{72,12,66},{72,13,65},{72,14,79},{72,15,80},{72,16,64},{72,17,63},{72,18,81},{72,19,82},{72,20,62},{72,21,61},{72,22,83},{72,23,84},{72,24,60},{72,25,59},{72,26,85},{72,27,86},{72,28,58},{72,29,57},{72,30,87},{72,31,88},{72,32,56},{72,33,55},{72,34,89},{72,35,90},{72,36,54},{72,37,53},{72,38,91},{72,39,92},{72,40,52},{72,41,51},{72,42,93},{72,43,94},{72,44,50},{72,45,49},{72,46,95},{72,47,96},{72,48,48},{73,0,73},{73,1,74},{73,2,72},{73,3,71},{73,4,75},{73,5,76},{73,6,70},{73,7,69},{73,8,77},{73,9,78},{73,10,68},{73,11,67},{73,12,79},{73,13,80},{73,14,66},{73,15,65},{73,16,81},{73,17,82},{73,18,64},{73,19,63},{73,20,83},{73,21,84},{73,22,62},{73,23,61},{73,24,85},{73,25,86},{73,26,60},{73,27,59},{73,28,87},{73,29,88},{73,30,58},{73,31,57},{73,32,89},{73,33,90},{73,34,56},{73,35,55},{73,36,91},{73,37,92},{73,38,54},{73,39,53},{73,40,93},{73,41,94},{73,42,52},{73,43,51},{73,44,95},{73,45,96},{73,46,50},{73,47,49},{73,48,97},{73,49,98},{73,50,99},{73,51,100},{73,52,101},{73,53,102},{73,54,103},{73,55,104},{73,56,105},{73,57,106},{73,58,107},{73,59,108},{73,60,109},{73,61,110},{73,62,111},{73,63,112},{73,64,113},{73,65,114},{73,66,115},{73,67,116},{73,68,117},{73,69,118},{73,70,119},{73,71,120},{73,72,121},{73,73,122},{73,74,123},{73,75,124},{74,0,74},{74,1,73},{74,2,75},{74,3,76},{74,4,72},{74,5,71},{74,6,77},{74,7,78},{74,8,70},{74,9,69},{74,10,79},{74,11,80},{74,12,68},{74,13,67},{74,14,81},{74,15,82},{74,16,66},{74,17,65},{74,18,83},{74,19,84},{74,20,64},{74,21,63},{74,22,85},{74,23,86},{74,24,62},{74,25,61},{74,26,87},{74,27,88},{74,28,60},{74,29,59},{74,30,89},{74,31,90},{74,32,58},{74,33,57},{74,34,91},{74,35,92},{74,36,56},{74,37,55},{74,38,93},{74,39,94},{74,40,54},{74,41,53},{74,42,95},{74,43,96},{74,44,52},{74,45,51},{74,46,97},{74,47,98},{74,48,50},{74,49,49},{75,0,75},{75,1,76},{75,2,74},{75,3,73},{75,4,77},{75,5,78},{75,6,72},{75,7,71},{75,8,79},{75,9,80},{75,10,70},{75,11,69},{75,12,81},{75,13,82},{75,14,68},{75,15,67},{75,16,83},{75,17,84},{75,18,66},{75,19,65},{75,20,85},{75,21,86},{75,22,64},{75,23,63},{75,24,87},{75,25,88},{75,26,62},{75,27,61},{75,28,89},{75,29,90},{75,30,60},{75,31,59},{75,32,91},{75,33,92},{75,34,58},{75,35,57},{75,36,93},{75,37,94},{75,38,56},{75,39,55},{75,40,95},{75,41,96},{75,42,54},{75,43,53},{75,44,97},{75,45,98},{75,46,52},{75,47,51},{75,48,99},{75,49,100},{75,50,50}},{{0,0,0},{1,0,1},{2,0,2},{2,1,3},{3,0,3},{3,1,2},{4,0,4},{4,1,5},{4,2,6},{4,3,7},{5,0,5},{5,1,4},{5,2,7},{5,3,6},{6,0,6},{6,1,7},{6,2,4},{7,0,7},{7,1,6},{7,2,5},{8,0,8},{8,1,9},{8,2,10},{8,3,11},{8,4,12},{8,5,13},{8,6,14},{8,7,15},{9,0,9},{9,1,8},{9,2,11},{9,3,10},{9,4,13},{9,5,12},{9,6,15},{9,7,14},{10,0,10},{10,1,11},{10,2,8},{10,3,9},{10,4,14},{10,5,15},{10,6,12},{11,0,11},{11,1,10},{11,2,9},{11,3,8},{11,4,15},{11,5,14},{11,6,13},{12,0,12},{12,1,13},{12,2,14},{12,3,15},{12,4,8},{13,0,13},{13,1,12},{13,2,15},{13,3,14},{13,4,9},{14,0,14},{14,1,15},{14,2,12},{14,3,13},{14,4,10},{14,5,11},{15,0,15},{15,1,14},{15,2,13},{15,3,12},{15,4,11},{15,5,10},{16,0,16},{16,1,17},{16,2,18},{16,3,19},{16,4,20},{16,5,21},{16,6,22},{16,7,23},{16,8,24},{16,9,25},{16,10,26},{16,11,27},{16,12,28},{16,13,29},{16,14,30},{16,15,31},{17,0,17},{17,1,16},{17,2,19},{17,3,18},{17,4,21},{17,5,20},{17,6,23},{17,7,22},{17,8,25},{17,9,24},{17,10,27},{17,11,26},{17,12,29},{17,13,28},{17,14,31},{17,15,30},{18,0,18},{18,1,19},{18,2,16},{18,3,17},{18,4,22},{18,5,23},{18,6,20},{18,7,21},{18,8,26},{18,9,27},{18,10,24},{18,11,25},{18,12,30},{18,13,31},{18,14,28},{19,0,19},{19,1,18},{19,2,17},{19,3,16},{19,4,23},{19,5,22},{19,6,21},{19,7,20},{19,8,27},{19,9,26},{19,10,25},{19,11,24},{19,12,31},{19,13,30},{19,14,29},{20,0,20},{20,1,21},{20,2,22},{20,3,23},{20,4,16},{20,5,17},{20,6,18},{20,7,19},{20,8,28},{20,9,29},{20,10,30},{20,11,31},{20,12,24},{21,0,21},{21,1,20},{21,2,23},{21,3,22},{21,4,17},{21,5,16},{21,6,19},{21,7,18},{21,8,29},{21,9,28},{21,10,31},{21,11,30},{21,12,25},{22,0,22},{22,1,23},{22,2,20},{22,3,21},{22,4,18},{22,5,19},{22,6,16},{22,7,17},{22,8,30},{22,9,31},{22,10,28},{22,11,29},{22,12,26},{22,13,27},{23,0,23},{23,1,22},{23,2,21},{23,3,20},{23,4,19},{23,5,18},{23,6,17},{23,7,16},{23,8,31},{23,9,30},{23,10,29},{23,11,28},{23,12,27},{23,13,26},{24,0,24},{24,1,25},{24,2,26},{24,3,27},{24,4,28},{24,5,29},{24,6,30},{24,7,31},{24,8,16},{25,0,25},{25,1,24},{25,2,27},{25,3,26},{25,4,29},{25,5,28},{25,6,31},{25,7,30},{25,8,17},{26,0,26},{26,1,27},{26,2,24},{26,3,25},{26,4,30},{26,5,31},{26,6,28},{26,7,29},{26,8,18},{26,9,19},{27,0,27},{27,1,26},{27,2,25},{27,3,24},{27,4,31},{27,5,30},{27,6,29},{27,7,28},{27,8,19},{27,9,18},{28,0,28},{28,1,29},{28,2,30},{28,3,31},{28,4,24},{28,5,25},{28,6,26},{28,7,27},{28,8,20},{28,9,21},{28,10,22},{28,11,23},{29,0,29},{29,1,28},{29,2,31},{29,3,30},{29,4,25},{29,5,24},{29,6,27},{29,7,26},{29,8,21},{29,9,20},{29,10,23},{29,11,22},{30,0,30},{30,1,31},{30,2,28},{30,3,29},{30,4,26},{30,5,27},{30,6,24},{30,7,25},{30,8,22},{30,9,23},{30,10,20},{31,0,31},{31,1,30},{31,2,29},{31,3,28},{31,4,27},{31,5,26},{31,6,25},{31,7,24},{31,8,23},{31,9,22},{31,10,21},{32,0,32},{32,1,33},{32,2,34},{32,3,35},{32,4,36},{32,5,37},{32,6,38},{32,7,39},{32,8,40},{32,9,41},{32,10,42},{32,11,43},{32,12,44},{32,13,45},{32,14,46},{32,15,47},{32,16,48},{32,17,49},{32,18,50},{32,19,51},{32,20,52},{32,21,53},{32,22,54},{32,23,55},{32,24,56},{32,25,57},{32,26,58},{32,27,59},{32,28,60},{32,29,61},{32,30,62},{32,31,63},{33,0,33},{33,1,32},{33,2,35},{33,3,34},{33,4,37},{33,5,36},{33,6,39},{33,7,38},{33,8,41},{33,9,40},{33,10,43},{33,11,42},{33,12,45},{33,13,44},{33,14,47},{33,15,46},{33,16,49},{33,17,48},{33,18,51},{33,19,50},{33,20,53},{33,21,52},{33,22,55},{33,23,54},{33,24,57},{33,25,56},{33,26,59},{33,27,58},{33,28,61},{33,29,60},{33,30,63},{33,31,62},{34,0,34},{34,1,35},{34,2,32},{34,3,33},{34,4,38},{34,5,39},{34,6,36},{34,7,37},{34,8,42},{34,9,43},{34,10,40},{34,11,41},{34,12,46},{34,13,47},{34,14,44},{34,15,45},{34,16,50},{34,17,51},{34,18,48},{34,19,49},{34,20,54},{34,21,55},{34,22,52},{34,23,53},{34,24,58},{34,25,59},{34,26,56},{34,27,57},{34,28,62},{34,29,63},{34,30,60},{35,0,35},{35,1,34},{35,2,33},{35,3,32},{35,4,39},{35,5,38},{35,6,37},{35,7,36},{35,8,43},{35,9,42},{35,10,41},{35,11,40},{35,12,47},{35,13,46},{35,14,45},{35,15,44},{35,16,51},{35,17,50},{35,18,49},{35,19,48},{35,20,55},{35,21,54},{35,22,53},{35,23,52},{35,24,59},{35,25,58},{35,26,57},{35,27,56},{35,28,63},{35,29,62},{35,30,61},{36,0,36},{36,1,37},{36,2,38},{36,3,39},{36,4,32},{36,5,33},{36,6,34},{36,7,35},{36,8,44},{36,9,45},{36,10,46},{36,11,47},{36,12,40},{36,13,41},{36,14,42},{36,15,43},{36,16,52},{36,17,53},{36,18,54},{36,19,55},{36,20,48},{36,21,49},{36,22,50},{36,23,51},{36,24,60},{36,25,61},{36,26,62},{36,27,63},{36,28,56},{37,0,37},{37,1,36},{37,2,39},{37,3,38},{37,4,33},{37,5,32},{37,6,35},{37,7,34},{37,8,45},{37,9,44},{37,10,47},{37,11,46},{37,12,41},{37,13,40},{37,14,43},{37,15,42},{37,16,53},{37,17,52},{37,18,55},{37,19,54},{37,20,49},{37,21,48},{37,22,51},{37,23,50},{37,24,61},{37,25,60},{37,26,63},{37,27,62},{37,28,57},{38,0,38},{38,1,39},{38,2,36},{38,3,37},{38,4,34},{38,5,35},{38,6,32},{38,7,33},{38,8,46},{38,9,47},{38,10,44},{38,11,45},{38,12,42},{38,13,43},{38,14,40},{38,15,41},{38,16,54},{38,17,55},{38,18,52},{38,19,53},{38,20,50},{38,21,51},{38,22,48},{38,23,49},{38,24,62},{38,25,63},{38,26,60},{38,27,61},{38,28,58},{38,29,59},{39,0,39},{39,1,38},{39,2,37},{39,3,36},{39,4,35},{39,5,34},{39,6,33},{39,7,32},{39,8,47},{39,9,46},{39,10,45},{39,11,44},{39,12,43},{39,13,42},{39,14,41},{39,15,40},{39,16,55},{39,17,54},{39,18,53},{39,19,52},{39,20,51},{39,21,50},{39,22,49},{39,23,48},{39,24,63},{39,25,62},{39,26,61},{39,27,60},{39,28,59},{39,29,58},{40,0,40},{40,1,41},{40,2,42},{40,3,43},{40,4,44},{40,5,45},{40,6,46},{40,7,47},{40,8,32},{40,9,33},{40,10,34},{40,11,35},{40,12,36},{40,13,37},{40,14,38},{40,15,39},{40,16,56},{40,17,57},{40,18,58},{40,19,59},{40,20,60},{40,21,61},{40,22,62},{40,23,63},{40,24,48},{41,0,41},{41,1,40},{41,2,43},{41,3,42},{41,4,45},{41,5,44},{41,6,47},{41,7,46},{41,8,33},{41,9,32},{41,10,35},{41,11,34},{41,12,37},{41,13,36},{41,14,39},{41,15,38},{41,16,57},{41,17,56},{41,18,59},{41,19,58},{41,20,61},{41,21,60},{41,22,63},{41,23,62},{41,24,49},{42,0,42},{42,1,43},{42,2,40},{42,3,41},{42,4,46},{42,5,47},{42,6,44},{42,7,45},{42,8,34},{42,9,35},{42,10,32},{42,11,33},{42,12,38},{42,13,39},{42,14,36},{42,15,37},{42,16,58},{42,17,59},{42,18,56},{42,19,57},{42,20,62},{42,21,63},{42,22,60},{42,23,61},{42,24,50},{42,25,51},{43,0,43},{43,1,42},{43,2,41},{43,3,40},{43,4,47},{43,5,46},{43,6,45},{43,7,44},{43,8,35},{43,9,34},{43,10,33},{43,11,32},{43,12,39},{43,13,38},{43,14,37},{43,15,36},{43,16,59},{43,17,58},{43,18,57},{43,19,56},{43,20,63},{43,21,62},{43,22,61},{43,23,60},{43,24,51},{43,25,50},{44,0,44},{44,1,45},{44,2,46},{44,3,47},{44,4,40},{44,5,41},{44,6,42},{44,7,43},{44,8,36},{44,9,37},{44,10,38},{44,11,39},{44,12,32},{44,13,33},{44,14,34},{44,15,35},{44,16,60},{44,17,61},{44,18,62},{44,19,63},{44,20,56},{44,21,57},{44,22,58},{44,23,59},{44,24,52},{44,25,53},{44,26,54},{44,27,55},{45,0,45},{45,1,44},{45,2,47},{45,3,46},{45,4,41},{45,5,40},{45,6,43},{45,7,42},{45,8,37},{45,9,36},{45,10,39},{45,11,38},{45,12,33},{45,13,32},{45,14,35},{45,15,34},{45,16,61},{45,17,60},{45,18,63},{45,19,62},{45,20,57},{45,21,56},{45,22,59},{45,23,58},{45,24,53},{45,25,52},{45,26,55},{45,27,54},{46,0,46},{46,1,47},{46,2,44},{46,3,45},{46,4,42},{46,5,43},{46,6,40},{46,7,41},{46,8,38},{46,9,39},{46,10,36},{46,11,37},{46,12,34},{46,13,35},{46,14,32},{46,15,33},{46,16,62},{46,17,63},{46,18,60},{46,19,61},{46,20,58},{46,21,59},{46,22,56},{46,23,57},{46,24,54},{46,25,55},{46,26,52},{47,0,47},{47,1,46},{47,2,45},{47,3,44},{47,4,43},{47,5,42},{47,6,41},{47,7,40},{47,8,39},{47,9,38},{47,10,37},{47,11,36},{47,12,35},{47,13,34},{47,14,33},{47,15,32},{47,16,63},{47,17,62},{47,18,61},{47,19,60},{47,20,59},{47,21,58},{47,22,57},{47,23,56},{47,24,55},{47,25,54},{47,26,53},{48,0,48},{48,1,49},{48,2,50},{48,3,51},{48,4,52},{48,5,53},{48,6,54},{48,7,55},{48,8,56},{48,9,57},{48,10,58},{48,11,59},{48,12,60},{48,13,61},{48,14,62},{48,15,63},{48,16,32},{49,0,49},{49,1,48},{49,2,51},{49,3,50},{49,4,53},{49,5,52},{49,6,55},{49,7,54},{49,8,57},{49,9,56},{49,10,59},{49,11,58},{49,12,61},{49,13,60},{49,14,63},{49,15,62},{49,16,33},{50,0,50},{50,1,51},{50,2,48},{50,3,49},{50,4,54},{50,5,55},{50,6,52},{50,7,53},{50,8,58},{50,9,59},{50,10,56},{50,11,57},{50,12,62},{50,13,63},{50,14,60},{50,15,61},{50,16,34},{50,17,35},{51,0,51},{51,1,50},{51,2,49},{51,3,48},{51,4,55},{51,5,54},{51,6,53},{51,7,52},{51,8,59},{51,9,58},{51,10,57},{51,11,56},{51,12,63},{51,13,62},{51,14,61},{51,15,60},{51,16,35},{51,17,34},{52,0,52},{52,1,53},{52,2,54},{52,3,55},{52,4,48},{52,5,49},{52,6,50},{52,7,51},{52,8,60},{52,9,61},{52,10,62},{52,11,63},{52,12,56},{52,13,57},{52,14,58},{52,15,59},{52,16,36},{52,17,37},{52,18,38},{52,19,39},{53,0,53},{53,1,52},{53,2,55},{53,3,54},{53,4,49},{53,5,48},{53,6,51},{53,7,50},{53,8,61},{53,9,60},{53,10,63},{53,11,62},{53,12,57},{53,13,56},{53,14,59},{53,15,58},{53,16,37},{53,17,36},{53,18,39},{53,19,38},{54,0,54},{54,1,55},{54,2,52},{54,3,53},{54,4,50},{54,5,51},{54,6,48},{54,7,49},{54,8,62},{54,9,63},{54,10,60},{54,11,61},{54,12,58},{54,13,59},{54,14,56},{54,15,57},{54,16,38},{54,17,39},{54,18,36},{55,0,55},{55,1,54},{55,2,53},{55,3,52},{55,4,51},{55,5,50},{55,6,49},{55,7,48},{55,8,63},{55,9,62},{55,10,61},{55,11,60},{55,12,59},{55,13,58},{55,14,57},{55,15,56},{55,16,39},{55,17,38},{55,18,37},{56,0,56},{56,1,57},{56,2,58},{56,3,59},{56,4,60},{56,5,61},{56,6,62},{56,7,63},{56,8,48},{56,9,49},{56,10,50},{56,11,51},{56,12,52},{56,13,53},{56,14,54},{56,15,55},{56,16,40},{56,17,41},{56,18,42},{56,19,43},{56,20,44},{56,21,45},{56,22,46},{56,23,47},{57,0,57},{57,1,56},{57,2,59},{57,3,58},{57,4,61},{57,5,60},{57,6,63},{57,7,62},{57,8,49},{57,9,48},{57,10,51},{57,11,50},{57,12,53},{57,13,52},{57,14,55},{57,15,54},{57,16,41},{57,17,40},{57,18,43},{57,19,42},{57,20,45},{57,21,44},{57,22,47},{57,23,46},{58,0,58},{58,1,59},{58,2,56},{58,3,57},{58,4,62},{58,5,63},{58,6,60},{58,7,61},{58,8,50},{58,9,51},{58,10,48},{58,11,49},{58,12,54},{58,13,55},{58,14,52},{58,15,53},{58,16,42},{58,17,43},{58,18,40},{58,19,41},{58,20,46},{58,21,47},{58,22,44},{59,0,59},{59,1,58},{59,2,57},{59,3,56},{59,4,63},{59,5,62},{59,6,61},{59,7,60},{59,8,51},{59,9,50},{59,10,49},{59,11,48},{59,12,55},{59,13,54},{59,14,53},{59,15,52},{59,16,43},{59,17,42},{59,18,41},{59,19,40},{59,20,47},{59,21,46},{59,22,45},{60,0,60},{60,1,61},{60,2,62},{60,3,63},{60,4,56},{60,5,57},{60,6,58},{60,7,59},{60,8,52},{60,9,53},{60,10,54},{60,11,55},{60,12,48},{60,13,49},{60,14,50},{60,15,51},{60,16,44},{60,17,45},{60,18,46},{60,19,47},{60,20,40},{61,0,61},{61,1,60},{61,2,63},{61,3,62},{61,4,57},{61,5,56},{61,6,59},{61,7,58},{61,8,53},{61,9,52},{61,10,55},{61,11,54},{61,12,49},{61,13,48},{61,14,51},{61,15,50},{61,16,45},{61,17,44},{61,18,47},{61,19,46},{61,20,41},{62,0,62},{62,1,63},{62,2,60},{62,3,61},{62,4,58},{62,5,59},{62,6,56},{62,7,57},{62,8,54},{62,9,55},{62,10,52},{62,11,53},{62,12,50},{62,13,51},{62,14,48},{62,15,49},{62,16,46},{62,17,47},{62,18,44},{62,19,45},{62,20,42},{62,21,43},{63,0,63},{63,1,62},{63,2,61},{63,3,60},{63,4,59},{63,5,58},{63,6,57},{63,7,56},{63,8,55},{63,9,54},{63,10,53},{63,11,52},{63,12,51},{63,13,50},{63,14,49},{63,15,48},{63,16,47},{63,17,46},{63,18,45},{63,19,44},{63,20,43},{63,21,42},{64,0,64},{64,1,65},{64,2,66},{64,3,67},{64,4,68},{64,5,69},{64,6,70},{64,7,71},{64,8,72},{64,9,73},{64,10,74},{64,11,75},{64,12,76},{64,13,77},{64,14,78},{64,15,79},{64,16,80},{64,17,81},{64,18,82},{64,19,83},{64,20,84},{64,21,85},{64,22,86},{64,23,87},{64,24,88},{64,25,89},{64,26,90},{64,27,91},{64,28,92},{64,29,93},{64,30,94},{64,31,95},{64,32,96},{64,33,97},{64,34,98},{64,35,99},{64,36,100},{64,37,101},{64,38,102},{64,39,103},{64,40,104},{64,41,105},{64,42,106},{64,43,107},{64,44,108},{64,45,109},{64,46,110},{64,47,111},{64,48,112},{64,49,113},{64,50,114},{64,51,115},{64,52,116},{64,53,117},{64,54,118},{64,55,119},{64,56,120},{64,57,121},{64,58,122},{64,59,123},{64,60,124},{64,61,125},{64,62,126},{64,63,127},{65,0,65},{65,1,64},{65,2,67},{65,3,66},{65,4,69},{65,5,68},{65,6,71},{65,7,70},{65,8,73},{65,9,72},{65,10,75},{65,11,74},{65,12,77},{65,13,76},{65,14,79},{65,15,78},{65,16,81},{65,17,80},{65,18,83},{65,19,82},{65,20,85},{65,21,84},{65,22,87},{65,23,86},{65,24,89},{65,25,88},{65,26,91},{65,27,90},{65,28,93},{65,29,92},{65,30,95},{65,31,94},{65,32,97},{65,33,96},{65,34,99},{65,35,98},{65,36,101},{65,37,100},{65,38,103},{65,39,102},{65,40,105},{65,41,104},{65,42,107},{65,43,106},{65,44,109},{65,45,108},{65,46,111},{65,47,110},{65,48,113},{65,49,112},{65,50,115},{65,51,114},{65,52,117},{65,53,116},{65,54,119},{65,55,118},{65,56,121},{65,57,120},{65,58,123},{65,59,122},{65,60,125},{65,61,124},{65,62,127},{65,63,126},{66,0,66},{66,1,67},{66,2,64},{66,3,65},{66,4,70},{66,5,71},{66,6,68},{66,7,69},{66,8,74},{66,9,75},{66,10,72},{66,11,73},{66,12,78},{66,13,79},{66,14,76},{66,15,77},{66,16,82},{66,17,83},{66,18,80},{66,19,81},{66,20,86},{66,21,87},{66,22,84},{66,23,85},{66,24,90},{66,25,91},{66,26,88},{66,27,89},{66,28,94},{66,29,95},{66,30,92},{66,31,93},{66,32,98},{66,33,99},{66,34,96},{66,35,97},{66,36,102},{66,37,103},{66,38,100},{66,39,101},{66,40,106},{66,41,107},{66,42,104},{66,43,105},{66,44,110},{66,45,111},{66,46,108},{66,47,109},{66,48,114},{66,49,115},{66,50,112},{66,51,113},{66,52,118},{66,53,119},{66,54,116},{66,55,117},{66,56,122},{66,57,123},{66,58,120},{66,59,121},{66,60,126},{66,61,127},{66,62,124},{67,0,67},{67,1,66},{67,2,65},{67,3,64},{67,4,71},{67,5,70},{67,6,69},{67,7,68},{67,8,75},{67,9,74},{67,10,73},{67,11,72},{67,12,79},{67,13,78},{67,14,77},{67,15,76},{67,16,83},{67,17,82},{67,18,81},{67,19,80},{67,20,87},{67,21,86},{67,22,85},{67,23,84},{67,24,91},{67,25,90},{67,26,89},{67,27,88},{67,28,95},{67,29,94},{67,30,93},{67,31,92},{67,32,99},{67,33,98},{67,34,97},{67,35,96},{67,36,103},{67,37,102},{67,38,101},{67,39,100},{67,40,107},{67,41,106},{67,42,105},{67,43,104},{67,44,111},{67,45,110},{67,46,109},{67,47,108},{67,48,115},{67,49,114},{67,50,113},{67,51,112},{67,52,119},{67,53,118},{67,54,117},{67,55,116},{67,56,123},{67,57,122},{67,58,121},{67,59,120},{67,60,127},{67,61,126},{67,62,125},{68,0,68},{68,1,69},{68,2,70},{68,3,71},{68,4,64},{68,5,65},{68,6,66},{68,7,67},{68,8,76},{68,9,77},{68,10,78},{68,11,79},{68,12,72},{68,13,73},{68,14,74},{68,15,75},{68,16,84},{68,17,85},{68,18,86},{68,19,87},{68,20,80},{68,21,81},{68,22,82},{68,23,83},{68,24,92},{68,25,93},{68,26,94},{68,27,95},{68,28,88},{68,29,89},{68,30,90},{68,31,91},{68,32,100},{68,33,101},{68,34,102},{68,35,103},{68,36,96},{68,37,97},{68,38,98},{68,39,99},{68,40,108},{68,41,109},{68,42,110},{68,43,111},{68,44,104},{68,45,105},{68,46,106},{68,47,107},{68,48,116},{68,49,117},{68,50,118},{68,51,119},{68,52,112},{68,53,113},{68,54,114},{68,55,115},{68,56,124},{68,57,125},{68,58,126},{68,59,127},{68,60,120},{69,0,69},{69,1,68},{69,2,71},{69,3,70},{69,4,65},{69,5,64},{69,6,67},{69,7,66},{69,8,77},{69,9,76},{69,10,79},{69,11,78},{69,12,73},{69,13,72},{69,14,75},{69,15,74},{69,16,85},{69,17,84},{69,18,87},{69,19,86},{69,20,81},{69,21,80},{69,22,83},{69,23,82},{69,24,93},{69,25,92},{69,26,95},{69,27,94},{69,28,89},{69,29,88},{69,30,91},{69,31,90},{69,32,101},{69,33,100},{69,34,103},{69,35,102},{69,36,97},{69,37,96},{69,38,99},{69,39,98},{69,40,109},{69,41,108},{69,42,111},{69,43,110},{69,44,105},{69,45,104},{69,46,107},{69,47,106},{69,48,117},{69,49,116},{69,50,119},{69,51,118},{69,52,113},{69,53,112},{69,54,115},{69,55,114},{69,56,125},{69,57,124},{69,58,127},{69,59,126},{69,60,121},{70,0,70},{70,1,71},{70,2,68},{70,3,69},{70,4,66},{70,5,67},{70,6,64},{70,7,65},{70,8,78},{70,9,79},{70,10,76},{70,11,77},{70,12,74},{70,13,75},{70,14,72},{70,15,73},{70,16,86},{70,17,87},{70,18,84},{70,19,85},{70,20,82},{70,21,83},{70,22,80},{70,23,81},{70,24,94},{70,25,95},{70,26,92},{70,27,93},{70,28,90},{70,29,91},{70,30,88},{70,31,89},{70,32,102},{70,33,103},{70,34,100},{70,35,101},{70,36,98},{70,37,99},{70,38,96},{70,39,97},{70,40,110},{70,41,111},{70,42,108},{70,43,109},{70,44,106},{70,45,107},{70,46,104},{70,47,105},{70,48,118},{70,49,119},{70,50,116},{70,51,117},{70,52,114},{70,53,115},{70,54,112},{70,55,113},{70,56,126},{70,57,127},{70,58,124},{70,59,125},{70,60,122},{70,61,123},{71,0,71},{71,1,70},{71,2,69},{71,3,68},{71,4,67},{71,5,66},{71,6,65},{71,7,64},{71,8,79},{71,9,78},{71,10,77},{71,11,76},{71,12,75},{71,13,74},{71,14,73},{71,15,72},{71,16,87},{71,17,86},{71,18,85},{71,19,84},{71,20,83},{71,21,82},{71,22,81},{71,23,80},{71,24,95},{71,25,94},{71,26,93},{71,27,92},{71,28,91},{71,29,90},{71,30,89},{71,31,88},{71,32,103},{71,33,102},{71,34,101},{71,35,100},{71,36,99},{71,37,98},{71,38,97},{71,39,96},{71,40,111},{71,41,110},{71,42,109},{71,43,108},{71,44,107},{71,45,106},{71,46,105},{71,47,104},{71,48,119},{71,49,118},{71,50,117},{71,51,116},{71,52,115},{71,53,114},{71,54,113},{71,55,112},{71,56,127},{71,57,126},{71,58,125},{71,59,124},{71,60,123},{71,61,122},{72,0,72},{72,1,73},{72,2,74},{72,3,75},{72,4,76},{72,5,77},{72,6,78},{72,7,79},{72,8,64},{72,9,65},{72,10,66},{72,11,67},{72,12,68},{72,13,69},{72,14,70},{72,15,71},{72,16,88},{72,17,89},{72,18,90},{72,19,91},{72,20,92},{72,21,93},{72,22,94},{72,23,95},{72,24,80},{72,25,81},{72,26,82},{72,27,83},{72,28,84},{72,29,85},{72,30,86},{72,31,87},{72,32,104},{72,33,105},{72,34,106},{72,35,107},{72,36,108},{72,37,109},{72,38,110},{72,39,111},{72,40,96},{72,41,97},{72,42,98},{72,43,99},{72,44,100},{72,45,101},{72,46,102},{72,47,103},{72,48,120},{72,49,121},{72,50,122},{72,51,123},{72,52,124},{72,53,125},{72,54,126},{72,55,127},{72,56,112},{73,0,73},{73,1,72},{73,2,75},{73,3,74},{73,4,77},{73,5,76},{73,6,79},{73,7,78},{73,8,65},{73,9,64},{73,10,67},{73,11,66},{73,12,69},{73,13,68},{73,14,71},{73,15,70},{73,16,89},{73,17,88},{73,18,91},{73,19,90},{73,20,93},{73,21,92},{73,22,95},{73,23,94},{73,24,81},{73,25,80},{73,26,83},{73,27,82},{73,28,85},{73,29,84},{73,30,87},{73,31,86},{73,32,105},{73,33,104},{73,34,107},{73,35,106},{73,36,109},{73,37,108},{73,38,111},{73,39,110},{73,40,97},{73,41,96},{73,42,99},{73,43,98},{73,44,101},{73,45,100},{73,46,103},{73,47,102},{73,48,121},{73,49,120},{73,50,123},{73,51,122},{73,52,125},{73,53,124},{73,54,127},{73,55,126},{73,56,113},{74,0,74},{74,1,75},{74,2,72},{74,3,73},{74,4,78},{74,5,79},{74,6,76},{74,7,77},{74,8,66},{74,9,67},{74,10,64},{74,11,65},{74,12,70},{74,13,71},{74,14,68},{74,15,69},{74,16,90},{74,17,91},{74,18,88},{74,19,89},{74,20,94},{74,21,95},{74,22,92},{74,23,93},{74,24,82},{74,25,83},{74,26,80},{74,27,81},{74,28,86},{74,29,87},{74,30,84},{74,31,85},{74,32,106},{74,33,107},{74,34,104},{74,35,105},{74,36,110},{74,37,111},{74,38,108},{74,39,109},{74,40,98},{74,41,99},{74,42,96},{74,43,97},{74,44,102},{74,45,103},{74,46,100},{74,47,101},{74,48,122},{74,49,123},{74,50,120},{74,51,121},{74,52,126},{74,53,127},{74,54,124},{74,55,125},{74,56,114},{74,57,115},{75,0,75},{75,1,74},{75,2,73},{75,3,72},{75,4,79},{75,5,78},{75,6,77},{75,7,76},{75,8,67},{75,9,66},{75,10,65},{75,11,64},{75,12,71},{75,13,70},{75,14,69},{75,15,68},{75,16,91},{75,17,90},{75,18,89},{75,19,88},{75,20,95},{75,21,94},{75,22,93},{75,23,92},{75,24,83},{75,25,82},{75,26,81},{75,27,80},{75,28,87},{75,29,86},{75,30,85},{75,31,84},{75,32,107},{75,33,106},{75,34,105},{75,35,104},{75,36,111},{75,37,110},{75,38,109},{75,39,108},{75,40,99},{75,41,98},{75,42,97},{75,43,96},{75,44,103},{75,45,102},{75,46,101},{75,47,100},{75,48,123},{75,49,122},{75,50,121},{75,51,120},{75,52,127},{75,53,126},{75,54,125},{75,55,124},{75,56,115},{75,57,114}},{{0,0,0},{1,0,1},{2,0,2},{3,0,3},{3,1,4},{4,0,4},{4,1,3},{5,0,5},{5,1,6},{5,2,7},{6,0,6},{6,1,5},{7,0,7},{7,1,8},{7,2,6},{8,0,8},{8,1,7},{8,2,9},{8,3,10},{9,0,9},{9,1,10},{9,2,8},{10,0,10},{10,1,9},{10,2,11},{10,3,12},{10,4,13},{11,0,11},{11,1,12},{11,2,10},{11,3,9},{12,0,12},{12,1,11},{12,2,13},{12,3,14},{12,4,15},{12,5,16},{13,0,13},{13,1,14},{13,2,12},{13,3,11},{14,0,14},{14,1,13},{14,2,15},{14,3,16},{14,4,12},{15,0,15},{15,1,16},{15,2,14},{15,3,13},{15,4,17},{15,5,18},{15,6,19},{16,0,16},{16,1,15},{16,2,17},{16,3,18},{16,4,14},{17,0,17},{17,1,18},{17,2,16},{17,3,15},{17,4,19},{17,5,20},{17,6,21},{17,7,22},{18,0,18},{18,1,17},{18,2,19},{18,3,20},{18,4,16},{18,5,15},{19,0,19},{19,1,20},{19,2,18},{19,3,17},{19,4,21},{19,5,22},{19,6,23},{19,7,24},{19,8,25},{20,0,20},{20,1,19},{20,2,21},{20,3,22},{20,4,18},{20,5,17},{21,0,21},{21,1,22},{21,2,20},{21,3,19},{21,4,23},{21,5,24},{21,6,18},{22,0,22},{22,1,21},{22,2,23},{22,3,24},{22,4,20},{22,5,19},{22,6,25},{22,7,26},{22,8,27},{22,9,28},{23,0,23},{23,1,24},{23,2,22},{23,3,21},{23,4,25},{23,5,26},{23,6,20},{24,0,24},{24,1,23},{24,2,25},{24,3,26},{24,4,22},{24,5,21},{24,6,27},{24,7,28},{24,8,29},{24,9,30},{24,10,31},{25,0,25},{25,1,26},{25,2,24},{25,3,23},{25,4,27},{25,5,28},{25,6,22},{25,7,21},{26,0,26},{26,1,25},{26,2,27},{26,3,28},{26,4,24},{26,5,23},{26,6,29},{26,7,30},{26,8,31},{26,9,32},{26,10,33},{26,11,34},{27,0,27},{27,1,28},{27,2,26},{27,3,25},{27,4,29},{27,5,30},{27,6,24},{27,7,23},{28,0,28},{28,1,27},{28,2,29},{28,3,30},{28,4,26},{28,5,25},{28,6,31},{28,7,32},{28,8,24},{29,0,29},{29,1,30},{29,2,28},{29,3,27},{29,4,31},{29,5,32},{29,6,26},{29,7,25},{29,8,33},{29,9,34},{29,10,35},{29,11,36},{29,12,37},{30,0,30},{30,1,29},{30,2,31},{30,3,32},{30,4,28},{30,5,27},{30,6,33},{30,7,34},{30,8,26},{31,0,31},{31,1,32},{31,2,30},{31,3,29},{31,4,33},{31,5,34},{31,6,28},{31,7,27},{31,8,35},{31,9,36},{31,10,37},{31,11,38},{31,12,39},{31,13,40},{32,0,32},{32,1,31},{32,2,33},{32,3,34},{32,4,30},{32,5,29},{32,6,35},{32,7,36},{32,8,28},{32,9,27},{33,0,33},{33,1,34},{33,2,32},{33,3,31},{33,4,35},{33,5,36},{33,6,30},{33,7,29},{33,8,37},{33,9,38},{33,10,39},{33,11,40},{33,12,41},{33,13,42},{33,14,43},{34,0,34},{34,1,33},{34,2,35},{34,3,36},{34,4,32},{34,5,31},{34,6,37},{34,7,38},{34,8,30},{34,9,29},{35,0,35},{35,1,36},{35,2,34},{35,3,33},{35,4,37},{35,5,38},{35,6,32},{35,7,31},{35,8,39},{35,9,40},{35,10,30},{36,0,36},{36,1,35},{36,2,37},{36,3,38},{36,4,34},{36,5,33},{36,6,39},{36,7,40},{36,8,32},{36,9,31},{36,10,41},{36,11,42},{36,12,43},{36,13,44},{36,14,45},{36,15,46},{37,0,37},{37,1,38},{37,2,36},{37,3,35},{37,4,39},{37,5,40},{37,6,34},{37,7,33},{37,8,41},{37,9,42},{37,10,32},{38,0,38},{38,1,37},{38,2,39},{38,3,40},{38,4,36},{38,5,35},{38,6,41},{38,7,42},{38,8,34},{38,9,33},{38,10,43},{38,11,44},{38,12,45},{38,13,46},{38,14,47},{38,15,48},{38,16,49},{39,0,39},{39,1,40},{39,2,38},{39,3,37},{39,4,41},{39,5,42},{39,6,36},{39,7,35},{39,8,43},{39,9,44},{39,10,34},{39,11,33},{40,0,40},{40,1,39},{40,2,41},{40,3,42},{40,4,38},{40,5,37},{40,6,43},{40,7,44},{40,8,36},{40,9,35},{40,10,45},{40,11,46},{40,12,47},{40,13,48},{40,14,49},{40,15,50},{40,16,51},{40,17,52},{41,0,41},{41,1,42},{41,2,40},{41,3,39},{41,4,43},{41,5,44},{41,6,38},{41,7,37},{41,8,45},{41,9,46},{41,10,36},{41,11,35},{42,0,42},{42,1,41},{42,2,43},{42,3,44},{42,4,40},{42,5,39},{42,6,45},{42,7,46},{42,8,38},{42,9,37},{42,10,47},{42,11,48},{42,12,36},{43,0,43},{43,1,44},{43,2,42},{43,3,41},{43,4,45},{43,5,46},{43,6,40},{43,7,39},{43,8,47},{43,9,48},{43,10,38},{43,11,37},{43,12,49},{43,13,50},{43,14,51},{43,15,52},{43,16,53},{43,17,54},{43,18,55},{44,0,44},{44,1,43},{44,2,45},{44,3,46},{44,4,42},{44,5,41},{44,6,47},{44,7,48},{44,8,40},{44,9,39},{44,10,49},{44,11,50},{44,12,38},{45,0,45},{45,1,46},{45,2,44},{45,3,43},{45,4,47},{45,5,48},{45,6,42},{45,7,41},{45,8,49},{45,9,50},{45,10,40},{45,11,39},{45,12,51},{45,13,52},{45,14,53},{45,15,54},{45,16,55},{45,17,56},{45,18,57},{45,19,58},{46,0,46},{46,1,45},{46,2,47},{46,3,48},{46,4,44},{46,5,43},{46,6,49},{46,7,50},{46,8,42},{46,9,41},{46,10,51},{46,11,52},{46,12,40},{46,13,39},{47,0,47},{47,1,48},{47,2,46},{47,3,45},{47,4,49},{47,5,50},{47,6,44},{47,7,43},{47,8,51},{47,9,52},{47,10,42},{47,11,41},{47,12,53},{47,13,54},{47,14,55},{47,15,56},{47,16,57},{47,17,58},{47,18,59},{47,19,60},{47,20,61},{48,0,48},{48,1,47},{48,2,49},{48,3,50},{48,4,46},{48,5,45},{48,6,51},{48,7,52},{48,8,44},{48,9,43},{48,10,53},{48,11,54},{48,12,42},{48,13,41},{49,0,49},{49,1,50},{49,2,48},{49,3,47},{49,4,51},{49,5,52},{49,6,46},{49,7,45},{49,8,53},{49,9,54},{49,10,44},{49,11,43},{49,12,55},{49,13,56},{49,14,42},{50,0,50},{50,1,49},{50,2,51},{50,3,52},{50,4,48},{50,5,47},{50,6,53},{50,7,54},{50,8,46},{50,9,45},{50,10,55},{50,11,56},{50,12,44},{50,13,43},{50,14,57},{50,15,58},{50,16,59},{50,17,60},{50,18,61},{50,19,62},{50,20,63},{50,21,64},{51,0,51},{51,1,52},{51,2,50},{51,3,49},{51,4,53},{51,5,54},{51,6,48},{51,7,47},{51,8,55},{51,9,56},{51,10,46},{51,11,45},{51,12,57},{51,13,58},{51,14,44},{52,0,52},{52,1,51},{52,2,53},{52,3,54},{52,4,50},{52,5,49},{52,6,55},{52,7,56},{52,8,48},{52,9,47},{52,10,57},{52,11,58},{52,12,46},{52,13,45},{52,14,59},{52,15,60},{52,16,61},{52,17,62},{52,18,63},{52,19,64},{52,20,65},{52,21,66},{52,22,67},{53,0,53},{53,1,54},{53,2,52},{53,3,51},{53,4,55},{53,5,56},{53,6,50},{53,7,49},{53,8,57},{53,9,58},{53,10,48},{53,11,47},{53,12,59},{53,13,60},{53,14,46},{53,15,45},{54,0,54},{54,1,53},{54,2,55},{54,3,56},{54,4,52},{54,5,51},{54,6,57},{54,7,58},{54,8,50},{54,9,49},{54,10,59},{54,11,60},{54,12,48},{54,13,47},{54,14,61},{54,15,62},{54,16,63},{54,17,64},{54,18,65},{54,19,66},{54,20,67},{54,21,68},{54,22,69},{54,23,70},{55,0,55},{55,1,56},{55,2,54},{55,3,53},{55,4,57},{55,5,58},{55,6,52},{55,7,51},{55,8,59},{55,9,60},{55,10,50},{55,11,49},{55,12,61},{55,13,62},{55,14,48},{55,15,47},{56,0,56},{56,1,55},{56,2,57},{56,3,58},{56,4,54},{56,5,53},{56,6,59},{56,7,60},{56,8,52},{56,9,51},{56,10,61},{56,11,62},{56,12,50},{56,13,49},{56,14,63},{56,15,64},{56,16,48},{57,0,57},{57,1,58},{57,2,56},{57,3,55},{57,4,59},{57,5,60},{57,6,54},{57,7,53},{57,8,61},{57,9,62},{57,10,52},{57,11,51},{57,12,63},{57,13,64},{57,14,50},{57,15,49},{57,16,65},{57,17,66},{57,18,67},{57,19,68},{57,20,69},{57,21,70},{57,22,71},{57,23,72},{57,24,73},{58,0,58},{58,1,57},{58,2,59},{58,3,60},{58,4,56},{58,5,55},{58,6,61},{58,7,62},{58,8,54},{58,9,53},{58,10,63},{58,11,64},{58,12,52},{58,13,51},{58,14,65},{58,15,66},{58,16,50},{59,0,59},{59,1,60},{59,2,58},{59,3,57},{59,4,61},{59,5,62},{59,6,56},{59,7,55},{59,8,63},{59,9,64},{59,10,54},{59,11,53},{59,12,65},{59,13,66},{59,14,52},{59,15,51},{59,16,67},{59,17,68},{59,18,69},{59,19,70},{59,20,71},{59,21,72},{59,22,73},{59,23,74},{59,24,75},{59,25,76},{60,0,60},{60,1,59},{60,2,61},{60,3,62},{60,4,58},{60,5,57},{60,6,63},{60,7,64},{60,8,56},{60,9,55},{60,10,65},{60,11,66},{60,12,54},{60,13,53},{60,14,67},{60,15,68},{60,16,52},{60,17,51},{61,0,61},{61,1,62},{61,2,60},{61,3,59},{61,4,63},{61,5,64},{61,6,58},{61,7,57},{61,8,65},{61,9,66},{61,10,56},{61,11,55},{61,12,67},{61,13,68},{61,14,54},{61,15,53},{61,16,69},{61,17,70},{61,18,71},{61,19,72},{61,20,73},{61,21,74},{61,22,75},{61,23,76},{61,24,77},{61,25,78},{61,26,79},{62,0,62},{62,1,61},{62,2,63},{62,3,64},{62,4,60},{62,5,59},{62,6,65},{62,7,66},{62,8,58},{62,9,57},{62,10,67},{62,11,68},{62,12,56},{62,13,55},{62,14,69},{62,15,70},{62,16,54},{62,17,53},{63,0,63},{63,1,64},{63,2,62},{63,3,61},{63,4,65},{63,5,66},{63,6,60},{63,7,59},{63,8,67},{63,9,68},{63,10,58},{63,11,57},{63,12,69},{63,13,70},{63,14,56},{63,15,55},{63,16,71},{63,17,72},{63,18,54},{64,0,64},{64,1,63},{64,2,65},{64,3,66},{64,4,62},{64,5,61},{64,6,67},{64,7,68},{64,8,60},{64,9,59},{64,10,69},{64,11,70},{64,12,58},{64,13,57},{64,14,71},{64,15,72},{64,16,56},{64,17,55},{64,18,73},{64,19,74},{64,20,75},{64,21,76},{64,22,77},{64,23,78},{64,24,79},{64,25,80},{64,26,81},{64,27,82},{65,0,65},{65,1,66},{65,2,64},{65,3,63},{65,4,67},{65,5,68},{65,6,62},{65,7,61},{65,8,69},{65,9,70},{65,10,60},{65,11,59},{65,12,71},{65,13,72},{65,14,58},{65,15,57},{65,16,73},{65,17,74},{65,18,56},{66,0,66},{66,1,65},{66,2,67},{66,3,68},{66,4,64},{66,5,63},{66,6,69},{66,7,70},{66,8,62},{66,9,61},{66,10,71},{66,11,72},{66,12,60},{66,13,59},{66,14,73},{66,15,74},{66,16,58},{66,17,57},{66,18,75},{66,19,76},{66,20,77},{66,21,78},{66,22,79},{66,23,80},{66,24,81},{66,25,82},{66,26,83},{66,27,84},{66,28,85},{67,0,67},{67,1,68},{67,2,66},{67,3,65},{67,4,69},{67,5,70},{67,6,64},{67,7,63},{67,8,71},{67,9,72},{67,10,62},{67,11,61},{67,12,73},{67,13,74},{67,14,60},{67,15,59},{67,16,75},{67,17,76},{67,18,58},{67,19,57},{68,0,68},{68,1,67},{68,2,69},{68,3,70},{68,4,66},{68,5,65},{68,6,71},{68,7,72},{68,8,64},{68,9,63},{68,10,73},{68,11,74},{68,12,62},{68,13,61},{68,14,75},{68,15,76},{68,16,60},{68,17,59},{68,18,77},{68,19,78},{68,20,79},{68,21,80},{68,22,81},{68,23,82},{68,24,83},{68,25,84},{68,26,85},{68,27,86},{68,28,87},{68,29,88},{69,0,69},{69,1,70},{69,2,68},{69,3,67},{69,4,71},{69,5,72},{69,6,66},{69,7,65},{69,8,73},{69,9,74},{69,10,64},{69,11,63},{69,12,75},{69,13,76},{69,14,62},{69,15,61},{69,16,77},{69,17,78},{69,18,60},{69,19,59},{70,0,70},{70,1,69},{70,2,71},{70,3,72},{70,4,68},{70,5,67},{70,6,73},{70,7,74},{70,8,66},{70,9,65},{70,10,75},{70,11,76},{70,12,64},{70,13,63},{70,14,77},{70,15,78},{70,16,62},{70,17,61},{70,18,79},{70,19,80},{70,20,60},{71,0,71},{71,1,72},{71,2,70},{71,3,69},{71,4,73},{71,5,74},{71,6,68},{71,7,67},{71,8,75},{71,9,76},{71,10,66},{71,11,65},{71,12,77},{71,13,78},{71,14,64},{71,15,63},{71,16,79},{71,17,80},{71,18,62},{71,19,61},{71,20,81},{71,21,82},{71,22,83},{71,23,84},{71,24,85},{71,25,86},{71,26,87},{71,27,88},{71,28,89},{71,29,90},{71,30,91},{72,0,72},{72,1,71},{72,2,73},{72,3,74},{72,4,70},{72,5,69},{72,6,75},{72,7,76},{72,8,68},{72,9,67},{72,10,77},{72,11,78},{72,12,66},{72,13,65},{72,14,79},{72,15,80},{72,16,64},{72,17,63},{72,18,81},{72,19,82},{72,20,62},{73,0,73},{73,1,74},{73,2,72},{73,3,71},{73,4,75},{73,5,76},{73,6,70},{73,7,69},{73,8,77},{73,9,78},{73,10,68},{73,11,67},{73,12,79},{73,13,80},{73,14,66},{73,15,65},{73,16,81},{73,17,82},{73,18,64},{73,19,63},{73,20,83},{73,21,84},{73,22,85},{73,23,86},{73,24,87},{73,25,88},{73,26,89},{73,27,90},{73,28,91},{73,29,92},{73,30,93},{73,31,94},{74,0,74},{74,1,73},{74,2,75},{74,3,76},{74,4,72},{74,5,71},{74,6,77},{74,7,78},{74,8,70},{74,9,69},{74,10,79},{74,11,80},{74,12,68},{74,13,67},{74,14,81},{74,15,82},{74,16,66},{74,17,65},{74,18,83},{74,19,84},{74,20,64},{74,21,63},{75,0,75},{75,1,76},{75,2,74},{75,3,73},{75,4,77},{75,5,78},{75,6,72},{75,7,71},{75,8,79},{75,9,80},{75,10,70},{75,11,69},{75,12,81},{75,13,82},{75,14,68},{75,15,67},{75,16,83},{75,17,84},{75,18,66},{75,19,65},{75,20,85},{75,21,86},{75,22,87},{75,23,88},{75,24,89},{75,25,90},{75,26,91},{75,27,92},{75,28,93},{75,29,94},{75,30,95},{75,31,96},{75,32,97}},{{0,0,0},{1,0,1},{2,0,2},{3,0,3},{4,0,4},{4,1,5},{5,0,5},{5,1,4},{6,0,6},{6,1,7},{7,0,7},{7,1,6},{8,0,8},{8,1,9},{8,2,10},{9,0,9},{9,1,8},{9,2,11},{10,0,10},{10,1,11},{10,2,8},{11,0,11},{11,1,10},{11,2,9},{12,0,12},{12,1,13},{12,2,14},{12,3,15},{13,0,13},{13,1,12},{13,2,15},{13,3,14},{14,0,14},{14,1,15},{14,2,12},{14,3,13},{15,0,15},{15,1,14},{15,2,13},{15,3,12},{16,0,16},{16,1,17},{16,2,18},{16,3,19},{16,4,20},{16,5,21},{17,0,17},{17,1,16},{17,2,19},{17,3,18},{17,4,21},{17,5,20},{18,0,18},{18,1,19},{18,2,16},{18,3,17},{18,4,22},{18,5,23},{19,0,19},{19,1,18},{19,2,17},{19,3,16},{19,4,23},{19,5,22},{20,0,20},{20,1,21},{20,2,22},{20,3,23},{20,4,16},{21,0,21},{21,1,20},{21,2,23},{21,3,22},{21,4,17},{22,0,22},{22,1,23},{22,2,20},{22,3,21},{22,4,18},{23,0,23},{23,1,22},{23,2,21},{23,3,20},{23,4,19},{24,0,24},{24,1,25},{24,2,26},{24,3,27},{24,4,28},{24,5,29},{24,6,30},{24,7,31},{25,0,25},{25,1,24},{25,2,27},{25,3,26},{25,4,29},{25,5,28},{25,6,31},{25,7,30},{26,0,26},{26,1,27},{26,2,24},{26,3,25},{26,4,30},{26,5,31},{26,6,28},{26,7,29},{27,0,27},{27,1,26},{27,2,25},{27,3,24},{27,4,31},{27,5,30},{27,6,29},{27,7,28},{28,0,28},{28,1,29},{28,2,30},{28,3,31},{28,4,24},{28,5,25},{28,6,26},{29,0,29},{29,1,28},{29,2,31},{29,3,30},{29,4,25},{29,5,24},{29,6,27},{30,0,30},{30,1,31},{30,2,28},{30,3,29},{30,4,26},{30,5,27},{30,6,24},{31,0,31},{31,1,30},{31,2,29},{31,3,28},{31,4,27},{31,5,26},{31,6,25},{32,0,32},{32,1,33},{32,2,34},{32,3,35},{32,4,36},{32,5,37},{32,6,38},{32,7,39},{32,8,40},{32,9,41},{32,10,42},{33,0,33},{33,1,32},{33,2,35},{33,3,34},{33,4,37},{33,5,36},{33,6,39},{33,7,38},{33,8,41},{33,9,40},{33,10,43},{34,0,34},{34,1,35},{34,2,32},{34,3,33},{34,4,38},{34,5,39},{34,6,36},{34,7,37},{34,8,42},{34,9,43},{34,10,40},{35,0,35},{35,1,34},{35,2,33},{35,3,32},{35,4,39},{35,5,38},{35,6,37},{35,7,36},{35,8,43},{35,9,42},{35,10,41},{36,0,36},{36,1,37},{36,2,38},{36,3,39},{36,4,32},{36,5,33},{36,6,34},{36,7,35},{36,8,44},{36,9,45},{36,10,46},{36,11,47},{37,0,37},{37,1,36},{37,2,39},{37,3,38},{37,4,33},{37,5,32},{37,6,35},{37,7,34},{37,8,45},{37,9,44},{37,10,47},{37,11,46},{38,0,38},{38,1,39},{38,2,36},{38,3,37},{38,4,34},{38,5,35},{38,6,32},{38,7,33},{38,8,46},{38,9,47},{38,10,44},{38,11,45},{39,0,39},{39,1,38},{39,2,37},{39,3,36},{39,4,35},{39,5,34},{39,6,33},{39,7,32},{39,8,47},{39,9,46},{39,10,45},{39,11,44},{40,0,40},{40,1,41},{40,2,42},{40,3,43},{40,4,44},{40,5,45},{40,6,46},{40,7,47},{40,8,32},{41,0,41},{41,1,40},{41,2,43},{41,3,42},{41,4,45},{41,5,44},{41,6,47},{41,7,46},{41,8,33},{42,0,42},{42,1,43},{42,2,40},{42,3,41},{42,4,46},{42,5,47},{42,6,44},{42,7,45},{42,8,34},{43,0,43},{43,1,42},{43,2,41},{43,3,40},{43,4,47},{43,5,46},{43,6,45},{43,7,44},{43,8,35},{44,0,44},{44,1,45},{44,2,46},{44,3,47},{44,4,40},{44,5,41},{44,6,42},{44,7,43},{44,8,36},{44,9,37},{45,0,45},{45,1,44},{45,2,47},{45,3,46},{45,4,41},{45,5,40},{45,6,43},{45,7,42},{45,8,37},{45,9,36},{46,0,46},{46,1,47},{46,2,44},{46,3,45},{46,4,42},{46,5,43},{46,6,40},{46,7,41},{46,8,38},{46,9,39},{47,0,47},{47,1,46},{47,2,45},{47,3,44},{47,4,43},{47,5,42},{47,6,41},{47,7,40},{47,8,39},{47,9,38},{48,0,48},{48,1,49},{48,2,50},{48,3,51},{48,4,52},{48,5,53},{48,6,54},{48,7,55},{48,8,56},{48,9,57},{48,10,58},{48,11,59},{48,12,60},{48,13,61},{48,14,62},{48,15,63},{49,0,49},{49,1,48},{49,2,51},{49,3,50},{49,4,53},{49,5,52},{49,6,55},{49,7,54},{49,8,57},{49,9,56},{49,10,59},{49,11,58},{49,12,61},{49,13,60},{49,14,63},{49,15,62},{50,0,50},{50,1,51},{50,2,48},{50,3,49},{50,4,54},{50,5,55},{50,6,52},{50,7,53},{50,8,58},{50,9,59},{50,10,56},{50,11,57},{50,12,62},{50,13,63},{50,14,60},{50,15,61},{51,0,51},{51,1,50},{51,2,49},{51,3,48},{51,4,55},{51,5,54},{51,6,53},{51,7,52},{51,8,59},{51,9,58},{51,10,57},{51,11,56},{51,12,63},{51,13,62},{51,14,61},{51,15,60},{52,0,52},{52,1,53},{52,2,54},{52,3,55},{52,4,48},{52,5,49},{52,6,50},{52,7,51},{52,8,60},{52,9,61},{52,10,62},{52,11,63},{52,12,56},{52,13,57},{52,14,58},{53,0,53},{53,1,52},{53,2,55},{53,3,54},{53,4,49},{53,5,48},{53,6,51},{53,7,50},{53,8,61},{53,9,60},{53,10,63},{53,11,62},{53,12,57},{53,13,56},{53,14,59},{54,0,54},{54,1,55},{54,2,52},{54,3,53},{54,4,50},{54,5,51},{54,6,48},{54,7,49},{54,8,62},{54,9,63},{54,10,60},{54,11,61},{54,12,58},{54,13,59},{54,14,56},{55,0,55},{55,1,54},{55,2,53},{55,3,52},{55,4,51},{55,5,50},{55,6,49},{55,7,48},{55,8,63},{55,9,62},{55,10,61},{55,11,60},{55,12,59},{55,13,58},{55,14,57},{56,0,56},{56,1,57},{56,2,58},{56,3,59},{56,4,60},{56,5,61},{56,6,62},{56,7,63},{56,8,48},{56,9,49},{56,10,50},{56,11,51},{56,12,52},{56,13,53},{57,0,57},{57,1,56},{57,2,59},{57,3,58},{57,4,61},{57,5,60},{57,6,63},{57,7,62},{57,8,49},{57,9,48},{57,10,51},{57,11,50},{57,12,53},{57,13,52},{58,0,58},{58,1,59},{58,2,56},{58,3,57},{58,4,62},{58,5,63},{58,6,60},{58,7,61},{58,8,50},{58,9,51},{58,10,48},{58,11,49},{58,12,54},{58,13,55},{59,0,59},{59,1,58},{59,2,57},{59,3,56},{59,4,63},{59,5,62},{59,6,61},{59,7,60},{59,8,51},{59,9,50},{59,10,49},{59,11,48},{59,12,55},{59,13,54},{60,0,60},{60,1,61},{60,2,62},{60,3,63},{60,4,56},{60,5,57},{60,6,58},{60,7,59},{60,8,52},{60,9,53},{60,10,54},{60,11,55},{60,12,48},{61,0,61},{61,1,60},{61,2,63},{61,3,62},{61,4,57},{61,5,56},{61,6,59},{61,7,58},{61,8,53},{61,9,52},{61,10,55},{61,11,54},{61,12,49},{62,0,62},{62,1,63},{62,2,60},{62,3,61},{62,4,58},{62,5,59},{62,6,56},{62,7,57},{62,8,54},{62,9,55},{62,10,52},{62,11,53},{62,12,50},{63,0,63},{63,1,62},{63,2,61},{63,3,60},{63,4,59},{63,5,58},{63,6,57},{63,7,56},{63,8,55},{63,9,54},{63,10,53},{63,11,52},{63,12,51},{64,0,64},{64,1,65},{64,2,66},{64,3,67},{64,4,68},{64,5,69},{64,6,70},{64,7,71},{64,8,72},{64,9,73},{64,10,74},{64,11,75},{64,12,76},{64,13,77},{64,14,78},{64,15,79},{64,16,80},{64,17,81},{64,18,82},{64,19,83},{64,20,84},{64,21,85},{65,0,65},{65,1,64},{65,2,67},{65,3,66},{65,4,69},{65,5,68},{65,6,71},{65,7,70},{65,8,73},{65,9,72},{65,10,75},{65,11,74},{65,12,77},{65,13,76},{65,14,79},{65,15,78},{65,16,81},{65,17,80},{65,18,83},{65,19,82},{65,20,85},{65,21,84},{66,0,66},{66,1,67},{66,2,64},{66,3,65},{66,4,70},{66,5,71},{66,6,68},{66,7,69},{66,8,74},{66,9,75},{66,10,72},{66,11,73},{66,12,78},{66,13,79},{66,14,76},{66,15,77},{66,16,82},{66,17,83},{66,18,80},{66,19,81},{66,20,86},{66,21,87},{67,0,67},{67,1,66},{67,2,65},{67,3,64},{67,4,71},{67,5,70},{67,6,69},{67,7,68},{67,8,75},{67,9,74},{67,10,73},{67,11,72},{67,12,79},{67,13,78},{67,14,77},{67,15,76},{67,16,83},{67,17,82},{67,18,81},{67,19,80},{67,20,87},{67,21,86},{68,0,68},{68,1,69},{68,2,70},{68,3,71},{68,4,64},{68,5,65},{68,6,66},{68,7,67},{68,8,76},{68,9,77},{68,10,78},{68,11,79},{68,12,72},{68,13,73},{68,14,74},{68,15,75},{68,16,84},{68,17,85},{68,18,86},{68,19,87},{68,20,80},{69,0,69},{69,1,68},{69,2,71},{69,3,70},{69,4,65},{69,5,64},{69,6,67},{69,7,66},{69,8,77},{69,9,76},{69,10,79},{69,11,78},{69,12,73},{69,13,72},{69,14,75},{69,15,74},{69,16,85},{69,17,84},{69,18,87},{69,19,86},{69,20,81},{70,0,70},{70,1,71},{70,2,68},{70,3,69},{70,4,66},{70,5,67},{70,6,64},{70,7,65},{70,8,78},{70,9,79},{70,10,76},{70,11,77},{70,12,74},{70,13,75},{70,14,72},{70,15,73},{70,16,86},{70,17,87},{70,18,84},{70,19,85},{70,20,82},{71,0,71},{71,1,70},{71,2,69},{71,3,68},{71,4,67},{71,5,66},{71,6,65},{71,7,64},{71,8,79},{71,9,78},{71,10,77},{71,11,76},{71,12,75},{71,13,74},{71,14,73},{71,15,72},{71,16,87},{71,17,86},{71,18,85},{71,19,84},{71,20,83},{72,0,72},{72,1,73},{72,2,74},{72,3,75},{72,4,76},{72,5,77},{72,6,78},{72,7,79},{72,8,64},{72,9,65},{72,10,66},{72,11,67},{72,12,68},{72,13,69},{72,14,70},{72,15,71},{72,16,88},{72,17,89},{72,18,90},{72,19,91},{72,20,92},{72,21,93},{72,22,94},{72,23,95},{73,0,73},{73,1,72},{73,2,75},{73,3,74},{73,4,77},{73,5,76},{73,6,79},{73,7,78},{73,8,65},{73,9,64},{73,10,67},{73,11,66},{73,12,69},{73,13,68},{73,14,71},{73,15,70},{73,16,89},{73,17,88},{73,18,91},{73,19,90},{73,20,93},{73,21,92},{73,22,95},{73,23,94},{74,0,74},{74,1,75},{74,2,72},{74,3,73},{74,4,78},{74,5,79},{74,6,76},{74,7,77},{74,8,66},{74,9,67},{74,10,64},{74,11,65},{74,12,70},{74,13,71},{74,14,68},{74,15,69},{74,16,90},{74,17,91},{74,18,88},{74,19,89},{74,20,94},{74,21,95},{74,22,92},{74,23,93},{75,0,75},{75,1,74},{75,2,73},{75,3,72},{75,4,79},{75,5,78},{75,6,77},{75,7,76},{75,8,67},{75,9,66},{75,10,65},{75,11,64},{75,12,71},{75,13,70},{75,14,69},{75,15,68},{75,16,91},{75,17,90},{75,18,89},{75,19,88},{75,20,95},{75,21,94},{75,22,93},{75,23,92}},{{0,0,0},{1,0,1},{2,0,2},{3,0,3},{4,0,4},{5,0,5},{5,1,6},{6,0,6},{6,1,5},{7,0,7},{7,1,8},{8,0,8},{8,1,7},{9,0,9},{9,1,10},{9,2,11},{10,0,10},{10,1,9},{11,0,11},{11,1,12},{11,2,10},{12,0,12},{12,1,11},{12,2,13},{13,0,13},{13,1,14},{13,2,12},{14,0,14},{14,1,13},{14,2,15},{14,3,16},{15,0,15},{15,1,16},{15,2,14},{16,0,16},{16,1,15},{16,2,17},{16,3,18},{17,0,17},{17,1,18},{17,2,16},{17,3,15},{18,0,18},{18,1,17},{18,2,19},{18,3,20},{18,4,21},{19,0,19},{19,1,20},{19,2,18},{19,3,17},{20,0,20},{20,1,19},{20,2,21},{20,3,22},{20,4,23},{21,0,21},{21,1,22},{21,2,20},{21,3,19},{22,0,22},{22,1,21},{22,2,23},{22,3,24},{22,4,20},{23,0,23},{23,1,24},{23,2,22},{23,3,21},{23,4,25},{23,5,26},{24,0,24},{24,1,23},{24,2,25},{24,3,26},{24,4,22},{25,0,25},{25,1,26},{25,2,24},{25,3,23},{25,4,27},{25,5,28},{26,0,26},{26,1,25},{26,2,27},{26,3,28},{26,4,24},{27,0,27},{27,1,28},{27,2,26},{27,3,25},{27,4,29},{27,5,30},{27,6,31},{28,0,28},{28,1,27},{28,2,29},{28,3,30},{28,4,26},{28,5,25},{29,0,29},{29,1,30},{29,2,28},{29,3,27},{29,4,31},{29,5,32},{29,6,33},{30,0,30},{30,1,29},{30,2,31},{30,3,32},{30,4,28},{30,5,27},{31,0,31},{31,1,32},{31,2,30},{31,3,29},{31,4,33},{31,5,34},{31,6,35},{31,7,36},{32,0,32},{32,1,31},{32,2,33},{32,3,34},{32,4,30},{32,5,29},{33,0,33},{33,1,34},{33,2,32},{33,3,31},{33,4,35},{33,5,36},{33,6,30},{34,0,34},{34,1,33},{34,2,35},{34,3,36},{34,4,32},{34,5,31},{34,6,37},{34,7,38},{35,0,35},{35,1,36},{35,2,34},{35,3,33},{35,4,37},{35,5,38},{35,6,32},{36,0,36},{36,1,35},{36,2,37},{36,3,38},{36,4,34},{36,5,33},{36,6,39},{36,7,40},{36,8,41},{37,0,37},{37,1,38},{37,2,36},{37,3,35},{37,4,39},{37,5,40},{37,6,34},{38,0,38},{38,1,37},{38,2,39},{38,3,40},{38,4,36},{38,5,35},{38,6,41},{38,7,42},{38,8,43},{39,0,39},{39,1,40},{39,2,38},{39,3,37},{39,4,41},{39,5,42},{39,6,36},{39,7,35},{40,0,40},{40,1,39},{40,2,41},{40,3,42},{40,4,38},{40,5,37},{40,6,43},{40,7,44},{40,8,45},{40,9,46},{41,0,41},{41,1,42},{41,2,40},{41,3,39},{41,4,43},{41,5,44},{41,6,38},{41,7,37},{42,0,42},{42,1,41},{42,2,43},{42,3,44},{42,4,40},{42,5,39},{42,6,45},{42,7,46},{42,8,47},{42,9,48},{43,0,43},{43,1,44},{43,2,42},{43,3,41},{43,4,45},{43,5,46},{43,6,40},{43,7,39},{44,0,44},{44,1,43},{44,2,45},{44,3,46},{44,4,42},{44,5,41},{44,6,47},{44,7,48},{44,8,40},{45,0,45},{45,1,46},{45,2,44},{45,3,43},{45,4,47},{45,5,48},{45,6,42},{45,7,41},{45,8,49},{45,9,50},{45,10,51},{46,0,46},{46,1,45},{46,2,47},{46,3,48},{46,4,44},{46,5,43},{46,6,49},{46,7,50},{46,8,42},{47,0,47},{47,1,48},{47,2,46},{47,3,45},{47,4,49},{47,5,50},{47,6,44},{47,7,43},{47,8,51},{47,9,52},{47,10,53},{48,0,48},{48,1,47},{48,2,49},{48,3,50},{48,4,46},{48,5,45},{48,6,51},{48,7,52},{48,8,44},{49,0,49},{49,1,50},{49,2,48},{49,3,47},{49,4,51},{49,5,52},{49,6,46},{49,7,45},{49,8,53},{49,9,54},{49,10,55},{49,11,56},{50,0,50},{50,1,49},{50,2,51},{50,3,52},{50,4,48},{50,5,47},{50,6,53},{50,7,54},{50,8,46},{50,9,45},{51,0,51},{51,1,52},{51,2,50},{51,3,49},{51,4,53},{51,5,54},{51,6,48},{51,7,47},{51,8,55},{51,9,56},{51,10,57},{51,11,58},{52,0,52},{52,1,51},{52,2,53},{52,3,54},{52,4,50},{52,5,49},{52,6,55},{52,7,56},{52,8,48},{52,9,47},{53,0,53},{53,1,54},{53,2,52},{53,3,51},{53,4,55},{53,5,56},{53,6,50},{53,7,49},{53,8,57},{53,9,58},{53,10,59},{53,11,60},{53,12,61},{54,0,54},{54,1,53},{54,2,55},{54,3,56},{54,4,52},{54,5,51},{54,6,57},{54,7,58},{54,8,50},{54,9,49},{55,0,55},{55,1,56},{55,2,54},{55,3,53},{55,4,57},{55,5,58},{55,6,52},{55,7,51},{55,8,59},{55,9,60},{55,10,50},{56,0,56},{56,1,55},{56,2,57},{56,3,58},{56,4,54},{56,5,53},{56,6,59},{56,7,60},{56,8,52},{56,9,51},{56,10,61},{56,11,62},{56,12,63},{57,0,57},{57,1,58},{57,2,56},{57,3,55},{57,4,59},{57,5,60},{57,6,54},{57,7,53},{57,8,61},{57,9,62},{57,10,52},{58,0,58},{58,1,57},{58,2,59},{58,3,60},{58,4,56},{58,5,55},{58,6,61},{58,7,62},{58,8,54},{58,9,53},{58,10,63},{58,11,64},{58,12,65},{58,13,66},{59,0,59},{59,1,60},{59,2,58},{59,3,57},{59,4,61},{59,5,62},{59,6,56},{59,7,55},{59,8,63},{59,9,64},{59,10,54},{60,0,60},{60,1,59},{60,2,61},{60,3,62},{60,4,58},{60,5,57},{60,6,63},{60,7,64},{60,8,56},{60,9,55},{60,10,65},{60,11,66},{60,12,67},{60,13,68},{61,0,61},{61,1,62},{61,2,60},{61,3,59},{61,4,63},{61,5,64},{61,6,58},{61,7,57},{61,8,65},{61,9,66},{61,10,56},{61,11,55},{62,0,62},{62,1,61},{62,2,63},{62,3,64},{62,4,60},{62,5,59},{62,6,65},{62,7,66},{62,8,58},{62,9,57},{62,10,67},{62,11,68},{62,12,69},{62,13,70},{62,14,71},{63,0,63},{63,1,64},{63,2,62},{63,3,61},{63,4,65},{63,5,66},{63,6,60},{63,7,59},{63,8,67},{63,9,68},{63,10,58},{63,11,57},{64,0,64},{64,1,63},{64,2,65},{64,3,66},{64,4,62},{64,5,61},{64,6,67},{64,7,68},{64,8,60},{64,9,59},{64,10,69},{64,11,70},{64,12,71},{64,13,72},{64,14,73},{65,0,65},{65,1,66},{65,2,64},{65,3,63},{65,4,67},{65,5,68},{65,6,62},{65,7,61},{65,8,69},{65,9,70},{65,10,60},{65,11,59},{66,0,66},{66,1,65},{66,2,67},{66,3,68},{66,4,64},{66,5,63},{66,6,69},{66,7,70},{66,8,62},{66,9,61},{66,10,71},{66,11,72},{66,12,60},{67,0,67},{67,1,68},{67,2,66},{67,3,65},{67,4,69},{67,5,70},{67,6,64},{67,7,63},{67,8,71},{67,9,72},{67,10,62},{67,11,61},{67,12,73},{67,13,74},{67,14,75},{67,15,76},{68,0,68},{68,1,67},{68,2,69},{68,3,70},{68,4,66},{68,5,65},{68,6,71},{68,7,72},{68,8,64},{68,9,63},{68,10,73},{68,11,74},{68,12,62},{69,0,69},{69,1,70},{69,2,68},{69,3,67},{69,4,71},{69,5,72},{69,6,66},{69,7,65},{69,8,73},{69,9,74},{69,10,64},{69,11,63},{69,12,75},{69,13,76},{69,14,77},{69,15,78},{70,0,70},{70,1,69},{70,2,71},{70,3,72},{70,4,68},{70,5,67},{70,6,73},{70,7,74},{70,8,66},{70,9,65},{70,10,75},{70,11,76},{70,12,64},{71,0,71},{71,1,72},{71,2,70},{71,3,69},{71,4,73},{71,5,74},{71,6,68},{71,7,67},{71,8,75},{71,9,76},{71,10,66},{71,11,65},{71,12,77},{71,13,78},{71,14,79},{71,15,80},{71,16,81},{72,0,72},{72,1,71},{72,2,73},{72,3,74},{72,4,70},{72,5,69},{72,6,75},{72,7,76},{72,8,68},{72,9,67},{72,10,77},{72,11,78},{72,12,66},{72,13,65},{73,0,73},{73,1,74},{73,2,72},{73,3,71},{73,4,75},{73,5,76},{73,6,70},{73,7,69},{73,8,77},{73,9,78},{73,10,68},{73,11,67},{73,12,79},{73,13,80},{73,14,81},{73,15,82},{73,16,83},{74,0,74},{74,1,73},{74,2,75},{74,3,76},{74,4,72},{74,5,71},{74,6,77},{74,7,78},{74,8,70},{74,9,69},{74,10,79},{74,11,80},{74,12,68},{74,13,67},{75,0,75},{75,1,76},{75,2,74},{75,3,73},{75,4,77},{75,5,78},{75,6,72},{75,7,71},{75,8,79},{75,9,80},{75,10,70},{75,11,69},{75,12,81},{75,13,82},{75,14,83},{75,15,84},{75,16,85},{75,17,86}}};
)]

2D and 3D Graphs of the Set of Losing States of the Triangular Chocolate Game with y≤(x+z)/k

Figure  shows that the graph is the Sierpinski gasket for odd k, so it seems that there may be a simple formula for the set of losing states in that case.

When k=1, by Proposition 3 there is a simple formula for the set of losing states. When k=3, the state {x,y,z} is a losing state of this chocolate game if and only if x⊕y⊕z=0 []. The authors are now trying to find a simple formula for the set of losing states for an arbitrary odd number k.

When k is even, the graph is very different from the Sierpinski gasket. Since the graph is quite complicated, it seems that there is no simple formula for the set of losing states.

Manipulate[
If[ns=="2D",
ListPlot[Map[{#[[2]],#[[1]]-#[[3]]}&,Select[dataxyz10[[k]],#[[1]]≤s&&#[[2]]≤s&&#[[3]]≤s&]],Background->Black,PlotStyle->Yellow,ImageSize->1.6{350,200}],
ListPointPlot3D[Map[{#[[1]],#[[2]],#[[3]]}&,Select[dataxyz10[[k]],#[[1]]≤s&&#[[2]]≤s&&#[[3]]≤s&]],Axes->False,Background->Black,ColorFunction->"Rainbow",PlotStyle->PointSize[0.01],ImageSize->1.6{350,200}]],
Row[{
Control@{{ns,"2D",""},{"2D","3D"},ControlType->Setter},
Spacer[30],
Control@{{k,1},1,5,1,Setter},
Spacer[30],
Control@{{s,50},1,75,1,ImageSize->Small,Appearance->"Labeled"}
}],
Initialization:>(
dataxyz10={{{0,0,0},{1,0,1},{1,1,2},{1,2,3},{1,3,4},{1,4,5},{1,5,6},{1,6,7},{1,7,8},{1,8,9},{1,9,10},{1,10,11},{1,11,12},{1,12,13},{1,13,14},{1,14,15},{1,15,16},{1,16,17},{1,17,18},{1,18,19},{1,19,20},{1,20,21},{1,21,22},{1,22,23},{1,23,24},{1,24,25},{1,25,26},{1,26,27},{1,27,28},{1,28,29},{1,29,30},{1,30,31},{1,31,32},{1,32,33},{1,33,34},{1,34,35},{1,35,36},{1,36,37},{1,37,38},{1,38,39},{1,39,40},{1,40,41},{1,41,42},{1,42,43},{1,43,44},{1,44,45},{1,45,46},{1,46,47},{1,47,48},{1,48,49},{1,49,50},{1,50,51},{1,51,52},{1,52,53},{1,53,54},{1,54,55},{1,55,56},{1,56,57},{1,57,58},{1,58,59},{1,59,60},{1,60,61},{1,61,62},{1,62,63},{1,63,64},{1,64,65},{1,65,66},{1,66,67},{1,67,68},{1,68,69},{1,69,70},{1,70,71},{1,71,72},{1,72,73},{1,73,74},{1,74,75},{1,75,76},{2,0,2},{2,1,1},{2,2,4},{2,3,3},{2,4,6},{2,5,5},{2,6,8},{2,7,7},{2,8,10},{2,9,9},{2,10,12},{2,11,11},{2,12,14},{2,13,13},{2,14,16},{2,15,15},{2,16,18},{2,17,17},{2,18,20},{2,19,19},{2,20,22},{2,21,21},{2,22,24},{2,23,23},{2,24,26},{2,25,25},{2,26,28},{2,27,27},{2,28,30},{2,29,29},{2,30,32},{2,31,31},{2,32,34},{2,33,33},{2,34,36},{2,35,35},{2,36,38},{2,37,37},{2,38,40},{2,39,39},{2,40,42},{2,41,41},{2,42,44},{2,43,43},{2,44,46},{2,45,45},{2,46,48},{2,47,47},{2,48,50},{2,49,49},{2,50,52},{2,51,51},{2,52,54},{2,53,53},{2,54,56},{2,55,55},{2,56,58},{2,57,57},{2,58,60},{2,59,59},{2,60,62},{2,61,61},{2,62,64},{2,63,63},{2,64,66},{2,65,65},{2,66,68},{2,67,67},{2,68,70},{2,69,69},{2,70,72},{2,71,71},{2,72,74},{2,73,73},{2,74,76},{2,75,75},{3,0,3},{3,1,4},{3,2,1},{3,3,2},{3,4,7},{3,5,8},{3,6,5},{3,7,6},{3,8,11},{3,9,12},{3,10,9},{3,11,10},{3,12,15},{3,13,16},{3,14,13},{3,15,14},{3,16,19},{3,17,20},{3,18,17},{3,19,18},{3,20,23},{3,21,24},{3,22,21},{3,23,22},{3,24,27},{3,25,28},{3,26,25},{3,27,26},{3,28,31},{3,29,32},{3,30,29},{3,31,30},{3,32,35},{3,33,36},{3,34,33},{3,35,34},{3,36,39},{3,37,40},{3,38,37},{3,39,38},{3,40,43},{3,41,44},{3,42,41},{3,43,42},{3,44,47},{3,45,48},{3,46,45},{3,47,46},{3,48,51},{3,49,52},{3,50,49},{3,51,50},{3,52,55},{3,53,56},{3,54,53},{3,55,54},{3,56,59},{3,57,60},{3,58,57},{3,59,58},{3,60,63},{3,61,64},{3,62,61},{3,63,62},{3,64,67},{3,65,68},{3,66,65},{3,67,66},{3,68,71},{3,69,72},{3,70,69},{3,71,70},{3,72,75},{3,73,76},{3,74,73},{3,75,74},{4,0,4},{4,1,3},{4,2,2},{4,3,1},{4,4,8},{4,5,7},{4,6,6},{4,7,5},{4,8,12},{4,9,11},{4,10,10},{4,11,9},{4,12,16},{4,13,15},{4,14,14},{4,15,13},{4,16,20},{4,17,19},{4,18,18},{4,19,17},{4,20,24},{4,21,23},{4,22,22},{4,23,21},{4,24,28},{4,25,27},{4,26,26},{4,27,25},{4,28,32},{4,29,31},{4,30,30},{4,31,29},{4,32,36},{4,33,35},{4,34,34},{4,35,33},{4,36,40},{4,37,39},{4,38,38},{4,39,37},{4,40,44},{4,41,43},{4,42,42},{4,43,41},{4,44,48},{4,45,47},{4,46,46},{4,47,45},{4,48,52},{4,49,51},{4,50,50},{4,51,49},{4,52,56},{4,53,55},{4,54,54},{4,55,53},{4,56,60},{4,57,59},{4,58,58},{4,59,57},{4,60,64},{4,61,63},{4,62,62},{4,63,61},{4,64,68},{4,65,67},{4,66,66},{4,67,65},{4,68,72},{4,69,71},{4,70,70},{4,71,69},{4,72,76},{4,73,75},{4,74,74},{4,75,73},{5,0,5},{5,1,6},{5,2,7},{5,3,8},{5,4,1},{5,5,2},{5,6,3},{5,7,4},{5,8,13},{5,9,14},{5,10,15},{5,11,16},{5,12,9},{5,13,10},{5,14,11},{5,15,12},{5,16,21},{5,17,22},{5,18,23},{5,19,24},{5,20,17},{5,21,18},{5,22,19},{5,23,20},{5,24,29},{5,25,30},{5,26,31},{5,27,32},{5,28,25},{5,29,26},{5,30,27},{5,31,28},{5,32,37},{5,33,38},{5,34,39},{5,35,40},{5,36,33},{5,37,34},{5,38,35},{5,39,36},{5,40,45},{5,41,46},{5,42,47},{5,43,48},{5,44,41},{5,45,42},{5,46,43},{5,47,44},{5,48,53},{5,49,54},{5,50,55},{5,51,56},{5,52,49},{5,53,50},{5,54,51},{5,55,52},{5,56,61},{5,57,62},{5,58,63},{5,59,64},{5,60,57},{5,61,58},{5,62,59},{5,63,60},{5,64,69},{5,65,70},{5,66,71},{5,67,72},{5,68,65},{5,69,66},{5,70,67},{5,71,68},{5,72,77},{5,73,78},{5,74,79},{5,75,80},{6,0,6},{6,1,5},{6,2,8},{6,3,7},{6,4,2},{6,5,1},{6,6,4},{6,7,3},{6,8,14},{6,9,13},{6,10,16},{6,11,15},{6,12,10},{6,13,9},{6,14,12},{6,15,11},{6,16,22},{6,17,21},{6,18,24},{6,19,23},{6,20,18},{6,21,17},{6,22,20},{6,23,19},{6,24,30},{6,25,29},{6,26,32},{6,27,31},{6,28,26},{6,29,25},{6,30,28},{6,31,27},{6,32,38},{6,33,37},{6,34,40},{6,35,39},{6,36,34},{6,37,33},{6,38,36},{6,39,35},{6,40,46},{6,41,45},{6,42,48},{6,43,47},{6,44,42},{6,45,41},{6,46,44},{6,47,43},{6,48,54},{6,49,53},{6,50,56},{6,51,55},{6,52,50},{6,53,49},{6,54,52},{6,55,51},{6,56,62},{6,57,61},{6,58,64},{6,59,63},{6,60,58},{6,61,57},{6,62,60},{6,63,59},{6,64,70},{6,65,69},{6,66,72},{6,67,71},{6,68,66},{6,69,65},{6,70,68},{6,71,67},{6,72,78},{6,73,77},{6,74,80},{6,75,79},{7,0,7},{7,1,8},{7,2,5},{7,3,6},{7,4,3},{7,5,4},{7,6,1},{7,7,2},{7,8,15},{7,9,16},{7,10,13},{7,11,14},{7,12,11},{7,13,12},{7,14,9},{7,15,10},{7,16,23},{7,17,24},{7,18,21},{7,19,22},{7,20,19},{7,21,20},{7,22,17},{7,23,18},{7,24,31},{7,25,32},{7,26,29},{7,27,30},{7,28,27},{7,29,28},{7,30,25},{7,31,26},{7,32,39},{7,33,40},{7,34,37},{7,35,38},{7,36,35},{7,37,36},{7,38,33},{7,39,34},{7,40,47},{7,41,48},{7,42,45},{7,43,46},{7,44,43},{7,45,44},{7,46,41},{7,47,42},{7,48,55},{7,49,56},{7,50,53},{7,51,54},{7,52,51},{7,53,52},{7,54,49},{7,55,50},{7,56,63},{7,57,64},{7,58,61},{7,59,62},{7,60,59},{7,61,60},{7,62,57},{7,63,58},{7,64,71},{7,65,72},{7,66,69},{7,67,70},{7,68,67},{7,69,68},{7,70,65},{7,71,66},{7,72,79},{7,73,80},{7,74,77},{7,75,78},{8,0,8},{8,1,7},{8,2,6},{8,3,5},{8,4,4},{8,5,3},{8,6,2},{8,7,1},{8,8,16},{8,9,15},{8,10,14},{8,11,13},{8,12,12},{8,13,11},{8,14,10},{8,15,9},{8,16,24},{8,17,23},{8,18,22},{8,19,21},{8,20,20},{8,21,19},{8,22,18},{8,23,17},{8,24,32},{8,25,31},{8,26,30},{8,27,29},{8,28,28},{8,29,27},{8,30,26},{8,31,25},{8,32,40},{8,33,39},{8,34,38},{8,35,37},{8,36,36},{8,37,35},{8,38,34},{8,39,33},{8,40,48},{8,41,47},{8,42,46},{8,43,45},{8,44,44},{8,45,43},{8,46,42},{8,47,41},{8,48,56},{8,49,55},{8,50,54},{8,51,53},{8,52,52},{8,53,51},{8,54,50},{8,55,49},{8,56,64},{8,57,63},{8,58,62},{8,59,61},{8,60,60},{8,61,59},{8,62,58},{8,63,57},{8,64,72},{8,65,71},{8,66,70},{8,67,69},{8,68,68},{8,69,67},{8,70,66},{8,71,65},{8,72,80},{8,73,79},{8,74,78},{8,75,77},{9,0,9},{9,1,10},{9,2,11},{9,3,12},{9,4,13},{9,5,14},{9,6,15},{9,7,16},{9,8,1},{9,9,2},{9,10,3},{9,11,4},{9,12,5},{9,13,6},{9,14,7},{9,15,8},{9,16,25},{9,17,26},{9,18,27},{9,19,28},{9,20,29},{9,21,30},{9,22,31},{9,23,32},{9,24,17},{9,25,18},{9,26,19},{9,27,20},{9,28,21},{9,29,22},{9,30,23},{9,31,24},{9,32,41},{9,33,42},{9,34,43},{9,35,44},{9,36,45},{9,37,46},{9,38,47},{9,39,48},{9,40,33},{9,41,34},{9,42,35},{9,43,36},{9,44,37},{9,45,38},{9,46,39},{9,47,40},{9,48,57},{9,49,58},{9,50,59},{9,51,60},{9,52,61},{9,53,62},{9,54,63},{9,55,64},{9,56,49},{9,57,50},{9,58,51},{9,59,52},{9,60,53},{9,61,54},{9,62,55},{9,63,56},{9,64,73},{9,65,74},{9,66,75},{9,67,76},{9,68,77},{9,69,78},{9,70,79},{9,71,80},{9,72,65},{9,73,66},{9,74,67},{9,75,68},{10,0,10},{10,1,9},{10,2,12},{10,3,11},{10,4,14},{10,5,13},{10,6,16},{10,7,15},{10,8,2},{10,9,1},{10,10,4},{10,11,3},{10,12,6},{10,13,5},{10,14,8},{10,15,7},{10,16,26},{10,17,25},{10,18,28},{10,19,27},{10,20,30},{10,21,29},{10,22,32},{10,23,31},{10,24,18},{10,25,17},{10,26,20},{10,27,19},{10,28,22},{10,29,21},{10,30,24},{10,31,23},{10,32,42},{10,33,41},{10,34,44},{10,35,43},{10,36,46},{10,37,45},{10,38,48},{10,39,47},{10,40,34},{10,41,33},{10,42,36},{10,43,35},{10,44,38},{10,45,37},{10,46,40},{10,47,39},{10,48,58},{10,49,57},{10,50,60},{10,51,59},{10,52,62},{10,53,61},{10,54,64},{10,55,63},{10,56,50},{10,57,49},{10,58,52},{10,59,51},{10,60,54},{10,61,53},{10,62,56},{10,63,55},{10,64,74},{10,65,73},{10,66,76},{10,67,75},{10,68,78},{10,69,77},{10,70,80},{10,71,79},{10,72,66},{10,73,65},{10,74,68},{10,75,67},{11,0,11},{11,1,12},{11,2,9},{11,3,10},{11,4,15},{11,5,16},{11,6,13},{11,7,14},{11,8,3},{11,9,4},{11,10,1},{11,11,2},{11,12,7},{11,13,8},{11,14,5},{11,15,6},{11,16,27},{11,17,28},{11,18,25},{11,19,26},{11,20,31},{11,21,32},{11,22,29},{11,23,30},{11,24,19},{11,25,20},{11,26,17},{11,27,18},{11,28,23},{11,29,24},{11,30,21},{11,31,22},{11,32,43},{11,33,44},{11,34,41},{11,35,42},{11,36,47},{11,37,48},{11,38,45},{11,39,46},{11,40,35},{11,41,36},{11,42,33},{11,43,34},{11,44,39},{11,45,40},{11,46,37},{11,47,38},{11,48,59},{11,49,60},{11,50,57},{11,51,58},{11,52,63},{11,53,64},{11,54,61},{11,55,62},{11,56,51},{11,57,52},{11,58,49},{11,59,50},{11,60,55},{11,61,56},{11,62,53},{11,63,54},{11,64,75},{11,65,76},{11,66,73},{11,67,74},{11,68,79},{11,69,80},{11,70,77},{11,71,78},{11,72,67},{11,73,68},{11,74,65},{11,75,66},{12,0,12},{12,1,11},{12,2,10},{12,3,9},{12,4,16},{12,5,15},{12,6,14},{12,7,13},{12,8,4},{12,9,3},{12,10,2},{12,11,1},{12,12,8},{12,13,7},{12,14,6},{12,15,5},{12,16,28},{12,17,27},{12,18,26},{12,19,25},{12,20,32},{12,21,31},{12,22,30},{12,23,29},{12,24,20},{12,25,19},{12,26,18},{12,27,17},{12,28,24},{12,29,23},{12,30,22},{12,31,21},{12,32,44},{12,33,43},{12,34,42},{12,35,41},{12,36,48},{12,37,47},{12,38,46},{12,39,45},{12,40,36},{12,41,35},{12,42,34},{12,43,33},{12,44,40},{12,45,39},{12,46,38},{12,47,37},{12,48,60},{12,49,59},{12,50,58},{12,51,57},{12,52,64},{12,53,63},{12,54,62},{12,55,61},{12,56,52},{12,57,51},{12,58,50},{12,59,49},{12,60,56},{12,61,55},{12,62,54},{12,63,53},{12,64,76},{12,65,75},{12,66,74},{12,67,73},{12,68,80},{12,69,79},{12,70,78},{12,71,77},{12,72,68},{12,73,67},{12,74,66},{12,75,65},{13,0,13},{13,1,14},{13,2,15},{13,3,16},{13,4,9},{13,5,10},{13,6,11},{13,7,12},{13,8,5},{13,9,6},{13,10,7},{13,11,8},{13,12,1},{13,13,2},{13,14,3},{13,15,4},{13,16,29},{13,17,30},{13,18,31},{13,19,32},{13,20,25},{13,21,26},{13,22,27},{13,23,28},{13,24,21},{13,25,22},{13,26,23},{13,27,24},{13,28,17},{13,29,18},{13,30,19},{13,31,20},{13,32,45},{13,33,46},{13,34,47},{13,35,48},{13,36,41},{13,37,42},{13,38,43},{13,39,44},{13,40,37},{13,41,38},{13,42,39},{13,43,40},{13,44,33},{13,45,34},{13,46,35},{13,47,36},{13,48,61},{13,49,62},{13,50,63},{13,51,64},{13,52,57},{13,53,58},{13,54,59},{13,55,60},{13,56,53},{13,57,54},{13,58,55},{13,59,56},{13,60,49},{13,61,50},{13,62,51},{13,63,52},{13,64,77},{13,65,78},{13,66,79},{13,67,80},{13,68,73},{13,69,74},{13,70,75},{13,71,76},{13,72,69},{13,73,70},{13,74,71},{13,75,72},{14,0,14},{14,1,13},{14,2,16},{14,3,15},{14,4,10},{14,5,9},{14,6,12},{14,7,11},{14,8,6},{14,9,5},{14,10,8},{14,11,7},{14,12,2},{14,13,1},{14,14,4},{14,15,3},{14,16,30},{14,17,29},{14,18,32},{14,19,31},{14,20,26},{14,21,25},{14,22,28},{14,23,27},{14,24,22},{14,25,21},{14,26,24},{14,27,23},{14,28,18},{14,29,17},{14,30,20},{14,31,19},{14,32,46},{14,33,45},{14,34,48},{14,35,47},{14,36,42},{14,37,41},{14,38,44},{14,39,43},{14,40,38},{14,41,37},{14,42,40},{14,43,39},{14,44,34},{14,45,33},{14,46,36},{14,47,35},{14,48,62},{14,49,61},{14,50,64},{14,51,63},{14,52,58},{14,53,57},{14,54,60},{14,55,59},{14,56,54},{14,57,53},{14,58,56},{14,59,55},{14,60,50},{14,61,49},{14,62,52},{14,63,51},{14,64,78},{14,65,77},{14,66,80},{14,67,79},{14,68,74},{14,69,73},{14,70,76},{14,71,75},{14,72,70},{14,73,69},{14,74,72},{14,75,71},{15,0,15},{15,1,16},{15,2,13},{15,3,14},{15,4,11},{15,5,12},{15,6,9},{15,7,10},{15,8,7},{15,9,8},{15,10,5},{15,11,6},{15,12,3},{15,13,4},{15,14,1},{15,15,2},{15,16,31},{15,17,32},{15,18,29},{15,19,30},{15,20,27},{15,21,28},{15,22,25},{15,23,26},{15,24,23},{15,25,24},{15,26,21},{15,27,22},{15,28,19},{15,29,20},{15,30,17},{15,31,18},{15,32,47},{15,33,48},{15,34,45},{15,35,46},{15,36,43},{15,37,44},{15,38,41},{15,39,42},{15,40,39},{15,41,40},{15,42,37},{15,43,38},{15,44,35},{15,45,36},{15,46,33},{15,47,34},{15,48,63},{15,49,64},{15,50,61},{15,51,62},{15,52,59},{15,53,60},{15,54,57},{15,55,58},{15,56,55},{15,57,56},{15,58,53},{15,59,54},{15,60,51},{15,61,52},{15,62,49},{15,63,50},{15,64,79},{15,65,80},{15,66,77},{15,67,78},{15,68,75},{15,69,76},{15,70,73},{15,71,74},{15,72,71},{15,73,72},{15,74,69},{15,75,70},{16,0,16},{16,1,15},{16,2,14},{16,3,13},{16,4,12},{16,5,11},{16,6,10},{16,7,9},{16,8,8},{16,9,7},{16,10,6},{16,11,5},{16,12,4},{16,13,3},{16,14,2},{16,15,1},{16,16,32},{16,17,31},{16,18,30},{16,19,29},{16,20,28},{16,21,27},{16,22,26},{16,23,25},{16,24,24},{16,25,23},{16,26,22},{16,27,21},{16,28,20},{16,29,19},{16,30,18},{16,31,17},{16,32,48},{16,33,47},{16,34,46},{16,35,45},{16,36,44},{16,37,43},{16,38,42},{16,39,41},{16,40,40},{16,41,39},{16,42,38},{16,43,37},{16,44,36},{16,45,35},{16,46,34},{16,47,33},{16,48,64},{16,49,63},{16,50,62},{16,51,61},{16,52,60},{16,53,59},{16,54,58},{16,55,57},{16,56,56},{16,57,55},{16,58,54},{16,59,53},{16,60,52},{16,61,51},{16,62,50},{16,63,49},{16,64,80},{16,65,79},{16,66,78},{16,67,77},{16,68,76},{16,69,75},{16,70,74},{16,71,73},{16,72,72},{16,73,71},{16,74,70},{16,75,69},{17,0,17},{17,1,18},{17,2,19},{17,3,20},{17,4,21},{17,5,22},{17,6,23},{17,7,24},{17,8,25},{17,9,26},{17,10,27},{17,11,28},{17,12,29},{17,13,30},{17,14,31},{17,15,32},{17,16,1},{17,17,2},{17,18,3},{17,19,4},{17,20,5},{17,21,6},{17,22,7},{17,23,8},{17,24,9},{17,25,10},{17,26,11},{17,27,12},{17,28,13},{17,29,14},{17,30,15},{17,31,16},{17,32,49},{17,33,50},{17,34,51},{17,35,52},{17,36,53},{17,37,54},{17,38,55},{17,39,56},{17,40,57},{17,41,58},{17,42,59},{17,43,60},{17,44,61},{17,45,62},{17,46,63},{17,47,64},{17,48,33},{17,49,34},{17,50,35},{17,51,36},{17,52,37},{17,53,38},{17,54,39},{17,55,40},{17,56,41},{17,57,42},{17,58,43},{17,59,44},{17,60,45},{17,61,46},{17,62,47},{17,63,48},{17,64,81},{17,65,82},{17,66,83},{17,67,84},{17,68,85},{17,69,86},{17,70,87},{17,71,88},{17,72,89},{17,73,90},{17,74,91},{17,75,92},{18,0,18},{18,1,17},{18,2,20},{18,3,19},{18,4,22},{18,5,21},{18,6,24},{18,7,23},{18,8,26},{18,9,25},{18,10,28},{18,11,27},{18,12,30},{18,13,29},{18,14,32},{18,15,31},{18,16,2},{18,17,1},{18,18,4},{18,19,3},{18,20,6},{18,21,5},{18,22,8},{18,23,7},{18,24,10},{18,25,9},{18,26,12},{18,27,11},{18,28,14},{18,29,13},{18,30,16},{18,31,15},{18,32,50},{18,33,49},{18,34,52},{18,35,51},{18,36,54},{18,37,53},{18,38,56},{18,39,55},{18,40,58},{18,41,57},{18,42,60},{18,43,59},{18,44,62},{18,45,61},{18,46,64},{18,47,63},{18,48,34},{18,49,33},{18,50,36},{18,51,35},{18,52,38},{18,53,37},{18,54,40},{18,55,39},{18,56,42},{18,57,41},{18,58,44},{18,59,43},{18,60,46},{18,61,45},{18,62,48},{18,63,47},{18,64,82},{18,65,81},{18,66,84},{18,67,83},{18,68,86},{18,69,85},{18,70,88},{18,71,87},{18,72,90},{18,73,89},{18,74,92},{18,75,91},{19,0,19},{19,1,20},{19,2,17},{19,3,18},{19,4,23},{19,5,24},{19,6,21},{19,7,22},{19,8,27},{19,9,28},{19,10,25},{19,11,26},{19,12,31},{19,13,32},{19,14,29},{19,15,30},{19,16,3},{19,17,4},{19,18,1},{19,19,2},{19,20,7},{19,21,8},{19,22,5},{19,23,6},{19,24,11},{19,25,12},{19,26,9},{19,27,10},{19,28,15},{19,29,16},{19,30,13},{19,31,14},{19,32,51},{19,33,52},{19,34,49},{19,35,50},{19,36,55},{19,37,56},{19,38,53},{19,39,54},{19,40,59},{19,41,60},{19,42,57},{19,43,58},{19,44,63},{19,45,64},{19,46,61},{19,47,62},{19,48,35},{19,49,36},{19,50,33},{19,51,34},{19,52,39},{19,53,40},{19,54,37},{19,55,38},{19,56,43},{19,57,44},{19,58,41},{19,59,42},{19,60,47},{19,61,48},{19,62,45},{19,63,46},{19,64,83},{19,65,84},{19,66,81},{19,67,82},{19,68,87},{19,69,88},{19,70,85},{19,71,86},{19,72,91},{19,73,92},{19,74,89},{19,75,90},{20,0,20},{20,1,19},{20,2,18},{20,3,17},{20,4,24},{20,5,23},{20,6,22},{20,7,21},{20,8,28},{20,9,27},{20,10,26},{20,11,25},{20,12,32},{20,13,31},{20,14,30},{20,15,29},{20,16,4},{20,17,3},{20,18,2},{20,19,1},{20,20,8},{20,21,7},{20,22,6},{20,23,5},{20,24,12},{20,25,11},{20,26,10},{20,27,9},{20,28,16},{20,29,15},{20,30,14},{20,31,13},{20,32,52},{20,33,51},{20,34,50},{20,35,49},{20,36,56},{20,37,55},{20,38,54},{20,39,53},{20,40,60},{20,41,59},{20,42,58},{20,43,57},{20,44,64},{20,45,63},{20,46,62},{20,47,61},{20,48,36},{20,49,35},{20,50,34},{20,51,33},{20,52,40},{20,53,39},{20,54,38},{20,55,37},{20,56,44},{20,57,43},{20,58,42},{20,59,41},{20,60,48},{20,61,47},{20,62,46},{20,63,45},{20,64,84},{20,65,83},{20,66,82},{20,67,81},{20,68,88},{20,69,87},{20,70,86},{20,71,85},{20,72,92},{20,73,91},{20,74,90},{20,75,89},{21,0,21},{21,1,22},{21,2,23},{21,3,24},{21,4,17},{21,5,18},{21,6,19},{21,7,20},{21,8,29},{21,9,30},{21,10,31},{21,11,32},{21,12,25},{21,13,26},{21,14,27},{21,15,28},{21,16,5},{21,17,6},{21,18,7},{21,19,8},{21,20,1},{21,21,2},{21,22,3},{21,23,4},{21,24,13},{21,25,14},{21,26,15},{21,27,16},{21,28,9},{21,29,10},{21,30,11},{21,31,12},{21,32,53},{21,33,54},{21,34,55},{21,35,56},{21,36,49},{21,37,50},{21,38,51},{21,39,52},{21,40,61},{21,41,62},{21,42,63},{21,43,64},{21,44,57},{21,45,58},{21,46,59},{21,47,60},{21,48,37},{21,49,38},{21,50,39},{21,51,40},{21,52,33},{21,53,34},{21,54,35},{21,55,36},{21,56,45},{21,57,46},{21,58,47},{21,59,48},{21,60,41},{21,61,42},{21,62,43},{21,63,44},{21,64,85},{21,65,86},{21,66,87},{21,67,88},{21,68,81},{21,69,82},{21,70,83},{21,71,84},{21,72,93},{21,73,94},{21,74,95},{21,75,96},{22,0,22},{22,1,21},{22,2,24},{22,3,23},{22,4,18},{22,5,17},{22,6,20},{22,7,19},{22,8,30},{22,9,29},{22,10,32},{22,11,31},{22,12,26},{22,13,25},{22,14,28},{22,15,27},{22,16,6},{22,17,5},{22,18,8},{22,19,7},{22,20,2},{22,21,1},{22,22,4},{22,23,3},{22,24,14},{22,25,13},{22,26,16},{22,27,15},{22,28,10},{22,29,9},{22,30,12},{22,31,11},{22,32,54},{22,33,53},{22,34,56},{22,35,55},{22,36,50},{22,37,49},{22,38,52},{22,39,51},{22,40,62},{22,41,61},{22,42,64},{22,43,63},{22,44,58},{22,45,57},{22,46,60},{22,47,59},{22,48,38},{22,49,37},{22,50,40},{22,51,39},{22,52,34},{22,53,33},{22,54,36},{22,55,35},{22,56,46},{22,57,45},{22,58,48},{22,59,47},{22,60,42},{22,61,41},{22,62,44},{22,63,43},{22,64,86},{22,65,85},{22,66,88},{22,67,87},{22,68,82},{22,69,81},{22,70,84},{22,71,83},{22,72,94},{22,73,93},{22,74,96},{22,75,95},{23,0,23},{23,1,24},{23,2,21},{23,3,22},{23,4,19},{23,5,20},{23,6,17},{23,7,18},{23,8,31},{23,9,32},{23,10,29},{23,11,30},{23,12,27},{23,13,28},{23,14,25},{23,15,26},{23,16,7},{23,17,8},{23,18,5},{23,19,6},{23,20,3},{23,21,4},{23,22,1},{23,23,2},{23,24,15},{23,25,16},{23,26,13},{23,27,14},{23,28,11},{23,29,12},{23,30,9},{23,31,10},{23,32,55},{23,33,56},{23,34,53},{23,35,54},{23,36,51},{23,37,52},{23,38,49},{23,39,50},{23,40,63},{23,41,64},{23,42,61},{23,43,62},{23,44,59},{23,45,60},{23,46,57},{23,47,58},{23,48,39},{23,49,40},{23,50,37},{23,51,38},{23,52,35},{23,53,36},{23,54,33},{23,55,34},{23,56,47},{23,57,48},{23,58,45},{23,59,46},{23,60,43},{23,61,44},{23,62,41},{23,63,42},{23,64,87},{23,65,88},{23,66,85},{23,67,86},{23,68,83},{23,69,84},{23,70,81},{23,71,82},{23,72,95},{23,73,96},{23,74,93},{23,75,94},{24,0,24},{24,1,23},{24,2,22},{24,3,21},{24,4,20},{24,5,19},{24,6,18},{24,7,17},{24,8,32},{24,9,31},{24,10,30},{24,11,29},{24,12,28},{24,13,27},{24,14,26},{24,15,25},{24,16,8},{24,17,7},{24,18,6},{24,19,5},{24,20,4},{24,21,3},{24,22,2},{24,23,1},{24,24,16},{24,25,15},{24,26,14},{24,27,13},{24,28,12},{24,29,11},{24,30,10},{24,31,9},{24,32,56},{24,33,55},{24,34,54},{24,35,53},{24,36,52},{24,37,51},{24,38,50},{24,39,49},{24,40,64},{24,41,63},{24,42,62},{24,43,61},{24,44,60},{24,45,59},{24,46,58},{24,47,57},{24,48,40},{24,49,39},{24,50,38},{24,51,37},{24,52,36},{24,53,35},{24,54,34},{24,55,33},{24,56,48},{24,57,47},{24,58,46},{24,59,45},{24,60,44},{24,61,43},{24,62,42},{24,63,41},{24,64,88},{24,65,87},{24,66,86},{24,67,85},{24,68,84},{24,69,83},{24,70,82},{24,71,81},{24,72,96},{24,73,95},{24,74,94},{24,75,93},{25,0,25},{25,1,26},{25,2,27},{25,3,28},{25,4,29},{25,5,30},{25,6,31},{25,7,32},{25,8,17},{25,9,18},{25,10,19},{25,11,20},{25,12,21},{25,13,22},{25,14,23},{25,15,24},{25,16,9},{25,17,10},{25,18,11},{25,19,12},{25,20,13},{25,21,14},{25,22,15},{25,23,16},{25,24,1},{25,25,2},{25,26,3},{25,27,4},{25,28,5},{25,29,6},{25,30,7},{25,31,8},{25,32,57},{25,33,58},{25,34,59},{25,35,60},{25,36,61},{25,37,62},{25,38,63},{25,39,64},{25,40,49},{25,41,50},{25,42,51},{25,43,52},{25,44,53},{25,45,54},{25,46,55},{25,47,56},{25,48,41},{25,49,42},{25,50,43},{25,51,44},{25,52,45},{25,53,46},{25,54,47},{25,55,48},{25,56,33},{25,57,34},{25,58,35},{25,59,36},{25,60,37},{25,61,38},{25,62,39},{25,63,40},{25,64,89},{25,65,90},{25,66,91},{25,67,92},{25,68,93},{25,69,94},{25,70,95},{25,71,96},{25,72,81},{25,73,82},{25,74,83},{25,75,84},{26,0,26},{26,1,25},{26,2,28},{26,3,27},{26,4,30},{26,5,29},{26,6,32},{26,7,31},{26,8,18},{26,9,17},{26,10,20},{26,11,19},{26,12,22},{26,13,21},{26,14,24},{26,15,23},{26,16,10},{26,17,9},{26,18,12},{26,19,11},{26,20,14},{26,21,13},{26,22,16},{26,23,15},{26,24,2},{26,25,1},{26,26,4},{26,27,3},{26,28,6},{26,29,5},{26,30,8},{26,31,7},{26,32,58},{26,33,57},{26,34,60},{26,35,59},{26,36,62},{26,37,61},{26,38,64},{26,39,63},{26,40,50},{26,41,49},{26,42,52},{26,43,51},{26,44,54},{26,45,53},{26,46,56},{26,47,55},{26,48,42},{26,49,41},{26,50,44},{26,51,43},{26,52,46},{26,53,45},{26,54,48},{26,55,47},{26,56,34},{26,57,33},{26,58,36},{26,59,35},{26,60,38},{26,61,37},{26,62,40},{26,63,39},{26,64,90},{26,65,89},{26,66,92},{26,67,91},{26,68,94},{26,69,93},{26,70,96},{26,71,95},{26,72,82},{26,73,81},{26,74,84},{26,75,83},{27,0,27},{27,1,28},{27,2,25},{27,3,26},{27,4,31},{27,5,32},{27,6,29},{27,7,30},{27,8,19},{27,9,20},{27,10,17},{27,11,18},{27,12,23},{27,13,24},{27,14,21},{27,15,22},{27,16,11},{27,17,12},{27,18,9},{27,19,10},{27,20,15},{27,21,16},{27,22,13},{27,23,14},{27,24,3},{27,25,4},{27,26,1},{27,27,2},{27,28,7},{27,29,8},{27,30,5},{27,31,6},{27,32,59},{27,33,60},{27,34,57},{27,35,58},{27,36,63},{27,37,64},{27,38,61},{27,39,62},{27,40,51},{27,41,52},{27,42,49},{27,43,50},{27,44,55},{27,45,56},{27,46,53},{27,47,54},{27,48,43},{27,49,44},{27,50,41},{27,51,42},{27,52,47},{27,53,48},{27,54,45},{27,55,46},{27,56,35},{27,57,36},{27,58,33},{27,59,34},{27,60,39},{27,61,40},{27,62,37},{27,63,38},{27,64,91},{27,65,92},{27,66,89},{27,67,90},{27,68,95},{27,69,96},{27,70,93},{27,71,94},{27,72,83},{27,73,84},{27,74,81},{27,75,82},{28,0,28},{28,1,27},{28,2,26},{28,3,25},{28,4,32},{28,5,31},{28,6,30},{28,7,29},{28,8,20},{28,9,19},{28,10,18},{28,11,17},{28,12,24},{28,13,23},{28,14,22},{28,15,21},{28,16,12},{28,17,11},{28,18,10},{28,19,9},{28,20,16},{28,21,15},{28,22,14},{28,23,13},{28,24,4},{28,25,3},{28,26,2},{28,27,1},{28,28,8},{28,29,7},{28,30,6},{28,31,5},{28,32,60},{28,33,59},{28,34,58},{28,35,57},{28,36,64},{28,37,63},{28,38,62},{28,39,61},{28,40,52},{28,41,51},{28,42,50},{28,43,49},{28,44,56},{28,45,55},{28,46,54},{28,47,53},{28,48,44},{28,49,43},{28,50,42},{28,51,41},{28,52,48},{28,53,47},{28,54,46},{28,55,45},{28,56,36},{28,57,35},{28,58,34},{28,59,33},{28,60,40},{28,61,39},{28,62,38},{28,63,37},{28,64,92},{28,65,91},{28,66,90},{28,67,89},{28,68,96},{28,69,95},{28,70,94},{28,71,93},{28,72,84},{28,73,83},{28,74,82},{28,75,81},{29,0,29},{29,1,30},{29,2,31},{29,3,32},{29,4,25},{29,5,26},{29,6,27},{29,7,28},{29,8,21},{29,9,22},{29,10,23},{29,11,24},{29,12,17},{29,13,18},{29,14,19},{29,15,20},{29,16,13},{29,17,14},{29,18,15},{29,19,16},{29,20,9},{29,21,10},{29,22,11},{29,23,12},{29,24,5},{29,25,6},{29,26,7},{29,27,8},{29,28,1},{29,29,2},{29,30,3},{29,31,4},{29,32,61},{29,33,62},{29,34,63},{29,35,64},{29,36,57},{29,37,58},{29,38,59},{29,39,60},{29,40,53},{29,41,54},{29,42,55},{29,43,56},{29,44,49},{29,45,50},{29,46,51},{29,47,52},{29,48,45},{29,49,46},{29,50,47},{29,51,48},{29,52,41},{29,53,42},{29,54,43},{29,55,44},{29,56,37},{29,57,38},{29,58,39},{29,59,40},{29,60,33},{29,61,34},{29,62,35},{29,63,36},{29,64,93},{29,65,94},{29,66,95},{29,67,96},{29,68,89},{29,69,90},{29,70,91},{29,71,92},{29,72,85},{29,73,86},{29,74,87},{29,75,88},{30,0,30},{30,1,29},{30,2,32},{30,3,31},{30,4,26},{30,5,25},{30,6,28},{30,7,27},{30,8,22},{30,9,21},{30,10,24},{30,11,23},{30,12,18},{30,13,17},{30,14,20},{30,15,19},{30,16,14},{30,17,13},{30,18,16},{30,19,15},{30,20,10},{30,21,9},{30,22,12},{30,23,11},{30,24,6},{30,25,5},{30,26,8},{30,27,7},{30,28,2},{30,29,1},{30,30,4},{30,31,3},{30,32,62},{30,33,61},{30,34,64},{30,35,63},{30,36,58},{30,37,57},{30,38,60},{30,39,59},{30,40,54},{30,41,53},{30,42,56},{30,43,55},{30,44,50},{30,45,49},{30,46,52},{30,47,51},{30,48,46},{30,49,45},{30,50,48},{30,51,47},{30,52,42},{30,53,41},{30,54,44},{30,55,43},{30,56,38},{30,57,37},{30,58,40},{30,59,39},{30,60,34},{30,61,33},{30,62,36},{30,63,35},{30,64,94},{30,65,93},{30,66,96},{30,67,95},{30,68,90},{30,69,89},{30,70,92},{30,71,91},{30,72,86},{30,73,85},{30,74,88},{30,75,87},{31,0,31},{31,1,32},{31,2,29},{31,3,30},{31,4,27},{31,5,28},{31,6,25},{31,7,26},{31,8,23},{31,9,24},{31,10,21},{31,11,22},{31,12,19},{31,13,20},{31,14,17},{31,15,18},{31,16,15},{31,17,16},{31,18,13},{31,19,14},{31,20,11},{31,21,12},{31,22,9},{31,23,10},{31,24,7},{31,25,8},{31,26,5},{31,27,6},{31,28,3},{31,29,4},{31,30,1},{31,31,2},{31,32,63},{31,33,64},{31,34,61},{31,35,62},{31,36,59},{31,37,60},{31,38,57},{31,39,58},{31,40,55},{31,41,56},{31,42,53},{31,43,54},{31,44,51},{31,45,52},{31,46,49},{31,47,50},{31,48,47},{31,49,48},{31,50,45},{31,51,46},{31,52,43},{31,53,44},{31,54,41},{31,55,42},{31,56,39},{31,57,40},{31,58,37},{31,59,38},{31,60,35},{31,61,36},{31,62,33},{31,63,34},{31,64,95},{31,65,96},{31,66,93},{31,67,94},{31,68,91},{31,69,92},{31,70,89},{31,71,90},{31,72,87},{31,73,88},{31,74,85},{31,75,86},{32,0,32},{32,1,31},{32,2,30},{32,3,29},{32,4,28},{32,5,27},{32,6,26},{32,7,25},{32,8,24},{32,9,23},{32,10,22},{32,11,21},{32,12,20},{32,13,19},{32,14,18},{32,15,17},{32,16,16},{32,17,15},{32,18,14},{32,19,13},{32,20,12},{32,21,11},{32,22,10},{32,23,9},{32,24,8},{32,25,7},{32,26,6},{32,27,5},{32,28,4},{32,29,3},{32,30,2},{32,31,1},{32,32,64},{32,33,63},{32,34,62},{32,35,61},{32,36,60},{32,37,59},{32,38,58},{32,39,57},{32,40,56},{32,41,55},{32,42,54},{32,43,53},{32,44,52},{32,45,51},{32,46,50},{32,47,49},{32,48,48},{32,49,47},{32,50,46},{32,51,45},{32,52,44},{32,53,43},{32,54,42},{32,55,41},{32,56,40},{32,57,39},{32,58,38},{32,59,37},{32,60,36},{32,61,35},{32,62,34},{32,63,33},{32,64,96},{32,65,95},{32,66,94},{32,67,93},{32,68,92},{32,69,91},{32,70,90},{32,71,89},{32,72,88},{32,73,87},{32,74,86},{32,75,85},{33,0,33},{33,1,34},{33,2,35},{33,3,36},{33,4,37},{33,5,38},{33,6,39},{33,7,40},{33,8,41},{33,9,42},{33,10,43},{33,11,44},{33,12,45},{33,13,46},{33,14,47},{33,15,48},{33,16,49},{33,17,50},{33,18,51},{33,19,52},{33,20,53},{33,21,54},{33,22,55},{33,23,56},{33,24,57},{33,25,58},{33,26,59},{33,27,60},{33,28,61},{33,29,62},{33,30,63},{33,31,64},{33,32,1},{33,33,2},{33,34,3},{33,35,4},{33,36,5},{33,37,6},{33,38,7},{33,39,8},{33,40,9},{33,41,10},{33,42,11},{33,43,12},{33,44,13},{33,45,14},{33,46,15},{33,47,16},{33,48,17},{33,49,18},{33,50,19},{33,51,20},{33,52,21},{33,53,22},{33,54,23},{33,55,24},{33,56,25},{33,57,26},{33,58,27},{33,59,28},{33,60,29},{33,61,30},{33,62,31},{33,63,32},{33,64,97},{33,65,98},{33,66,99},{33,67,100},{33,68,101},{33,69,102},{33,70,103},{33,71,104},{33,72,105},{33,73,106},{33,74,107},{33,75,108},{34,0,34},{34,1,33},{34,2,36},{34,3,35},{34,4,38},{34,5,37},{34,6,40},{34,7,39},{34,8,42},{34,9,41},{34,10,44},{34,11,43},{34,12,46},{34,13,45},{34,14,48},{34,15,47},{34,16,50},{34,17,49},{34,18,52},{34,19,51},{34,20,54},{34,21,53},{34,22,56},{34,23,55},{34,24,58},{34,25,57},{34,26,60},{34,27,59},{34,28,62},{34,29,61},{34,30,64},{34,31,63},{34,32,2},{34,33,1},{34,34,4},{34,35,3},{34,36,6},{34,37,5},{34,38,8},{34,39,7},{34,40,10},{34,41,9},{34,42,12},{34,43,11},{34,44,14},{34,45,13},{34,46,16},{34,47,15},{34,48,18},{34,49,17},{34,50,20},{34,51,19},{34,52,22},{34,53,21},{34,54,24},{34,55,23},{34,56,26},{34,57,25},{34,58,28},{34,59,27},{34,60,30},{34,61,29},{34,62,32},{34,63,31},{34,64,98},{34,65,97},{34,66,100},{34,67,99},{34,68,102},{34,69,101},{34,70,104},{34,71,103},{34,72,106},{34,73,105},{34,74,108},{34,75,107},{35,0,35},{35,1,36},{35,2,33},{35,3,34},{35,4,39},{35,5,40},{35,6,37},{35,7,38},{35,8,43},{35,9,44},{35,10,41},{35,11,42},{35,12,47},{35,13,48},{35,14,45},{35,15,46},{35,16,51},{35,17,52},{35,18,49},{35,19,50},{35,20,55},{35,21,56},{35,22,53},{35,23,54},{35,24,59},{35,25,60},{35,26,57},{35,27,58},{35,28,63},{35,29,64},{35,30,61},{35,31,62},{35,32,3},{35,33,4},{35,34,1},{35,35,2},{35,36,7},{35,37,8},{35,38,5},{35,39,6},{35,40,11},{35,41,12},{35,42,9},{35,43,10},{35,44,15},{35,45,16},{35,46,13},{35,47,14},{35,48,19},{35,49,20},{35,50,17},{35,51,18},{35,52,23},{35,53,24},{35,54,21},{35,55,22},{35,56,27},{35,57,28},{35,58,25},{35,59,26},{35,60,31},{35,61,32},{35,62,29},{35,63,30},{35,64,99},{35,65,100},{35,66,97},{35,67,98},{35,68,103},{35,69,104},{35,70,101},{35,71,102},{35,72,107},{35,73,108},{35,74,105},{35,75,106},{36,0,36},{36,1,35},{36,2,34},{36,3,33},{36,4,40},{36,5,39},{36,6,38},{36,7,37},{36,8,44},{36,9,43},{36,10,42},{36,11,41},{36,12,48},{36,13,47},{36,14,46},{36,15,45},{36,16,52},{36,17,51},{36,18,50},{36,19,49},{36,20,56},{36,21,55},{36,22,54},{36,23,53},{36,24,60},{36,25,59},{36,26,58},{36,27,57},{36,28,64},{36,29,63},{36,30,62},{36,31,61},{36,32,4},{36,33,3},{36,34,2},{36,35,1},{36,36,8},{36,37,7},{36,38,6},{36,39,5},{36,40,12},{36,41,11},{36,42,10},{36,43,9},{36,44,16},{36,45,15},{36,46,14},{36,47,13},{36,48,20},{36,49,19},{36,50,18},{36,51,17},{36,52,24},{36,53,23},{36,54,22},{36,55,21},{36,56,28},{36,57,27},{36,58,26},{36,59,25},{36,60,32},{36,61,31},{36,62,30},{36,63,29},{36,64,100},{36,65,99},{36,66,98},{36,67,97},{36,68,104},{36,69,103},{36,70,102},{36,71,101},{36,72,108},{36,73,107},{36,74,106},{36,75,105},{37,0,37},{37,1,38},{37,2,39},{37,3,40},{37,4,33},{37,5,34},{37,6,35},{37,7,36},{37,8,45},{37,9,46},{37,10,47},{37,11,48},{37,12,41},{37,13,42},{37,14,43},{37,15,44},{37,16,53},{37,17,54},{37,18,55},{37,19,56},{37,20,49},{37,21,50},{37,22,51},{37,23,52},{37,24,61},{37,25,62},{37,26,63},{37,27,64},{37,28,57},{37,29,58},{37,30,59},{37,31,60},{37,32,5},{37,33,6},{37,34,7},{37,35,8},{37,36,1},{37,37,2},{37,38,3},{37,39,4},{37,40,13},{37,41,14},{37,42,15},{37,43,16},{37,44,9},{37,45,10},{37,46,11},{37,47,12},{37,48,21},{37,49,22},{37,50,23},{37,51,24},{37,52,17},{37,53,18},{37,54,19},{37,55,20},{37,56,29},{37,57,30},{37,58,31},{37,59,32},{37,60,25},{37,61,26},{37,62,27},{37,63,28},{37,64,101},{37,65,102},{37,66,103},{37,67,104},{37,68,97},{37,69,98},{37,70,99},{37,71,100},{37,72,109},{37,73,110},{37,74,111},{37,75,112},{38,0,38},{38,1,37},{38,2,40},{38,3,39},{38,4,34},{38,5,33},{38,6,36},{38,7,35},{38,8,46},{38,9,45},{38,10,48},{38,11,47},{38,12,42},{38,13,41},{38,14,44},{38,15,43},{38,16,54},{38,17,53},{38,18,56},{38,19,55},{38,20,50},{38,21,49},{38,22,52},{38,23,51},{38,24,62},{38,25,61},{38,26,64},{38,27,63},{38,28,58},{38,29,57},{38,30,60},{38,31,59},{38,32,6},{38,33,5},{38,34,8},{38,35,7},{38,36,2},{38,37,1},{38,38,4},{38,39,3},{38,40,14},{38,41,13},{38,42,16},{38,43,15},{38,44,10},{38,45,9},{38,46,12},{38,47,11},{38,48,22},{38,49,21},{38,50,24},{38,51,23},{38,52,18},{38,53,17},{38,54,20},{38,55,19},{38,56,30},{38,57,29},{38,58,32},{38,59,31},{38,60,26},{38,61,25},{38,62,28},{38,63,27},{38,64,102},{38,65,101},{38,66,104},{38,67,103},{38,68,98},{38,69,97},{38,70,100},{38,71,99},{38,72,110},{38,73,109},{38,74,112},{38,75,111},{39,0,39},{39,1,40},{39,2,37},{39,3,38},{39,4,35},{39,5,36},{39,6,33},{39,7,34},{39,8,47},{39,9,48},{39,10,45},{39,11,46},{39,12,43},{39,13,44},{39,14,41},{39,15,42},{39,16,55},{39,17,56},{39,18,53},{39,19,54},{39,20,51},{39,21,52},{39,22,49},{39,23,50},{39,24,63},{39,25,64},{39,26,61},{39,27,62},{39,28,59},{39,29,60},{39,30,57},{39,31,58},{39,32,7},{39,33,8},{39,34,5},{39,35,6},{39,36,3},{39,37,4},{39,38,1},{39,39,2},{39,40,15},{39,41,16},{39,42,13},{39,43,14},{39,44,11},{39,45,12},{39,46,9},{39,47,10},{39,48,23},{39,49,24},{39,50,21},{39,51,22},{39,52,19},{39,53,20},{39,54,17},{39,55,18},{39,56,31},{39,57,32},{39,58,29},{39,59,30},{39,60,27},{39,61,28},{39,62,25},{39,63,26},{39,64,103},{39,65,104},{39,66,101},{39,67,102},{39,68,99},{39,69,100},{39,70,97},{39,71,98},{39,72,111},{39,73,112},{39,74,109},{39,75,110},{40,0,40},{40,1,39},{40,2,38},{40,3,37},{40,4,36},{40,5,35},{40,6,34},{40,7,33},{40,8,48},{40,9,47},{40,10,46},{40,11,45},{40,12,44},{40,13,43},{40,14,42},{40,15,41},{40,16,56},{40,17,55},{40,18,54},{40,19,53},{40,20,52},{40,21,51},{40,22,50},{40,23,49},{40,24,64},{40,25,63},{40,26,62},{40,27,61},{40,28,60},{40,29,59},{40,30,58},{40,31,57},{40,32,8},{40,33,7},{40,34,6},{40,35,5},{40,36,4},{40,37,3},{40,38,2},{40,39,1},{40,40,16},{40,41,15},{40,42,14},{40,43,13},{40,44,12},{40,45,11},{40,46,10},{40,47,9},{40,48,24},{40,49,23},{40,50,22},{40,51,21},{40,52,20},{40,53,19},{40,54,18},{40,55,17},{40,56,32},{40,57,31},{40,58,30},{40,59,29},{40,60,28},{40,61,27},{40,62,26},{40,63,25},{40,64,104},{40,65,103},{40,66,102},{40,67,101},{40,68,100},{40,69,99},{40,70,98},{40,71,97},{40,72,112},{40,73,111},{40,74,110},{40,75,109},{41,0,41},{41,1,42},{41,2,43},{41,3,44},{41,4,45},{41,5,46},{41,6,47},{41,7,48},{41,8,33},{41,9,34},{41,10,35},{41,11,36},{41,12,37},{41,13,38},{41,14,39},{41,15,40},{41,16,57},{41,17,58},{41,18,59},{41,19,60},{41,20,61},{41,21,62},{41,22,63},{41,23,64},{41,24,49},{41,25,50},{41,26,51},{41,27,52},{41,28,53},{41,29,54},{41,30,55},{41,31,56},{41,32,9},{41,33,10},{41,34,11},{41,35,12},{41,36,13},{41,37,14},{41,38,15},{41,39,16},{41,40,1},{41,41,2},{41,42,3},{41,43,4},{41,44,5},{41,45,6},{41,46,7},{41,47,8},{41,48,25},{41,49,26},{41,50,27},{41,51,28},{41,52,29},{41,53,30},{41,54,31},{41,55,32},{41,56,17},{41,57,18},{41,58,19},{41,59,20},{41,60,21},{41,61,22},{41,62,23},{41,63,24},{41,64,105},{41,65,106},{41,66,107},{41,67,108},{41,68,109},{41,69,110},{41,70,111},{41,71,112},{41,72,97},{41,73,98},{41,74,99},{41,75,100},{42,0,42},{42,1,41},{42,2,44},{42,3,43},{42,4,46},{42,5,45},{42,6,48},{42,7,47},{42,8,34},{42,9,33},{42,10,36},{42,11,35},{42,12,38},{42,13,37},{42,14,40},{42,15,39},{42,16,58},{42,17,57},{42,18,60},{42,19,59},{42,20,62},{42,21,61},{42,22,64},{42,23,63},{42,24,50},{42,25,49},{42,26,52},{42,27,51},{42,28,54},{42,29,53},{42,30,56},{42,31,55},{42,32,10},{42,33,9},{42,34,12},{42,35,11},{42,36,14},{42,37,13},{42,38,16},{42,39,15},{42,40,2},{42,41,1},{42,42,4},{42,43,3},{42,44,6},{42,45,5},{42,46,8},{42,47,7},{42,48,26},{42,49,25},{42,50,28},{42,51,27},{42,52,30},{42,53,29},{42,54,32},{42,55,31},{42,56,18},{42,57,17},{42,58,20},{42,59,19},{42,60,22},{42,61,21},{42,62,24},{42,63,23},{42,64,106},{42,65,105},{42,66,108},{42,67,107},{42,68,110},{42,69,109},{42,70,112},{42,71,111},{42,72,98},{42,73,97},{42,74,100},{42,75,99},{43,0,43},{43,1,44},{43,2,41},{43,3,42},{43,4,47},{43,5,48},{43,6,45},{43,7,46},{43,8,35},{43,9,36},{43,10,33},{43,11,34},{43,12,39},{43,13,40},{43,14,37},{43,15,38},{43,16,59},{43,17,60},{43,18,57},{43,19,58},{43,20,63},{43,21,64},{43,22,61},{43,23,62},{43,24,51},{43,25,52},{43,26,49},{43,27,50},{43,28,55},{43,29,56},{43,30,53},{43,31,54},{43,32,11},{43,33,12},{43,34,9},{43,35,10},{43,36,15},{43,37,16},{43,38,13},{43,39,14},{43,40,3},{43,41,4},{43,42,1},{43,43,2},{43,44,7},{43,45,8},{43,46,5},{43,47,6},{43,48,27},{43,49,28},{43,50,25},{43,51,26},{43,52,31},{43,53,32},{43,54,29},{43,55,30},{43,56,19},{43,57,20},{43,58,17},{43,59,18},{43,60,23},{43,61,24},{43,62,21},{43,63,22},{43,64,107},{43,65,108},{43,66,105},{43,67,106},{43,68,111},{43,69,112},{43,70,109},{43,71,110},{43,72,99},{43,73,100},{43,74,97},{43,75,98},{44,0,44},{44,1,43},{44,2,42},{44,3,41},{44,4,48},{44,5,47},{44,6,46},{44,7,45},{44,8,36},{44,9,35},{44,10,34},{44,11,33},{44,12,40},{44,13,39},{44,14,38},{44,15,37},{44,16,60},{44,17,59},{44,18,58},{44,19,57},{44,20,64},{44,21,63},{44,22,62},{44,23,61},{44,24,52},{44,25,51},{44,26,50},{44,27,49},{44,28,56},{44,29,55},{44,30,54},{44,31,53},{44,32,12},{44,33,11},{44,34,10},{44,35,9},{44,36,16},{44,37,15},{44,38,14},{44,39,13},{44,40,4},{44,41,3},{44,42,2},{44,43,1},{44,44,8},{44,45,7},{44,46,6},{44,47,5},{44,48,28},{44,49,27},{44,50,26},{44,51,25},{44,52,32},{44,53,31},{44,54,30},{44,55,29},{44,56,20},{44,57,19},{44,58,18},{44,59,17},{44,60,24},{44,61,23},{44,62,22},{44,63,21},{44,64,108},{44,65,107},{44,66,106},{44,67,105},{44,68,112},{44,69,111},{44,70,110},{44,71,109},{44,72,100},{44,73,99},{44,74,98},{44,75,97},{45,0,45},{45,1,46},{45,2,47},{45,3,48},{45,4,41},{45,5,42},{45,6,43},{45,7,44},{45,8,37},{45,9,38},{45,10,39},{45,11,40},{45,12,33},{45,13,34},{45,14,35},{45,15,36},{45,16,61},{45,17,62},{45,18,63},{45,19,64},{45,20,57},{45,21,58},{45,22,59},{45,23,60},{45,24,53},{45,25,54},{45,26,55},{45,27,56},{45,28,49},{45,29,50},{45,30,51},{45,31,52},{45,32,13},{45,33,14},{45,34,15},{45,35,16},{45,36,9},{45,37,10},{45,38,11},{45,39,12},{45,40,5},{45,41,6},{45,42,7},{45,43,8},{45,44,1},{45,45,2},{45,46,3},{45,47,4},{45,48,29},{45,49,30},{45,50,31},{45,51,32},{45,52,25},{45,53,26},{45,54,27},{45,55,28},{45,56,21},{45,57,22},{45,58,23},{45,59,24},{45,60,17},{45,61,18},{45,62,19},{45,63,20},{45,64,109},{45,65,110},{45,66,111},{45,67,112},{45,68,105},{45,69,106},{45,70,107},{45,71,108},{45,72,101},{45,73,102},{45,74,103},{45,75,104},{46,0,46},{46,1,45},{46,2,48},{46,3,47},{46,4,42},{46,5,41},{46,6,44},{46,7,43},{46,8,38},{46,9,37},{46,10,40},{46,11,39},{46,12,34},{46,13,33},{46,14,36},{46,15,35},{46,16,62},{46,17,61},{46,18,64},{46,19,63},{46,20,58},{46,21,57},{46,22,60},{46,23,59},{46,24,54},{46,25,53},{46,26,56},{46,27,55},{46,28,50},{46,29,49},{46,30,52},{46,31,51},{46,32,14},{46,33,13},{46,34,16},{46,35,15},{46,36,10},{46,37,9},{46,38,12},{46,39,11},{46,40,6},{46,41,5},{46,42,8},{46,43,7},{46,44,2},{46,45,1},{46,46,4},{46,47,3},{46,48,30},{46,49,29},{46,50,32},{46,51,31},{46,52,26},{46,53,25},{46,54,28},{46,55,27},{46,56,22},{46,57,21},{46,58,24},{46,59,23},{46,60,18},{46,61,17},{46,62,20},{46,63,19},{46,64,110},{46,65,109},{46,66,112},{46,67,111},{46,68,106},{46,69,105},{46,70,108},{46,71,107},{46,72,102},{46,73,101},{46,74,104},{46,75,103},{47,0,47},{47,1,48},{47,2,45},{47,3,46},{47,4,43},{47,5,44},{47,6,41},{47,7,42},{47,8,39},{47,9,40},{47,10,37},{47,11,38},{47,12,35},{47,13,36},{47,14,33},{47,15,34},{47,16,63},{47,17,64},{47,18,61},{47,19,62},{47,20,59},{47,21,60},{47,22,57},{47,23,58},{47,24,55},{47,25,56},{47,26,53},{47,27,54},{47,28,51},{47,29,52},{47,30,49},{47,31,50},{47,32,15},{47,33,16},{47,34,13},{47,35,14},{47,36,11},{47,37,12},{47,38,9},{47,39,10},{47,40,7},{47,41,8},{47,42,5},{47,43,6},{47,44,3},{47,45,4},{47,46,1},{47,47,2},{47,48,31},{47,49,32},{47,50,29},{47,51,30},{47,52,27},{47,53,28},{47,54,25},{47,55,26},{47,56,23},{47,57,24},{47,58,21},{47,59,22},{47,60,19},{47,61,20},{47,62,17},{47,63,18},{47,64,111},{47,65,112},{47,66,109},{47,67,110},{47,68,107},{47,69,108},{47,70,105},{47,71,106},{47,72,103},{47,73,104},{47,74,101},{47,75,102},{48,0,48},{48,1,47},{48,2,46},{48,3,45},{48,4,44},{48,5,43},{48,6,42},{48,7,41},{48,8,40},{48,9,39},{48,10,38},{48,11,37},{48,12,36},{48,13,35},{48,14,34},{48,15,33},{48,16,64},{48,17,63},{48,18,62},{48,19,61},{48,20,60},{48,21,59},{48,22,58},{48,23,57},{48,24,56},{48,25,55},{48,26,54},{48,27,53},{48,28,52},{48,29,51},{48,30,50},{48,31,49},{48,32,16},{48,33,15},{48,34,14},{48,35,13},{48,36,12},{48,37,11},{48,38,10},{48,39,9},{48,40,8},{48,41,7},{48,42,6},{48,43,5},{48,44,4},{48,45,3},{48,46,2},{48,47,1},{48,48,32},{48,49,31},{48,50,30},{48,51,29},{48,52,28},{48,53,27},{48,54,26},{48,55,25},{48,56,24},{48,57,23},{48,58,22},{48,59,21},{48,60,20},{48,61,19},{48,62,18},{48,63,17},{48,64,112},{48,65,111},{48,66,110},{48,67,109},{48,68,108},{48,69,107},{48,70,106},{48,71,105},{48,72,104},{48,73,103},{48,74,102},{48,75,101},{49,0,49},{49,1,50},{49,2,51},{49,3,52},{49,4,53},{49,5,54},{49,6,55},{49,7,56},{49,8,57},{49,9,58},{49,10,59},{49,11,60},{49,12,61},{49,13,62},{49,14,63},{49,15,64},{49,16,33},{49,17,34},{49,18,35},{49,19,36},{49,20,37},{49,21,38},{49,22,39},{49,23,40},{49,24,41},{49,25,42},{49,26,43},{49,27,44},{49,28,45},{49,29,46},{49,30,47},{49,31,48},{49,32,17},{49,33,18},{49,34,19},{49,35,20},{49,36,21},{49,37,22},{49,38,23},{49,39,24},{49,40,25},{49,41,26},{49,42,27},{49,43,28},{49,44,29},{49,45,30},{49,46,31},{49,47,32},{49,48,1},{49,49,2},{49,50,3},{49,51,4},{49,52,5},{49,53,6},{49,54,7},{49,55,8},{49,56,9},{49,57,10},{49,58,11},{49,59,12},{49,60,13},{49,61,14},{49,62,15},{49,63,16},{49,64,113},{49,65,114},{49,66,115},{49,67,116},{49,68,117},{49,69,118},{49,70,119},{49,71,120},{49,72,121},{49,73,122},{49,74,123},{49,75,124},{50,0,50},{50,1,49},{50,2,52},{50,3,51},{50,4,54},{50,5,53},{50,6,56},{50,7,55},{50,8,58},{50,9,57},{50,10,60},{50,11,59},{50,12,62},{50,13,61},{50,14,64},{50,15,63},{50,16,34},{50,17,33},{50,18,36},{50,19,35},{50,20,38},{50,21,37},{50,22,40},{50,23,39},{50,24,42},{50,25,41},{50,26,44},{50,27,43},{50,28,46},{50,29,45},{50,30,48},{50,31,47},{50,32,18},{50,33,17},{50,34,20},{50,35,19},{50,36,22},{50,37,21},{50,38,24},{50,39,23},{50,40,26},{50,41,25},{50,42,28},{50,43,27},{50,44,30},{50,45,29},{50,46,32},{50,47,31},{50,48,2},{50,49,1},{50,50,4},{50,51,3},{50,52,6},{50,53,5},{50,54,8},{50,55,7},{50,56,10},{50,57,9},{50,58,12},{50,59,11},{50,60,14},{50,61,13},{50,62,16},{50,63,15},{50,64,114},{50,65,113},{50,66,116},{50,67,115},{50,68,118},{50,69,117},{50,70,120},{50,71,119},{50,72,122},{50,73,121},{50,74,124},{50,75,123},{51,0,51},{51,1,52},{51,2,49},{51,3,50},{51,4,55},{51,5,56},{51,6,53},{51,7,54},{51,8,59},{51,9,60},{51,10,57},{51,11,58},{51,12,63},{51,13,64},{51,14,61},{51,15,62},{51,16,35},{51,17,36},{51,18,33},{51,19,34},{51,20,39},{51,21,40},{51,22,37},{51,23,38},{51,24,43},{51,25,44},{51,26,41},{51,27,42},{51,28,47},{51,29,48},{51,30,45},{51,31,46},{51,32,19},{51,33,20},{51,34,17},{51,35,18},{51,36,23},{51,37,24},{51,38,21},{51,39,22},{51,40,27},{51,41,28},{51,42,25},{51,43,26},{51,44,31},{51,45,32},{51,46,29},{51,47,30},{51,48,3},{51,49,4},{51,50,1},{51,51,2},{51,52,7},{51,53,8},{51,54,5},{51,55,6},{51,56,11},{51,57,12},{51,58,9},{51,59,10},{51,60,15},{51,61,16},{51,62,13},{51,63,14},{51,64,115},{51,65,116},{51,66,113},{51,67,114},{51,68,119},{51,69,120},{51,70,117},{51,71,118},{51,72,123},{51,73,124},{51,74,121},{51,75,122},{52,0,52},{52,1,51},{52,2,50},{52,3,49},{52,4,56},{52,5,55},{52,6,54},{52,7,53},{52,8,60},{52,9,59},{52,10,58},{52,11,57},{52,12,64},{52,13,63},{52,14,62},{52,15,61},{52,16,36},{52,17,35},{52,18,34},{52,19,33},{52,20,40},{52,21,39},{52,22,38},{52,23,37},{52,24,44},{52,25,43},{52,26,42},{52,27,41},{52,28,48},{52,29,47},{52,30,46},{52,31,45},{52,32,20},{52,33,19},{52,34,18},{52,35,17},{52,36,24},{52,37,23},{52,38,22},{52,39,21},{52,40,28},{52,41,27},{52,42,26},{52,43,25},{52,44,32},{52,45,31},{52,46,30},{52,47,29},{52,48,4},{52,49,3},{52,50,2},{52,51,1},{52,52,8},{52,53,7},{52,54,6},{52,55,5},{52,56,12},{52,57,11},{52,58,10},{52,59,9},{52,60,16},{52,61,15},{52,62,14},{52,63,13},{52,64,116},{52,65,115},{52,66,114},{52,67,113},{52,68,120},{52,69,119},{52,70,118},{52,71,117},{52,72,124},{52,73,123},{52,74,122},{52,75,121},{53,0,53},{53,1,54},{53,2,55},{53,3,56},{53,4,49},{53,5,50},{53,6,51},{53,7,52},{53,8,61},{53,9,62},{53,10,63},{53,11,64},{53,12,57},{53,13,58},{53,14,59},{53,15,60},{53,16,37},{53,17,38},{53,18,39},{53,19,40},{53,20,33},{53,21,34},{53,22,35},{53,23,36},{53,24,45},{53,25,46},{53,26,47},{53,27,48},{53,28,41},{53,29,42},{53,30,43},{53,31,44},{53,32,21},{53,33,22},{53,34,23},{53,35,24},{53,36,17},{53,37,18},{53,38,19},{53,39,20},{53,40,29},{53,41,30},{53,42,31},{53,43,32},{53,44,25},{53,45,26},{53,46,27},{53,47,28},{53,48,5},{53,49,6},{53,50,7},{53,51,8},{53,52,1},{53,53,2},{53,54,3},{53,55,4},{53,56,13},{53,57,14},{53,58,15},{53,59,16},{53,60,9},{53,61,10},{53,62,11},{53,63,12},{53,64,117},{53,65,118},{53,66,119},{53,67,120},{53,68,113},{53,69,114},{53,70,115},{53,71,116},{53,72,125},{53,73,126},{53,74,127},{53,75,128},{54,0,54},{54,1,53},{54,2,56},{54,3,55},{54,4,50},{54,5,49},{54,6,52},{54,7,51},{54,8,62},{54,9,61},{54,10,64},{54,11,63},{54,12,58},{54,13,57},{54,14,60},{54,15,59},{54,16,38},{54,17,37},{54,18,40},{54,19,39},{54,20,34},{54,21,33},{54,22,36},{54,23,35},{54,24,46},{54,25,45},{54,26,48},{54,27,47},{54,28,42},{54,29,41},{54,30,44},{54,31,43},{54,32,22},{54,33,21},{54,34,24},{54,35,23},{54,36,18},{54,37,17},{54,38,20},{54,39,19},{54,40,30},{54,41,29},{54,42,32},{54,43,31},{54,44,26},{54,45,25},{54,46,28},{54,47,27},{54,48,6},{54,49,5},{54,50,8},{54,51,7},{54,52,2},{54,53,1},{54,54,4},{54,55,3},{54,56,14},{54,57,13},{54,58,16},{54,59,15},{54,60,10},{54,61,9},{54,62,12},{54,63,11},{54,64,118},{54,65,117},{54,66,120},{54,67,119},{54,68,114},{54,69,113},{54,70,116},{54,71,115},{54,72,126},{54,73,125},{54,74,128},{54,75,127},{55,0,55},{55,1,56},{55,2,53},{55,3,54},{55,4,51},{55,5,52},{55,6,49},{55,7,50},{55,8,63},{55,9,64},{55,10,61},{55,11,62},{55,12,59},{55,13,60},{55,14,57},{55,15,58},{55,16,39},{55,17,40},{55,18,37},{55,19,38},{55,20,35},{55,21,36},{55,22,33},{55,23,34},{55,24,47},{55,25,48},{55,26,45},{55,27,46},{55,28,43},{55,29,44},{55,30,41},{55,31,42},{55,32,23},{55,33,24},{55,34,21},{55,35,22},{55,36,19},{55,37,20},{55,38,17},{55,39,18},{55,40,31},{55,41,32},{55,42,29},{55,43,30},{55,44,27},{55,45,28},{55,46,25},{55,47,26},{55,48,7},{55,49,8},{55,50,5},{55,51,6},{55,52,3},{55,53,4},{55,54,1},{55,55,2},{55,56,15},{55,57,16},{55,58,13},{55,59,14},{55,60,11},{55,61,12},{55,62,9},{55,63,10},{55,64,119},{55,65,120},{55,66,117},{55,67,118},{55,68,115},{55,69,116},{55,70,113},{55,71,114},{55,72,127},{55,73,128},{55,74,125},{55,75,126},{56,0,56},{56,1,55},{56,2,54},{56,3,53},{56,4,52},{56,5,51},{56,6,50},{56,7,49},{56,8,64},{56,9,63},{56,10,62},{56,11,61},{56,12,60},{56,13,59},{56,14,58},{56,15,57},{56,16,40},{56,17,39},{56,18,38},{56,19,37},{56,20,36},{56,21,35},{56,22,34},{56,23,33},{56,24,48},{56,25,47},{56,26,46},{56,27,45},{56,28,44},{56,29,43},{56,30,42},{56,31,41},{56,32,24},{56,33,23},{56,34,22},{56,35,21},{56,36,20},{56,37,19},{56,38,18},{56,39,17},{56,40,32},{56,41,31},{56,42,30},{56,43,29},{56,44,28},{56,45,27},{56,46,26},{56,47,25},{56,48,8},{56,49,7},{56,50,6},{56,51,5},{56,52,4},{56,53,3},{56,54,2},{56,55,1},{56,56,16},{56,57,15},{56,58,14},{56,59,13},{56,60,12},{56,61,11},{56,62,10},{56,63,9},{56,64,120},{56,65,119},{56,66,118},{56,67,117},{56,68,116},{56,69,115},{56,70,114},{56,71,113},{56,72,128},{56,73,127},{56,74,126},{56,75,125},{57,0,57},{57,1,58},{57,2,59},{57,3,60},{57,4,61},{57,5,62},{57,6,63},{57,7,64},{57,8,49},{57,9,50},{57,10,51},{57,11,52},{57,12,53},{57,13,54},{57,14,55},{57,15,56},{57,16,41},{57,17,42},{57,18,43},{57,19,44},{57,20,45},{57,21,46},{57,22,47},{57,23,48},{57,24,33},{57,25,34},{57,26,35},{57,27,36},{57,28,37},{57,29,38},{57,30,39},{57,31,40},{57,32,25},{57,33,26},{57,34,27},{57,35,28},{57,36,29},{57,37,30},{57,38,31},{57,39,32},{57,40,17},{57,41,18},{57,42,19},{57,43,20},{57,44,21},{57,45,22},{57,46,23},{57,47,24},{57,48,9},{57,49,10},{57,50,11},{57,51,12},{57,52,13},{57,53,14},{57,54,15},{57,55,16},{57,56,1},{57,57,2},{57,58,3},{57,59,4},{57,60,5},{57,61,6},{57,62,7},{57,63,8},{57,64,121},{57,65,122},{57,66,123},{57,67,124},{57,68,125},{57,69,126},{57,70,127},{57,71,128},{57,72,113},{57,73,114},{57,74,115},{57,75,116},{58,0,58},{58,1,57},{58,2,60},{58,3,59},{58,4,62},{58,5,61},{58,6,64},{58,7,63},{58,8,50},{58,9,49},{58,10,52},{58,11,51},{58,12,54},{58,13,53},{58,14,56},{58,15,55},{58,16,42},{58,17,41},{58,18,44},{58,19,43},{58,20,46},{58,21,45},{58,22,48},{58,23,47},{58,24,34},{58,25,33},{58,26,36},{58,27,35},{58,28,38},{58,29,37},{58,30,40},{58,31,39},{58,32,26},{58,33,25},{58,34,28},{58,35,27},{58,36,30},{58,37,29},{58,38,32},{58,39,31},{58,40,18},{58,41,17},{58,42,20},{58,43,19},{58,44,22},{58,45,21},{58,46,24},{58,47,23},{58,48,10},{58,49,9},{58,50,12},{58,51,11},{58,52,14},{58,53,13},{58,54,16},{58,55,15},{58,56,2},{58,57,1},{58,58,4},{58,59,3},{58,60,6},{58,61,5},{58,62,8},{58,63,7},{58,64,122},{58,65,121},{58,66,124},{58,67,123},{58,68,126},{58,69,125},{58,70,128},{58,71,127},{58,72,114},{58,73,113},{58,74,116},{58,75,115},{59,0,59},{59,1,60},{59,2,57},{59,3,58},{59,4,63},{59,5,64},{59,6,61},{59,7,62},{59,8,51},{59,9,52},{59,10,49},{59,11,50},{59,12,55},{59,13,56},{59,14,53},{59,15,54},{59,16,43},{59,17,44},{59,18,41},{59,19,42},{59,20,47},{59,21,48},{59,22,45},{59,23,46},{59,24,35},{59,25,36},{59,26,33},{59,27,34},{59,28,39},{59,29,40},{59,30,37},{59,31,38},{59,32,27},{59,33,28},{59,34,25},{59,35,26},{59,36,31},{59,37,32},{59,38,29},{59,39,30},{59,40,19},{59,41,20},{59,42,17},{59,43,18},{59,44,23},{59,45,24},{59,46,21},{59,47,22},{59,48,11},{59,49,12},{59,50,9},{59,51,10},{59,52,15},{59,53,16},{59,54,13},{59,55,14},{59,56,3},{59,57,4},{59,58,1},{59,59,2},{59,60,7},{59,61,8},{59,62,5},{59,63,6},{59,64,123},{59,65,124},{59,66,121},{59,67,122},{59,68,127},{59,69,128},{59,70,125},{59,71,126},{59,72,115},{59,73,116},{59,74,113},{59,75,114},{60,0,60},{60,1,59},{60,2,58},{60,3,57},{60,4,64},{60,5,63},{60,6,62},{60,7,61},{60,8,52},{60,9,51},{60,10,50},{60,11,49},{60,12,56},{60,13,55},{60,14,54},{60,15,53},{60,16,44},{60,17,43},{60,18,42},{60,19,41},{60,20,48},{60,21,47},{60,22,46},{60,23,45},{60,24,36},{60,25,35},{60,26,34},{60,27,33},{60,28,40},{60,29,39},{60,30,38},{60,31,37},{60,32,28},{60,33,27},{60,34,26},{60,35,25},{60,36,32},{60,37,31},{60,38,30},{60,39,29},{60,40,20},{60,41,19},{60,42,18},{60,43,17},{60,44,24},{60,45,23},{60,46,22},{60,47,21},{60,48,12},{60,49,11},{60,50,10},{60,51,9},{60,52,16},{60,53,15},{60,54,14},{60,55,13},{60,56,4},{60,57,3},{60,58,2},{60,59,1},{60,60,8},{60,61,7},{60,62,6},{60,63,5},{60,64,124},{60,65,123},{60,66,122},{60,67,121},{60,68,128},{60,69,127},{60,70,126},{60,71,125},{60,72,116},{60,73,115},{60,74,114},{60,75,113},{61,0,61},{61,1,62},{61,2,63},{61,3,64},{61,4,57},{61,5,58},{61,6,59},{61,7,60},{61,8,53},{61,9,54},{61,10,55},{61,11,56},{61,12,49},{61,13,50},{61,14,51},{61,15,52},{61,16,45},{61,17,46},{61,18,47},{61,19,48},{61,20,41},{61,21,42},{61,22,43},{61,23,44},{61,24,37},{61,25,38},{61,26,39},{61,27,40},{61,28,33},{61,29,34},{61,30,35},{61,31,36},{61,32,29},{61,33,30},{61,34,31},{61,35,32},{61,36,25},{61,37,26},{61,38,27},{61,39,28},{61,40,21},{61,41,22},{61,42,23},{61,43,24},{61,44,17},{61,45,18},{61,46,19},{61,47,20},{61,48,13},{61,49,14},{61,50,15},{61,51,16},{61,52,9},{61,53,10},{61,54,11},{61,55,12},{61,56,5},{61,57,6},{61,58,7},{61,59,8},{61,60,1},{61,61,2},{61,62,3},{61,63,4},{61,64,125},{61,65,126},{61,66,127},{61,67,128},{61,68,121},{61,69,122},{61,70,123},{61,71,124},{61,72,117},{61,73,118},{61,74,119},{61,75,120},{62,0,62},{62,1,61},{62,2,64},{62,3,63},{62,4,58},{62,5,57},{62,6,60},{62,7,59},{62,8,54},{62,9,53},{62,10,56},{62,11,55},{62,12,50},{62,13,49},{62,14,52},{62,15,51},{62,16,46},{62,17,45},{62,18,48},{62,19,47},{62,20,42},{62,21,41},{62,22,44},{62,23,43},{62,24,38},{62,25,37},{62,26,40},{62,27,39},{62,28,34},{62,29,33},{62,30,36},{62,31,35},{62,32,30},{62,33,29},{62,34,32},{62,35,31},{62,36,26},{62,37,25},{62,38,28},{62,39,27},{62,40,22},{62,41,21},{62,42,24},{62,43,23},{62,44,18},{62,45,17},{62,46,20},{62,47,19},{62,48,14},{62,49,13},{62,50,16},{62,51,15},{62,52,10},{62,53,9},{62,54,12},{62,55,11},{62,56,6},{62,57,5},{62,58,8},{62,59,7},{62,60,2},{62,61,1},{62,62,4},{62,63,3},{62,64,126},{62,65,125},{62,66,128},{62,67,127},{62,68,122},{62,69,121},{62,70,124},{62,71,123},{62,72,118},{62,73,117},{62,74,120},{62,75,119},{63,0,63},{63,1,64},{63,2,61},{63,3,62},{63,4,59},{63,5,60},{63,6,57},{63,7,58},{63,8,55},{63,9,56},{63,10,53},{63,11,54},{63,12,51},{63,13,52},{63,14,49},{63,15,50},{63,16,47},{63,17,48},{63,18,45},{63,19,46},{63,20,43},{63,21,44},{63,22,41},{63,23,42},{63,24,39},{63,25,40},{63,26,37},{63,27,38},{63,28,35},{63,29,36},{63,30,33},{63,31,34},{63,32,31},{63,33,32},{63,34,29},{63,35,30},{63,36,27},{63,37,28},{63,38,25},{63,39,26},{63,40,23},{63,41,24},{63,42,21},{63,43,22},{63,44,19},{63,45,20},{63,46,17},{63,47,18},{63,48,15},{63,49,16},{63,50,13},{63,51,14},{63,52,11},{63,53,12},{63,54,9},{63,55,10},{63,56,7},{63,57,8},{63,58,5},{63,59,6},{63,60,3},{63,61,4},{63,62,1},{63,63,2},{63,64,127},{63,65,128},{63,66,125},{63,67,126},{63,68,123},{63,69,124},{63,70,121},{63,71,122},{63,72,119},{63,73,120},{63,74,117},{63,75,118},{64,0,64},{64,1,63},{64,2,62},{64,3,61},{64,4,60},{64,5,59},{64,6,58},{64,7,57},{64,8,56},{64,9,55},{64,10,54},{64,11,53},{64,12,52},{64,13,51},{64,14,50},{64,15,49},{64,16,48},{64,17,47},{64,18,46},{64,19,45},{64,20,44},{64,21,43},{64,22,42},{64,23,41},{64,24,40},{64,25,39},{64,26,38},{64,27,37},{64,28,36},{64,29,35},{64,30,34},{64,31,33},{64,32,32},{64,33,31},{64,34,30},{64,35,29},{64,36,28},{64,37,27},{64,38,26},{64,39,25},{64,40,24},{64,41,23},{64,42,22},{64,43,21},{64,44,20},{64,45,19},{64,46,18},{64,47,17},{64,48,16},{64,49,15},{64,50,14},{64,51,13},{64,52,12},{64,53,11},{64,54,10},{64,55,9},{64,56,8},{64,57,7},{64,58,6},{64,59,5},{64,60,4},{64,61,3},{64,62,2},{64,63,1},{64,64,128},{64,65,127},{64,66,126},{64,67,125},{64,68,124},{64,69,123},{64,70,122},{64,71,121},{64,72,120},{64,73,119},{64,74,118},{64,75,117},{65,0,65},{65,1,66},{65,2,67},{65,3,68},{65,4,69},{65,5,70},{65,6,71},{65,7,72},{65,8,73},{65,9,74},{65,10,75},{65,11,76},{65,12,77},{65,13,78},{65,14,79},{65,15,80},{65,16,81},{65,17,82},{65,18,83},{65,19,84},{65,20,85},{65,21,86},{65,22,87},{65,23,88},{65,24,89},{65,25,90},{65,26,91},{65,27,92},{65,28,93},{65,29,94},{65,30,95},{65,31,96},{65,32,97},{65,33,98},{65,34,99},{65,35,100},{65,36,101},{65,37,102},{65,38,103},{65,39,104},{65,40,105},{65,41,106},{65,42,107},{65,43,108},{65,44,109},{65,45,110},{65,46,111},{65,47,112},{65,48,113},{65,49,114},{65,50,115},{65,51,116},{65,52,117},{65,53,118},{65,54,119},{65,55,120},{65,56,121},{65,57,122},{65,58,123},{65,59,124},{65,60,125},{65,61,126},{65,62,127},{65,63,128},{65,64,1},{65,65,2},{65,66,3},{65,67,4},{65,68,5},{65,69,6},{65,70,7},{65,71,8},{65,72,9},{65,73,10},{65,74,11},{65,75,12},{66,0,66},{66,1,65},{66,2,68},{66,3,67},{66,4,70},{66,5,69},{66,6,72},{66,7,71},{66,8,74},{66,9,73},{66,10,76},{66,11,75},{66,12,78},{66,13,77},{66,14,80},{66,15,79},{66,16,82},{66,17,81},{66,18,84},{66,19,83},{66,20,86},{66,21,85},{66,22,88},{66,23,87},{66,24,90},{66,25,89},{66,26,92},{66,27,91},{66,28,94},{66,29,93},{66,30,96},{66,31,95},{66,32,98},{66,33,97},{66,34,100},{66,35,99},{66,36,102},{66,37,101},{66,38,104},{66,39,103},{66,40,106},{66,41,105},{66,42,108},{66,43,107},{66,44,110},{66,45,109},{66,46,112},{66,47,111},{66,48,114},{66,49,113},{66,50,116},{66,51,115},{66,52,118},{66,53,117},{66,54,120},{66,55,119},{66,56,122},{66,57,121},{66,58,124},{66,59,123},{66,60,126},{66,61,125},{66,62,128},{66,63,127},{66,64,2},{66,65,1},{66,66,4},{66,67,3},{66,68,6},{66,69,5},{66,70,8},{66,71,7},{66,72,10},{66,73,9},{66,74,12},{66,75,11},{67,0,67},{67,1,68},{67,2,65},{67,3,66},{67,4,71},{67,5,72},{67,6,69},{67,7,70},{67,8,75},{67,9,76},{67,10,73},{67,11,74},{67,12,79},{67,13,80},{67,14,77},{67,15,78},{67,16,83},{67,17,84},{67,18,81},{67,19,82},{67,20,87},{67,21,88},{67,22,85},{67,23,86},{67,24,91},{67,25,92},{67,26,89},{67,27,90},{67,28,95},{67,29,96},{67,30,93},{67,31,94},{67,32,99},{67,33,100},{67,34,97},{67,35,98},{67,36,103},{67,37,104},{67,38,101},{67,39,102},{67,40,107},{67,41,108},{67,42,105},{67,43,106},{67,44,111},{67,45,112},{67,46,109},{67,47,110},{67,48,115},{67,49,116},{67,50,113},{67,51,114},{67,52,119},{67,53,120},{67,54,117},{67,55,118},{67,56,123},{67,57,124},{67,58,121},{67,59,122},{67,60,127},{67,61,128},{67,62,125},{67,63,126},{67,64,3},{67,65,4},{67,66,1},{67,67,2},{67,68,7},{67,69,8},{67,70,5},{67,71,6},{67,72,11},{67,73,12},{67,74,9},{67,75,10},{68,0,68},{68,1,67},{68,2,66},{68,3,65},{68,4,72},{68,5,71},{68,6,70},{68,7,69},{68,8,76},{68,9,75},{68,10,74},{68,11,73},{68,12,80},{68,13,79},{68,14,78},{68,15,77},{68,16,84},{68,17,83},{68,18,82},{68,19,81},{68,20,88},{68,21,87},{68,22,86},{68,23,85},{68,24,92},{68,25,91},{68,26,90},{68,27,89},{68,28,96},{68,29,95},{68,30,94},{68,31,93},{68,32,100},{68,33,99},{68,34,98},{68,35,97},{68,36,104},{68,37,103},{68,38,102},{68,39,101},{68,40,108},{68,41,107},{68,42,106},{68,43,105},{68,44,112},{68,45,111},{68,46,110},{68,47,109},{68,48,116},{68,49,115},{68,50,114},{68,51,113},{68,52,120},{68,53,119},{68,54,118},{68,55,117},{68,56,124},{68,57,123},{68,58,122},{68,59,121},{68,60,128},{68,61,127},{68,62,126},{68,63,125},{68,64,4},{68,65,3},{68,66,2},{68,67,1},{68,68,8},{68,69,7},{68,70,6},{68,71,5},{68,72,12},{68,73,11},{68,74,10},{68,75,9},{69,0,69},{69,1,70},{69,2,71},{69,3,72},{69,4,65},{69,5,66},{69,6,67},{69,7,68},{69,8,77},{69,9,78},{69,10,79},{69,11,80},{69,12,73},{69,13,74},{69,14,75},{69,15,76},{69,16,85},{69,17,86},{69,18,87},{69,19,88},{69,20,81},{69,21,82},{69,22,83},{69,23,84},{69,24,93},{69,25,94},{69,26,95},{69,27,96},{69,28,89},{69,29,90},{69,30,91},{69,31,92},{69,32,101},{69,33,102},{69,34,103},{69,35,104},{69,36,97},{69,37,98},{69,38,99},{69,39,100},{69,40,109},{69,41,110},{69,42,111},{69,43,112},{69,44,105},{69,45,106},{69,46,107},{69,47,108},{69,48,117},{69,49,118},{69,50,119},{69,51,120},{69,52,113},{69,53,114},{69,54,115},{69,55,116},{69,56,125},{69,57,126},{69,58,127},{69,59,128},{69,60,121},{69,61,122},{69,62,123},{69,63,124},{69,64,5},{69,65,6},{69,66,7},{69,67,8},{69,68,1},{69,69,2},{69,70,3},{69,71,4},{69,72,13},{69,73,14},{69,74,15},{69,75,16},{70,0,70},{70,1,69},{70,2,72},{70,3,71},{70,4,66},{70,5,65},{70,6,68},{70,7,67},{70,8,78},{70,9,77},{70,10,80},{70,11,79},{70,12,74},{70,13,73},{70,14,76},{70,15,75},{70,16,86},{70,17,85},{70,18,88},{70,19,87},{70,20,82},{70,21,81},{70,22,84},{70,23,83},{70,24,94},{70,25,93},{70,26,96},{70,27,95},{70,28,90},{70,29,89},{70,30,92},{70,31,91},{70,32,102},{70,33,101},{70,34,104},{70,35,103},{70,36,98},{70,37,97},{70,38,100},{70,39,99},{70,40,110},{70,41,109},{70,42,112},{70,43,111},{70,44,106},{70,45,105},{70,46,108},{70,47,107},{70,48,118},{70,49,117},{70,50,120},{70,51,119},{70,52,114},{70,53,113},{70,54,116},{70,55,115},{70,56,126},{70,57,125},{70,58,128},{70,59,127},{70,60,122},{70,61,121},{70,62,124},{70,63,123},{70,64,6},{70,65,5},{70,66,8},{70,67,7},{70,68,2},{70,69,1},{70,70,4},{70,71,3},{70,72,14},{70,73,13},{70,74,16},{70,75,15},{71,0,71},{71,1,72},{71,2,69},{71,3,70},{71,4,67},{71,5,68},{71,6,65},{71,7,66},{71,8,79},{71,9,80},{71,10,77},{71,11,78},{71,12,75},{71,13,76},{71,14,73},{71,15,74},{71,16,87},{71,17,88},{71,18,85},{71,19,86},{71,20,83},{71,21,84},{71,22,81},{71,23,82},{71,24,95},{71,25,96},{71,26,93},{71,27,94},{71,28,91},{71,29,92},{71,30,89},{71,31,90},{71,32,103},{71,33,104},{71,34,101},{71,35,102},{71,36,99},{71,37,100},{71,38,97},{71,39,98},{71,40,111},{71,41,112},{71,42,109},{71,43,110},{71,44,107},{71,45,108},{71,46,105},{71,47,106},{71,48,119},{71,49,120},{71,50,117},{71,51,118},{71,52,115},{71,53,116},{71,54,113},{71,55,114},{71,56,127},{71,57,128},{71,58,125},{71,59,126},{71,60,123},{71,61,124},{71,62,121},{71,63,122},{71,64,7},{71,65,8},{71,66,5},{71,67,6},{71,68,3},{71,69,4},{71,70,1},{71,71,2},{71,72,15},{71,73,16},{71,74,13},{71,75,14},{72,0,72},{72,1,71},{72,2,70},{72,3,69},{72,4,68},{72,5,67},{72,6,66},{72,7,65},{72,8,80},{72,9,79},{72,10,78},{72,11,77},{72,12,76},{72,13,75},{72,14,74},{72,15,73},{72,16,88},{72,17,87},{72,18,86},{72,19,85},{72,20,84},{72,21,83},{72,22,82},{72,23,81},{72,24,96},{72,25,95},{72,26,94},{72,27,93},{72,28,92},{72,29,91},{72,30,90},{72,31,89},{72,32,104},{72,33,103},{72,34,102},{72,35,101},{72,36,100},{72,37,99},{72,38,98},{72,39,97},{72,40,112},{72,41,111},{72,42,110},{72,43,109},{72,44,108},{72,45,107},{72,46,106},{72,47,105},{72,48,120},{72,49,119},{72,50,118},{72,51,117},{72,52,116},{72,53,115},{72,54,114},{72,55,113},{72,56,128},{72,57,127},{72,58,126},{72,59,125},{72,60,124},{72,61,123},{72,62,122},{72,63,121},{72,64,8},{72,65,7},{72,66,6},{72,67,5},{72,68,4},{72,69,3},{72,70,2},{72,71,1},{72,72,16},{72,73,15},{72,74,14},{72,75,13},{73,0,73},{73,1,74},{73,2,75},{73,3,76},{73,4,77},{73,5,78},{73,6,79},{73,7,80},{73,8,65},{73,9,66},{73,10,67},{73,11,68},{73,12,69},{73,13,70},{73,14,71},{73,15,72},{73,16,89},{73,17,90},{73,18,91},{73,19,92},{73,20,93},{73,21,94},{73,22,95},{73,23,96},{73,24,81},{73,25,82},{73,26,83},{73,27,84},{73,28,85},{73,29,86},{73,30,87},{73,31,88},{73,32,105},{73,33,106},{73,34,107},{73,35,108},{73,36,109},{73,37,110},{73,38,111},{73,39,112},{73,40,97},{73,41,98},{73,42,99},{73,43,100},{73,44,101},{73,45,102},{73,46,103},{73,47,104},{73,48,121},{73,49,122},{73,50,123},{73,51,124},{73,52,125},{73,53,126},{73,54,127},{73,55,128},{73,56,113},{73,57,114},{73,58,115},{73,59,116},{73,60,117},{73,61,118},{73,62,119},{73,63,120},{73,64,9},{73,65,10},{73,66,11},{73,67,12},{73,68,13},{73,69,14},{73,70,15},{73,71,16},{73,72,1},{73,73,2},{73,74,3},{73,75,4},{74,0,74},{74,1,73},{74,2,76},{74,3,75},{74,4,78},{74,5,77},{74,6,80},{74,7,79},{74,8,66},{74,9,65},{74,10,68},{74,11,67},{74,12,70},{74,13,69},{74,14,72},{74,15,71},{74,16,90},{74,17,89},{74,18,92},{74,19,91},{74,20,94},{74,21,93},{74,22,96},{74,23,95},{74,24,82},{74,25,81},{74,26,84},{74,27,83},{74,28,86},{74,29,85},{74,30,88},{74,31,87},{74,32,106},{74,33,105},{74,34,108},{74,35,107},{74,36,110},{74,37,109},{74,38,112},{74,39,111},{74,40,98},{74,41,97},{74,42,100},{74,43,99},{74,44,102},{74,45,101},{74,46,104},{74,47,103},{74,48,122},{74,49,121},{74,50,124},{74,51,123},{74,52,126},{74,53,125},{74,54,128},{74,55,127},{74,56,114},{74,57,113},{74,58,116},{74,59,115},{74,60,118},{74,61,117},{74,62,120},{74,63,119},{74,64,10},{74,65,9},{74,66,12},{74,67,11},{74,68,14},{74,69,13},{74,70,16},{74,71,15},{74,72,2},{74,73,1},{74,74,4},{74,75,3},{75,0,75},{75,1,76},{75,2,73},{75,3,74},{75,4,79},{75,5,80},{75,6,77},{75,7,78},{75,8,67},{75,9,68},{75,10,65},{75,11,66},{75,12,71},{75,13,72},{75,14,69},{75,15,70},{75,16,91},{75,17,92},{75,18,89},{75,19,90},{75,20,95},{75,21,96},{75,22,93},{75,23,94},{75,24,83},{75,25,84},{75,26,81},{75,27,82},{75,28,87},{75,29,88},{75,30,85},{75,31,86},{75,32,107},{75,33,108},{75,34,105},{75,35,106},{75,36,111},{75,37,112},{75,38,109},{75,39,110},{75,40,99},{75,41,100},{75,42,97},{75,43,98},{75,44,103},{75,45,104},{75,46,101},{75,47,102},{75,48,123},{75,49,124},{75,50,121},{75,51,122},{75,52,127},{75,53,128},{75,54,125},{75,55,126},{75,56,115},{75,57,116},{75,58,113},{75,59,114},{75,60,119},{75,61,120},{75,62,117},{75,63,118},{75,64,11},{75,65,12},{75,66,9},{75,67,10},{75,68,15},{75,69,16},{75,70,13},{75,71,14},{75,72,3},{75,73,4},{75,74,1},{75,75,2}},{{0,0,0},{1,0,1},{1,1,2},{2,0,2},{2,1,1},{3,0,3},{3,1,4},{3,2,5},{3,3,6},{3,4,7},{3,5,8},{4,0,4},{4,1,3},{4,2,6},{4,3,5},{4,4,8},{4,5,7},{5,0,5},{5,1,6},{5,2,3},{5,3,4},{5,4,9},{5,5,10},{5,6,11},{5,7,12},{5,8,13},{5,9,14},{6,0,6},{6,1,5},{6,2,4},{6,3,3},{6,4,10},{6,5,9},{6,6,12},{6,7,11},{6,8,14},{6,9,13},{7,0,7},{7,1,8},{7,2,9},{7,3,10},{7,4,3},{7,5,4},{8,0,8},{8,1,7},{8,2,10},{8,3,9},{8,4,4},{8,5,3},{9,0,9},{9,1,10},{9,2,7},{9,3,8},{9,4,5},{9,5,6},{9,6,13},{9,7,14},{9,8,11},{9,9,12},{9,10,15},{9,11,16},{9,12,17},{9,13,18},{10,0,10},{10,1,9},{10,2,8},{10,3,7},{10,4,6},{10,5,5},{10,6,14},{10,7,13},{10,8,12},{10,9,11},{10,10,16},{10,11,15},{10,12,18},{10,13,17},{11,0,11},{11,1,12},{11,2,13},{11,3,14},{11,4,15},{11,5,16},{11,6,5},{11,7,6},{11,8,9},{11,9,10},{11,10,17},{11,11,18},{11,12,19},{11,13,20},{11,14,21},{11,15,22},{11,16,23},{11,17,24},{12,0,12},{12,1,11},{12,2,14},{12,3,13},{12,4,16},{12,5,15},{12,6,6},{12,7,5},{12,8,10},{12,9,9},{12,10,18},{12,11,17},{12,12,20},{12,13,19},{12,14,22},{12,15,21},{12,16,24},{12,17,23},{13,0,13},{13,1,14},{13,2,11},{13,3,12},{13,4,17},{13,5,18},{13,6,9},{13,7,10},{13,8,5},{13,9,6},{14,0,14},{14,1,13},{14,2,12},{14,3,11},{14,4,18},{14,5,17},{14,6,10},{14,7,9},{14,8,6},{14,9,5},{15,0,15},{15,1,16},{15,2,17},{15,3,18},{15,4,11},{15,5,12},{15,6,19},{15,7,20},{15,8,21},{15,9,22},{15,10,9},{15,11,10},{15,12,23},{15,13,24},{15,14,25},{15,15,26},{15,16,27},{15,17,28},{15,18,29},{15,19,30},{15,20,31},{15,21,32},{15,22,33},{15,23,34},{15,24,35},{15,25,36},{16,0,16},{16,1,15},{16,2,18},{16,3,17},{16,4,12},{16,5,11},{16,6,20},{16,7,19},{16,8,22},{16,9,21},{16,10,10},{16,11,9},{16,12,24},{16,13,23},{16,14,26},{16,15,25},{16,16,28},{16,17,27},{16,18,30},{16,19,29},{16,20,32},{16,21,31},{16,22,34},{16,23,33},{16,24,36},{16,25,35},{17,0,17},{17,1,18},{17,2,15},{17,3,16},{17,4,13},{17,5,14},{17,6,21},{17,7,22},{17,8,19},{17,9,20},{17,10,11},{17,11,12},{17,12,9},{17,13,10},{18,0,18},{18,1,17},{18,2,16},{18,3,15},{18,4,14},{18,5,13},{18,6,22},{18,7,21},{18,8,20},{18,9,19},{18,10,12},{18,11,11},{18,12,10},{18,13,9},{19,0,19},{19,1,20},{19,2,21},{19,3,22},{19,4,23},{19,5,24},{19,6,15},{19,7,16},{19,8,17},{19,9,18},{19,10,25},{19,11,26},{19,12,11},{19,13,12},{19,14,27},{19,15,28},{19,16,29},{19,17,30},{19,18,31},{19,19,32},{19,20,33},{19,21,34},{19,22,35},{19,23,36},{19,24,37},{19,25,38},{19,26,39},{19,27,40},{19,28,41},{19,29,42},{19,30,43},{19,31,44},{20,0,20},{20,1,19},{20,2,22},{20,3,21},{20,4,24},{20,5,23},{20,6,16},{20,7,15},{20,8,18},{20,9,17},{20,10,26},{20,11,25},{20,12,12},{20,13,11},{20,14,28},{20,15,27},{20,16,30},{20,17,29},{20,18,32},{20,19,31},{20,20,34},{20,21,33},{20,22,36},{20,23,35},{20,24,38},{20,25,37},{20,26,40},{20,27,39},{20,28,42},{20,29,41},{20,30,44},{20,31,43},{21,0,21},{21,1,22},{21,2,19},{21,3,20},{21,4,25},{21,5,26},{21,6,17},{21,7,18},{21,8,15},{21,9,16},{21,10,23},{21,11,24},{21,12,27},{21,13,28},{21,14,11},{21,15,12},{21,16,31},{21,17,32},{21,18,33},{21,19,34},{21,20,29},{21,21,30},{21,22,37},{21,23,38},{21,24,39},{21,25,40},{21,26,41},{21,27,42},{21,28,43},{21,29,44},{21,30,45},{21,31,46},{21,32,47},{21,33,48},{21,34,49},{21,35,50},{22,0,22},{22,1,21},{22,2,20},{22,3,19},{22,4,26},{22,5,25},{22,6,18},{22,7,17},{22,8,16},{22,9,15},{22,10,24},{22,11,23},{22,12,28},{22,13,27},{22,14,12},{22,15,11},{22,16,32},{22,17,31},{22,18,34},{22,19,33},{22,20,30},{22,21,29},{22,22,38},{22,23,37},{22,24,40},{22,25,39},{22,26,42},{22,27,41},{22,28,44},{22,29,43},{22,30,46},{22,31,45},{22,32,48},{22,33,47},{22,34,50},{22,35,49},{23,0,23},{23,1,24},{23,2,25},{23,3,26},{23,4,19},{23,5,20},{23,6,27},{23,7,28},{23,8,29},{23,9,30},{23,10,21},{23,11,22},{23,12,15},{23,13,16},{23,14,31},{23,15,32},{23,16,11},{23,17,12},{24,0,24},{24,1,23},{24,2,26},{24,3,25},{24,4,20},{24,5,19},{24,6,28},{24,7,27},{24,8,30},{24,9,29},{24,10,22},{24,11,21},{24,12,16},{24,13,15},{24,14,32},{24,15,31},{24,16,12},{24,17,11},{25,0,25},{25,1,26},{25,2,23},{25,3,24},{25,4,21},{25,5,22},{25,6,29},{25,7,30},{25,8,27},{25,9,28},{25,10,19},{25,11,20},{25,12,31},{25,13,32},{25,14,15},{25,15,16},{25,16,33},{25,17,34},{25,18,35},{25,19,36},{25,20,37},{25,21,38},{25,22,39},{25,23,40},{25,24,41},{25,25,42},{25,26,43},{25,27,44},{25,28,45},{25,29,46},{25,30,47},{25,31,48},{25,32,49},{25,33,50},{25,34,51},{25,35,52},{25,36,53},{25,37,54},{25,38,55},{25,39,56},{25,40,57},{25,41,58},{26,0,26},{26,1,25},{26,2,24},{26,3,23},{26,4,22},{26,5,21},{26,6,30},{26,7,29},{26,8,28},{26,9,27},{26,10,20},{26,11,19},{26,12,32},{26,13,31},{26,14,16},{26,15,15},{26,16,34},{26,17,33},{26,18,36},{26,19,35},{26,20,38},{26,21,37},{26,22,40},{26,23,39},{26,24,42},{26,25,41},{26,26,44},{26,27,43},{26,28,46},{26,29,45},{26,30,48},{26,31,47},{26,32,50},{26,33,49},{26,34,52},{26,35,51},{26,36,54},{26,37,53},{26,38,56},{26,39,55},{26,40,58},{26,41,57},{27,0,27},{27,1,28},{27,2,29},{27,3,30},{27,4,31},{27,5,32},{27,6,23},{27,7,24},{27,8,25},{27,9,26},{27,10,33},{27,11,34},{27,12,21},{27,13,22},{27,14,19},{27,15,20},{27,16,15},{27,17,16},{27,18,37},{27,19,38},{27,20,35},{27,21,36},{27,22,41},{27,23,42},{27,24,43},{27,25,44},{27,26,45},{27,27,46},{27,28,39},{27,29,40},{27,30,49},{27,31,50},{27,32,51},{27,33,52},{27,34,47},{27,35,48},{27,36,55},{27,37,56},{27,38,53},{27,39,54},{27,40,59},{27,41,60},{27,42,61},{27,43,62},{27,44,63},{27,45,64},{28,0,28},{28,1,27},{28,2,30},{28,3,29},{28,4,32},{28,5,31},{28,6,24},{28,7,23},{28,8,26},{28,9,25},{28,10,34},{28,11,33},{28,12,22},{28,13,21},{28,14,20},{28,15,19},{28,16,16},{28,17,15},{28,18,38},{28,19,37},{28,20,36},{28,21,35},{28,22,42},{28,23,41},{28,24,44},{28,25,43},{28,26,46},{28,27,45},{28,28,40},{28,29,39},{28,30,50},{28,31,49},{28,32,52},{28,33,51},{28,34,48},{28,35,47},{28,36,56},{28,37,55},{28,38,54},{28,39,53},{28,40,60},{28,41,59},{28,42,62},{28,43,61},{28,44,64},{28,45,63},{29,0,29},{29,1,30},{29,2,27},{29,3,28},{29,4,33},{29,5,34},{29,6,25},{29,7,26},{29,8,23},{29,9,24},{29,10,31},{29,11,32},{29,12,35},{29,13,36},{29,14,37},{29,15,38},{29,16,19},{29,17,20},{29,18,15},{29,19,16},{29,20,21},{29,21,22},{29,22,43},{29,23,44},{29,24,45},{29,25,46},{29,26,47},{29,27,48},{29,28,49},{29,29,50},{29,30,39},{29,31,40},{29,32,41},{29,33,42},{29,34,53},{29,35,54},{29,36,51},{29,37,52},{29,38,57},{29,39,58},{29,40,55},{29,41,56},{29,42,59},{29,43,60},{29,44,61},{29,45,62},{30,0,30},{30,1,29},{30,2,28},{30,3,27},{30,4,34},{30,5,33},{30,6,26},{30,7,25},{30,8,24},{30,9,23},{30,10,32},{30,11,31},{30,12,36},{30,13,35},{30,14,38},{30,15,37},{30,16,20},{30,17,19},{30,18,16},{30,19,15},{30,20,22},{30,21,21},{30,22,44},{30,23,43},{30,24,46},{30,25,45},{30,26,48},{30,27,47},{30,28,50},{30,29,49},{30,30,40},{30,31,39},{30,32,42},{30,33,41},{30,34,54},{30,35,53},{30,36,52},{30,37,51},{30,38,58},{30,39,57},{30,40,56},{30,41,55},{30,42,60},{30,43,59},{30,44,62},{30,45,61},{31,0,31},{31,1,32},{31,2,33},{31,3,34},{31,4,27},{31,5,28},{31,6,35},{31,7,36},{31,8,37},{31,9,38},{31,10,29},{31,11,30},{31,12,25},{31,13,26},{31,14,23},{31,15,24},{31,16,21},{31,17,22},{31,18,19},{31,19,20},{31,20,15},{31,21,16},{31,22,45},{31,23,46},{31,24,47},{31,25,48},{31,26,49},{31,27,50},{31,28,51},{31,29,52},{31,30,41},{31,31,42},{31,32,39},{31,33,40},{31,34,55},{31,35,56},{31,36,57},{31,37,58},{31,38,59},{31,39,60},{31,40,53},{31,41,54},{31,42,63},{31,43,64},{31,44,65},{31,45,66},{31,46,67},{31,47,68},{31,48,69},{31,49,70},{31,50,71},{31,51,72},{32,0,32},{32,1,31},{32,2,34},{32,3,33},{32,4,28},{32,5,27},{32,6,36},{32,7,35},{32,8,38},{32,9,37},{32,10,30},{32,11,29},{32,12,26},{32,13,25},{32,14,24},{32,15,23},{32,16,22},{32,17,21},{32,18,20},{32,19,19},{32,20,16},{32,21,15},{32,22,46},{32,23,45},{32,24,48},{32,25,47},{32,26,50},{32,27,49},{32,28,52},{32,29,51},{32,30,42},{32,31,41},{32,32,40},{32,33,39},{32,34,56},{32,35,55},{32,36,58},{32,37,57},{32,38,60},{32,39,59},{32,40,54},{32,41,53},{32,42,64},{32,43,63},{32,44,66},{32,45,65},{32,46,68},{32,47,67},{32,48,70},{32,49,69},{32,50,72},{32,51,71},{33,0,33},{33,1,34},{33,2,31},{33,3,32},{33,4,29},{33,5,30},{33,6,37},{33,7,38},{33,8,35},{33,9,36},{33,10,27},{33,11,28},{33,12,39},{33,13,40},{33,14,41},{33,15,42},{33,16,25},{33,17,26},{33,18,21},{33,19,22},{33,20,19},{33,21,20},{33,22,15},{33,23,16},{33,24,49},{33,25,50},{33,26,51},{33,27,52},{33,28,47},{33,29,48},{33,30,53},{33,31,54},{33,32,45},{33,33,46},{33,34,57},{33,35,58},{33,36,59},{33,37,60},{33,38,61},{33,39,62},{33,40,63},{33,41,64},{33,42,55},{33,43,56},{33,44,67},{33,45,68},{33,46,65},{33,47,66},{33,48,71},{33,49,72},{33,50,69},{33,51,70},{34,0,34},{34,1,33},{34,2,32},{34,3,31},{34,4,30},{34,5,29},{34,6,38},{34,7,37},{34,8,36},{34,9,35},{34,10,28},{34,11,27},{34,12,40},{34,13,39},{34,14,42},{34,15,41},{34,16,26},{34,17,25},{34,18,22},{34,19,21},{34,20,20},{34,21,19},{34,22,16},{34,23,15},{34,24,50},{34,25,49},{34,26,52},{34,27,51},{34,28,48},{34,29,47},{34,30,54},{34,31,53},{34,32,46},{34,33,45},{34,34,58},{34,35,57},{34,36,60},{34,37,59},{34,38,62},{34,39,61},{34,40,64},{34,41,63},{34,42,56},{34,43,55},{34,44,68},{34,45,67},{34,46,66},{34,47,65},{34,48,72},{34,49,71},{34,50,70},{34,51,69},{35,0,35},{35,1,36},{35,2,37},{35,3,38},{35,4,39},{35,5,40},{35,6,31},{35,7,32},{35,8,33},{35,9,34},{35,10,41},{35,11,42},{35,12,29},{35,13,30},{35,14,43},{35,15,44},{35,16,45},{35,17,46},{35,18,25},{35,19,26},{35,20,27},{35,21,28},{35,22,19},{35,23,20},{35,24,15},{35,25,16},{36,0,36},{36,1,35},{36,2,38},{36,3,37},{36,4,40},{36,5,39},{36,6,32},{36,7,31},{36,8,34},{36,9,33},{36,10,42},{36,11,41},{36,12,30},{36,13,29},{36,14,44},{36,15,43},{36,16,46},{36,17,45},{36,18,26},{36,19,25},{36,20,28},{36,21,27},{36,22,20},{36,23,19},{36,24,16},{36,25,15},{37,0,37},{37,1,38},{37,2,35},{37,3,36},{37,4,41},{37,5,42},{37,6,33},{37,7,34},{37,8,31},{37,9,32},{37,10,39},{37,11,40},{37,12,43},{37,13,44},{37,14,29},{37,15,30},{37,16,47},{37,17,48},{37,18,27},{37,19,28},{37,20,25},{37,21,26},{37,22,21},{37,23,22},{37,24,19},{37,25,20},{37,26,53},{37,27,54},{37,28,55},{37,29,56},{37,30,51},{37,31,52},{37,32,57},{37,33,58},{37,34,45},{37,35,46},{37,36,61},{37,37,62},{37,38,63},{37,39,64},{37,40,65},{37,41,66},{37,42,67},{37,43,68},{37,44,59},{37,45,60},{37,46,69},{37,47,70},{37,48,73},{37,49,74},{37,50,75},{37,51,76},{37,52,77},{37,53,78},{37,54,79},{37,55,80},{37,56,81},{37,57,82},{37,58,83},{37,59,84},{37,60,85},{37,61,86},{38,0,38},{38,1,37},{38,2,36},{38,3,35},{38,4,42},{38,5,41},{38,6,34},{38,7,33},{38,8,32},{38,9,31},{38,10,40},{38,11,39},{38,12,44},{38,13,43},{38,14,30},{38,15,29},{38,16,48},{38,17,47},{38,18,28},{38,19,27},{38,20,26},{38,21,25},{38,22,22},{38,23,21},{38,24,20},{38,25,19},{38,26,54},{38,27,53},{38,28,56},{38,29,55},{38,30,52},{38,31,51},{38,32,58},{38,33,57},{38,34,46},{38,35,45},{38,36,62},{38,37,61},{38,38,64},{38,39,63},{38,40,66},{38,41,65},{38,42,68},{38,43,67},{38,44,60},{38,45,59},{38,46,70},{38,47,69},{38,48,74},{38,49,73},{38,50,76},{38,51,75},{38,52,78},{38,53,77},{38,54,80},{38,55,79},{38,56,82},{38,57,81},{38,58,84},{38,59,83},{38,60,86},{38,61,85},{39,0,39},{39,1,40},{39,2,41},{39,3,42},{39,4,35},{39,5,36},{39,6,43},{39,7,44},{39,8,45},{39,9,46},{39,10,37},{39,11,38},{39,12,33},{39,13,34},{39,14,47},{39,15,48},{39,16,49},{39,17,50},{39,18,51},{39,19,52},{39,20,53},{39,21,54},{39,22,25},{39,23,26},{39,24,21},{39,25,22},{39,26,19},{39,27,20},{39,28,27},{39,29,28},{39,30,29},{39,31,30},{39,32,31},{39,33,32},{39,34,59},{39,35,60},{39,36,63},{39,37,64},{39,38,65},{39,39,66},{39,40,61},{39,41,62},{39,42,69},{39,43,70},{39,44,55},{39,45,56},{39,46,71},{39,47,72},{39,48,67},{39,49,68},{39,50,73},{39,51,74},{39,52,75},{39,53,76},{39,54,77},{39,55,78},{39,56,79},{39,57,80},{39,58,81},{39,59,82},{39,60,83},{39,61,84},{40,0,40},{40,1,39},{40,2,42},{40,3,41},{40,4,36},{40,5,35},{40,6,44},{40,7,43},{40,8,46},{40,9,45},{40,10,38},{40,11,37},{40,12,34},{40,13,33},{40,14,48},{40,15,47},{40,16,50},{40,17,49},{40,18,52},{40,19,51},{40,20,54},{40,21,53},{40,22,26},{40,23,25},{40,24,22},{40,25,21},{40,26,20},{40,27,19},{40,28,28},{40,29,27},{40,30,30},{40,31,29},{40,32,32},{40,33,31},{40,34,60},{40,35,59},{40,36,64},{40,37,63},{40,38,66},{40,39,65},{40,40,62},{40,41,61},{40,42,70},{40,43,69},{40,44,56},{40,45,55},{40,46,72},{40,47,71},{40,48,68},{40,49,67},{40,50,74},{40,51,73},{40,52,76},{40,53,75},{40,54,78},{40,55,77},{40,56,80},{40,57,79},{40,58,82},{40,59,81},{40,60,84},{40,61,83},{41,0,41},{41,1,42},{41,2,39},{41,3,40},{41,4,37},{41,5,38},{41,6,45},{41,7,46},{41,8,43},{41,9,44},{41,10,35},{41,11,36},{41,12,47},{41,13,48},{41,14,33},{41,15,34},{41,16,51},{41,17,52},{41,18,49},{41,19,50},{41,20,55},{41,21,56},{41,22,27},{41,23,28},{41,24,25},{41,25,26},{41,26,21},{41,27,22},{41,28,19},{41,29,20},{41,30,31},{41,31,32},{41,32,29},{41,33,30},{41,34,61},{41,35,62},{41,36,65},{41,37,66},{41,38,67},{41,39,68},{41,40,69},{41,41,70},{41,42,53},{41,43,54},{41,44,71},{41,45,72},{41,46,59},{41,47,60},{41,48,75},{41,49,76},{41,50,77},{41,51,78},{41,52,73},{41,53,74},{41,54,81},{41,55,82},{41,56,83},{41,57,84},{41,58,79},{41,59,80},{41,60,87},{41,61,88},{41,62,89},{41,63,90},{41,64,91},{41,65,92},{41,66,93},{41,67,94},{42,0,42},{42,1,41},{42,2,40},{42,3,39},{42,4,38},{42,5,37},{42,6,46},{42,7,45},{42,8,44},{42,9,43},{42,10,36},{42,11,35},{42,12,48},{42,13,47},{42,14,34},{42,15,33},{42,16,52},{42,17,51},{42,18,50},{42,19,49},{42,20,56},{42,21,55},{42,22,28},{42,23,27},{42,24,26},{42,25,25},{42,26,22},{42,27,21},{42,28,20},{42,29,19},{42,30,32},{42,31,31},{42,32,30},{42,33,29},{42,34,62},{42,35,61},{42,36,66},{42,37,65},{42,38,68},{42,39,67},{42,40,70},{42,41,69},{42,42,54},{42,43,53},{42,44,72},{42,45,71},{42,46,60},{42,47,59},{42,48,76},{42,49,75},{42,50,78},{42,51,77},{42,52,74},{42,53,73},{42,54,82},{42,55,81},{42,56,84},{42,57,83},{42,58,80},{42,59,79},{42,60,88},{42,61,87},{42,62,90},{42,63,89},{42,64,92},{42,65,91},{42,66,94},{42,67,93},{43,0,43},{43,1,44},{43,2,45},{43,3,46},{43,4,47},{43,5,48},{43,6,39},{43,7,40},{43,8,41},{43,9,42},{43,10,49},{43,11,50},{43,12,37},{43,13,38},{43,14,35},{43,15,36},{43,16,53},{43,17,54},{43,18,55},{43,19,56},{43,20,51},{43,21,52},{43,22,29},{43,23,30},{43,24,27},{43,25,28},{43,26,25},{43,27,26},{43,28,21},{43,29,22},{43,30,19},{43,31,20},{44,0,44},{44,1,43},{44,2,46},{44,3,45},{44,4,48},{44,5,47},{44,6,40},{44,7,39},{44,8,42},{44,9,41},{44,10,50},{44,11,49},{44,12,38},{44,13,37},{44,14,36},{44,15,35},{44,16,54},{44,17,53},{44,18,56},{44,19,55},{44,20,52},{44,21,51},{44,22,30},{44,23,29},{44,24,28},{44,25,27},{44,26,26},{44,27,25},{44,28,22},{44,29,21},{44,30,20},{44,31,19},{45,0,45},{45,1,46},{45,2,43},{45,3,44},{45,4,49},{45,5,50},{45,6,41},{45,7,42},{45,8,39},{45,9,40},{45,10,47},{45,11,48},{45,12,51},{45,13,52},{45,14,53},{45,15,54},{45,16,35},{45,17,36},{45,18,57},{45,19,58},{45,20,59},{45,21,60},{45,22,31},{45,23,32},{45,24,29},{45,25,30},{45,26,27},{45,27,28},{45,28,25},{45,29,26},{45,30,21},{45,31,22},{45,32,33},{45,33,34},{45,34,37},{45,35,38},{45,36,67},{45,37,68},{45,38,69},{45,39,70},{45,40,71},{45,41,72},{45,42,65},{45,43,66},{45,44,73},{45,45,74},{45,46,55},{45,47,56},{45,48,77},{45,49,78},{45,50,79},{45,51,80},{45,52,81},{45,53,82},{45,54,75},{45,55,76},{45,56,85},{45,57,86},{45,58,87},{45,59,88},{45,60,89},{45,61,90},{45,62,91},{45,63,92},{45,64,93},{45,65,94},{45,66,95},{45,67,96},{45,68,97},{45,69,98},{45,70,99},{45,71,100},{45,72,101},{45,73,102},{46,0,46},{46,1,45},{46,2,44},{46,3,43},{46,4,50},{46,5,49},{46,6,42},{46,7,41},{46,8,40},{46,9,39},{46,10,48},{46,11,47},{46,12,52},{46,13,51},{46,14,54},{46,15,53},{46,16,36},{46,17,35},{46,18,58},{46,19,57},{46,20,60},{46,21,59},{46,22,32},{46,23,31},{46,24,30},{46,25,29},{46,26,28},{46,27,27},{46,28,26},{46,29,25},{46,30,22},{46,31,21},{46,32,34},{46,33,33},{46,34,38},{46,35,37},{46,36,68},{46,37,67},{46,38,70},{46,39,69},{46,40,72},{46,41,71},{46,42,66},{46,43,65},{46,44,74},{46,45,73},{46,46,56},{46,47,55},{46,48,78},{46,49,77},{46,50,80},{46,51,79},{46,52,82},{46,53,81},{46,54,76},{46,55,75},{46,56,86},{46,57,85},{46,58,88},{46,59,87},{46,60,90},{46,61,89},{46,62,92},{46,63,91},{46,64,94},{46,65,93},{46,66,96},{46,67,95},{46,68,98},{46,69,97},{46,70,100},{46,71,99},{46,72,102},{46,73,101},{47,0,47},{47,1,48},{47,2,49},{47,3,50},{47,4,43},{47,5,44},{47,6,51},{47,7,52},{47,8,53},{47,9,54},{47,10,45},{47,11,46},{47,12,41},{47,13,42},{47,14,39},{47,15,40},{47,16,37},{47,17,38},{47,18,59},{47,19,60},{47,20,57},{47,21,58},{47,22,55},{47,23,56},{47,24,31},{47,25,32},{47,26,29},{47,27,30},{47,28,33},{47,29,34},{47,30,25},{47,31,26},{47,32,21},{47,33,22},{47,34,27},{47,35,28},{47,36,69},{47,37,70},{47,38,71},{47,39,72},{47,40,67},{47,41,68},{47,42,73},{47,43,74},{47,44,75},{47,45,76},{47,46,77},{47,47,78},{47,48,65},{47,49,66},{47,50,81},{47,51,82},{47,52,79},{47,53,80},{47,54,83},{47,55,84},{47,56,87},{47,57,88},{47,58,85},{47,59,86},{47,60,91},{47,61,92},{47,62,93},{47,63,94},{47,64,89},{47,65,90},{47,66,97},{47,67,98},{47,68,95},{47,69,96},{47,70,101},{47,71,102},{47,72,99},{47,73,100},{48,0,48},{48,1,47},{48,2,50},{48,3,49},{48,4,44},{48,5,43},{48,6,52},{48,7,51},{48,8,54},{48,9,53},{48,10,46},{48,11,45},{48,12,42},{48,13,41},{48,14,40},{48,15,39},{48,16,38},{48,17,37},{48,18,60},{48,19,59},{48,20,58},{48,21,57},{48,22,56},{48,23,55},{48,24,32},{48,25,31},{48,26,30},{48,27,29},{48,28,34},{48,29,33},{48,30,26},{48,31,25},{48,32,22},{48,33,21},{48,34,28},{48,35,27},{48,36,70},{48,37,69},{48,38,72},{48,39,71},{48,40,68},{48,41,67},{48,42,74},{48,43,73},{48,44,76},{48,45,75},{48,46,78},{48,47,77},{48,48,66},{48,49,65},{48,50,82},{48,51,81},{48,52,80},{48,53,79},{48,54,84},{48,55,83},{48,56,88},{48,57,87},{48,58,86},{48,59,85},{48,60,92},{48,61,91},{48,62,94},{48,63,93},{48,64,90},{48,65,89},{48,66,98},{48,67,97},{48,68,96},{48,69,95},{48,70,102},{48,71,101},{48,72,100},{48,73,99},{49,0,49},{49,1,50},{49,2,47},{49,3,48},{49,4,45},{49,5,46},{49,6,53},{49,7,54},{49,8,51},{49,9,52},{49,10,43},{49,11,44},{49,12,55},{49,13,56},{49,14,57},{49,15,58},{49,16,39},{49,17,40},{49,18,41},{49,19,42},{49,20,61},{49,21,62},{49,22,59},{49,23,60},{49,24,33},{49,25,34},{49,26,31},{49,27,32},{49,28,29},{49,29,30},{49,30,27},{49,31,28},{49,32,25},{49,33,26},{49,34,21},{49,35,22},{50,0,50},{50,1,49},{50,2,48},{50,3,47},{50,4,46},{50,5,45},{50,6,54},{50,7,53},{50,8,52},{50,9,51},{50,10,44},{50,11,43},{50,12,56},{50,13,55},{50,14,58},{50,15,57},{50,16,40},{50,17,39},{50,18,42},{50,19,41},{50,20,62},{50,21,61},{50,22,60},{50,23,59},{50,24,34},{50,25,33},{50,26,32},{50,27,31},{50,28,30},{50,29,29},{50,30,28},{50,31,27},{50,32,26},{50,33,25},{50,34,22},{50,35,21},{51,0,51},{51,1,52},{51,2,53},{51,3,54},{51,4,55},{51,5,56},{51,6,47},{51,7,48},{51,8,49},{51,9,50},{51,10,57},{51,11,58},{51,12,45},{51,13,46},{51,14,59},{51,15,60},{51,16,41},{51,17,42},{51,18,39},{51,19,40},{51,20,43},{51,21,44},{51,22,61},{51,23,62},{51,24,63},{51,25,64},{51,26,33},{51,27,34},{51,28,31},{51,29,32},{51,30,37},{51,31,38},{51,32,27},{51,33,28},{51,34,25},{51,35,26},{51,36,29},{51,37,30},{51,38,73},{51,39,74},{51,40,75},{51,41,76},{51,42,71},{51,43,72},{51,44,69},{51,45,70},{51,46,79},{51,47,80},{51,48,81},{51,49,82},{51,50,65},{51,51,66},{51,52,67},{51,53,68},{51,54,85},{51,55,86},{51,56,77},{51,57,78},{51,58,89},{51,59,90},{51,60,93},{51,61,94},{51,62,87},{51,63,88},{51,64,95},{51,65,96},{51,66,91},{51,67,92},{51,68,99},{51,69,100},{51,70,97},{51,71,98},{51,72,103},{51,73,104},{51,74,105},{51,75,106},{52,0,52},{52,1,51},{52,2,54},{52,3,53},{52,4,56},{52,5,55},{52,6,48},{52,7,47},{52,8,50},{52,9,49},{52,10,58},{52,11,57},{52,12,46},{52,13,45},{52,14,60},{52,15,59},{52,16,42},{52,17,41},{52,18,40},{52,19,39},{52,20,44},{52,21,43},{52,22,62},{52,23,61},{52,24,64},{52,25,63},{52,26,34},{52,27,33},{52,28,32},{52,29,31},{52,30,38},{52,31,37},{52,32,28},{52,33,27},{52,34,26},{52,35,25},{52,36,30},{52,37,29},{52,38,74},{52,39,73},{52,40,76},{52,41,75},{52,42,72},{52,43,71},{52,44,70},{52,45,69},{52,46,80},{52,47,79},{52,48,82},{52,49,81},{52,50,66},{52,51,65},{52,52,68},{52,53,67},{52,54,86},{52,55,85},{52,56,78},{52,57,77},{52,58,90},{52,59,89},{52,60,94},{52,61,93},{52,62,88},{52,63,87},{52,64,96},{52,65,95},{52,66,92},{52,67,91},{52,68,100},{52,69,99},{52,70,98},{52,71,97},{52,72,104},{52,73,103},{52,74,106},{52,75,105},{53,0,53},{53,1,54},{53,2,51},{53,3,52},{53,4,57},{53,5,58},{53,6,49},{53,7,50},{53,8,47},{53,9,48},{53,10,55},{53,11,56},{53,12,59},{53,13,60},{53,14,45},{53,15,46},{53,16,43},{53,17,44},{53,18,61},{53,19,62},{53,20,39},{53,21,40},{53,22,63},{53,23,64},{53,24,65},{53,25,66},{53,26,37},{53,27,38},{53,28,67},{53,29,68},{53,30,33},{53,31,34},{53,32,69},{53,33,70},{53,34,29},{53,35,30},{53,36,25},{53,37,26},{53,38,27},{53,39,28},{53,40,31},{53,41,32},{53,42,41},{53,43,42},{53,44,77},{53,45,78},{53,46,73},{53,47,74},{53,48,79},{53,49,80},{53,50,83},{53,51,84},{53,52,85},{53,53,86},{53,54,87},{53,55,88},{53,56,75},{53,57,76},{53,58,91},{53,59,92},{53,60,81},{53,61,82},{53,62,95},{53,63,96},{53,64,97},{53,65,98},{53,66,89},{53,67,90},{53,68,101},{53,69,102},{53,70,103},{53,71,104},{53,72,105},{53,73,106},{53,74,107},{53,75,108},{54,0,54},{54,1,53},{54,2,52},{54,3,51},{54,4,58},{54,5,57},{54,6,50},{54,7,49},{54,8,48},{54,9,47},{54,10,56},{54,11,55},{54,12,60},{54,13,59},{54,14,46},{54,15,45},{54,16,44},{54,17,43},{54,18,62},{54,19,61},{54,20,40},{54,21,39},{54,22,64},{54,23,63},{54,24,66},{54,25,65},{54,26,38},{54,27,37},{54,28,68},{54,29,67},{54,30,34},{54,31,33},{54,32,70},{54,33,69},{54,34,30},{54,35,29},{54,36,26},{54,37,25},{54,38,28},{54,39,27},{54,40,32},{54,41,31},{54,42,42},{54,43,41},{54,44,78},{54,45,77},{54,46,74},{54,47,73},{54,48,80},{54,49,79},{54,50,84},{54,51,83},{54,52,86},{54,53,85},{54,54,88},{54,55,87},{54,56,76},{54,57,75},{54,58,92},{54,59,91},{54,60,82},{54,61,81},{54,62,96},{54,63,95},{54,64,98},{54,65,97},{54,66,90},{54,67,89},{54,68,102},{54,69,101},{54,70,104},{54,71,103},{54,72,106},{54,73,105},{54,74,108},{54,75,107},{55,0,55},{55,1,56},{55,2,57},{55,3,58},{55,4,51},{55,5,52},{55,6,59},{55,7,60},{55,8,61},{55,9,62},{55,10,53},{55,11,54},{55,12,49},{55,13,50},{55,14,63},{55,15,64},{55,16,65},{55,17,66},{55,18,43},{55,19,44},{55,20,41},{55,21,42},{55,22,47},{55,23,48},{55,24,67},{55,25,68},{55,26,69},{55,27,70},{55,28,37},{55,29,38},{55,30,71},{55,31,72},{55,32,73},{55,33,74},{55,34,31},{55,35,32},{55,36,27},{55,37,28},{55,38,25},{55,39,26},{55,40,29},{55,41,30},{55,42,33},{55,43,34},{55,44,39},{55,45,40},{55,46,45},{55,47,46},{55,48,83},{55,49,84},{55,50,85},{55,51,86},{55,52,87},{55,53,88},{55,54,89},{55,55,90},{55,56,91},{55,57,92},{55,58,75},{55,59,76},{55,60,77},{55,61,78},{55,62,79},{55,63,80},{55,64,81},{55,65,82},{55,66,99},{55,67,100},{55,68,103},{55,69,104},{55,70,95},{55,71,96},{55,72,97},{55,73,98},{55,74,109},{55,75,110},{56,0,56},{56,1,55},{56,2,58},{56,3,57},{56,4,52},{56,5,51},{56,6,60},{56,7,59},{56,8,62},{56,9,61},{56,10,54},{56,11,53},{56,12,50},{56,13,49},{56,14,64},{56,15,63},{56,16,66},{56,17,65},{56,18,44},{56,19,43},{56,20,42},{56,21,41},{56,22,48},{56,23,47},{56,24,68},{56,25,67},{56,26,70},{56,27,69},{56,28,38},{56,29,37},{56,30,72},{56,31,71},{56,32,74},{56,33,73},{56,34,32},{56,35,31},{56,36,28},{56,37,27},{56,38,26},{56,39,25},{56,40,30},{56,41,29},{56,42,34},{56,43,33},{56,44,40},{56,45,39},{56,46,46},{56,47,45},{56,48,84},{56,49,83},{56,50,86},{56,51,85},{56,52,88},{56,53,87},{56,54,90},{56,55,89},{56,56,92},{56,57,91},{56,58,76},{56,59,75},{56,60,78},{56,61,77},{56,62,80},{56,63,79},{56,64,82},{56,65,81},{56,66,100},{56,67,99},{56,68,104},{56,69,103},{56,70,96},{56,71,95},{56,72,98},{56,73,97},{56,74,110},{56,75,109},{57,0,57},{57,1,58},{57,2,55},{57,3,56},{57,4,53},{57,5,54},{57,6,61},{57,7,62},{57,8,59},{57,9,60},{57,10,51},{57,11,52},{57,12,63},{57,13,64},{57,14,49},{57,15,50},{57,16,67},{57,17,68},{57,18,45},{57,19,46},{57,20,47},{57,21,48},{57,22,65},{57,23,66},{57,24,69},{57,25,70},{57,26,71},{57,27,72},{57,28,73},{57,29,74},{57,30,75},{57,31,76},{57,32,37},{57,33,38},{57,34,33},{57,35,34},{57,36,31},{57,37,32},{57,38,29},{57,39,30},{57,40,25},{57,41,26},{58,0,58},{58,1,57},{58,2,56},{58,3,55},{58,4,54},{58,5,53},{58,6,62},{58,7,61},{58,8,60},{58,9,59},{58,10,52},{58,11,51},{58,12,64},{58,13,63},{58,14,50},{58,15,49},{58,16,68},{58,17,67},{58,18,46},{58,19,45},{58,20,48},{58,21,47},{58,22,66},{58,23,65},{58,24,70},{58,25,69},{58,26,72},{58,27,71},{58,28,74},{58,29,73},{58,30,76},{58,31,75},{58,32,38},{58,33,37},{58,34,34},{58,35,33},{58,36,32},{58,37,31},{58,38,30},{58,39,29},{58,40,26},{58,41,25},{59,0,59},{59,1,60},{59,2,61},{59,3,62},{59,4,63},{59,5,64},{59,6,55},{59,7,56},{59,8,57},{59,9,58},{59,10,65},{59,11,66},{59,12,53},{59,13,54},{59,14,51},{59,15,52},{59,16,69},{59,17,70},{59,18,47},{59,19,48},{59,20,45},{59,21,46},{59,22,49},{59,23,50},{59,24,71},{59,25,72},{59,26,67},{59,27,68},{59,28,75},{59,29,76},{59,30,73},{59,31,74},{59,32,77},{59,33,78},{59,34,39},{59,35,40},{59,36,33},{59,37,34},{59,38,31},{59,39,32},{59,40,27},{59,41,28},{59,42,29},{59,43,30},{59,44,37},{59,45,38},{59,46,41},{59,47,42},{59,48,85},{59,49,86},{59,50,87},{59,51,88},{59,52,83},{59,53,84},{59,54,91},{59,55,92},{59,56,89},{59,57,90},{59,58,93},{59,59,94},{59,60,79},{59,61,80},{59,62,81},{59,63,82},{59,64,99},{59,65,100},{59,66,101},{59,67,102},{59,68,105},{59,69,106},{59,70,107},{59,71,108},{59,72,95},{59,73,96},{59,74,97},{59,75,98},{60,0,60},{60,1,59},{60,2,62},{60,3,61},{60,4,64},{60,5,63},{60,6,56},{60,7,55},{60,8,58},{60,9,57},{60,10,66},{60,11,65},{60,12,54},{60,13,53},{60,14,52},{60,15,51},{60,16,70},{60,17,69},{60,18,48},{60,19,47},{60,20,46},{60,21,45},{60,22,50},{60,23,49},{60,24,72},{60,25,71},{60,26,68},{60,27,67},{60,28,76},{60,29,75},{60,30,74},{60,31,73},{60,32,78},{60,33,77},{60,34,40},{60,35,39},{60,36,34},{60,37,33},{60,38,32},{60,39,31},{60,40,28},{60,41,27},{60,42,30},{60,43,29},{60,44,38},{60,45,37},{60,46,42},{60,47,41},{60,48,86},{60,49,85},{60,50,88},{60,51,87},{60,52,84},{60,53,83},{60,54,92},{60,55,91},{60,56,90},{60,57,89},{60,58,94},{60,59,93},{60,60,80},{60,61,79},{60,62,82},{60,63,81},{60,64,100},{60,65,99},{60,66,102},{60,67,101},{60,68,106},{60,69,105},{60,70,108},{60,71,107},{60,72,96},{60,73,95},{60,74,98},{60,75,97},{61,0,61},{61,1,62},{61,2,59},{61,3,60},{61,4,65},{61,5,66},{61,6,57},{61,7,58},{61,8,55},{61,9,56},{61,10,63},{61,11,64},{61,12,67},{61,13,68},{61,14,69},{61,15,70},{61,16,71},{61,17,72},{61,18,53},{61,19,54},{61,20,49},{61,21,50},{61,22,51},{61,23,52},{61,24,73},{61,25,74},{61,26,75},{61,27,76},{61,28,77},{61,29,78},{61,30,79},{61,31,80},{61,32,81},{61,33,82},{61,34,41},{61,35,42},{61,36,37},{61,37,38},{61,38,33},{61,39,34},{61,40,39},{61,41,40},{61,42,27},{61,43,28},{61,44,29},{61,45,30},{62,0,62},{62,1,61},{62,2,60},{62,3,59},{62,4,66},{62,5,65},{62,6,58},{62,7,57},{62,8,56},{62,9,55},{62,10,64},{62,11,63},{62,12,68},{62,13,67},{62,14,70},{62,15,69},{62,16,72},{62,17,71},{62,18,54},{62,19,53},{62,20,50},{62,21,49},{62,22,52},{62,23,51},{62,24,74},{62,25,73},{62,26,76},{62,27,75},{62,28,78},{62,29,77},{62,30,80},{62,31,79},{62,32,82},{62,33,81},{62,34,42},{62,35,41},{62,36,38},{62,37,37},{62,38,34},{62,39,33},{62,40,40},{62,41,39},{62,42,28},{62,43,27},{62,44,30},{62,45,29},{63,0,63},{63,1,64},{63,2,65},{63,3,66},{63,4,59},{63,5,60},{63,6,67},{63,7,68},{63,8,69},{63,9,70},{63,10,61},{63,11,62},{63,12,57},{63,13,58},{63,14,55},{63,15,56},{63,16,73},{63,17,74},{63,18,71},{63,19,72},{63,20,75},{63,21,76},{63,22,53},{63,23,54},{63,24,51},{63,25,52},{63,26,77},{63,27,78},{63,28,79},{63,29,80},{63,30,81},{63,31,82},{63,32,83},{63,33,84},{63,34,85},{63,35,86},{63,36,39},{63,37,40},{63,38,37},{63,39,38},{63,40,33},{63,41,34},{63,42,31},{63,43,32},{63,44,27},{63,45,28},{64,0,64},{64,1,63},{64,2,66},{64,3,65},{64,4,60},{64,5,59},{64,6,68},{64,7,67},{64,8,70},{64,9,69},{64,10,62},{64,11,61},{64,12,58},{64,13,57},{64,14,56},{64,15,55},{64,16,74},{64,17,73},{64,18,72},{64,19,71},{64,20,76},{64,21,75},{64,22,54},{64,23,53},{64,24,52},{64,25,51},{64,26,78},{64,27,77},{64,28,80},{64,29,79},{64,30,82},{64,31,81},{64,32,84},{64,33,83},{64,34,86},{64,35,85},{64,36,40},{64,37,39},{64,38,38},{64,39,37},{64,40,34},{64,41,33},{64,42,32},{64,43,31},{64,44,28},{64,45,27},{65,0,65},{65,1,66},{65,2,63},{65,3,64},{65,4,61},{65,5,62},{65,6,69},{65,7,70},{65,8,67},{65,9,68},{65,10,59},{65,11,60},{65,12,71},{65,13,72},{65,14,73},{65,15,74},{65,16,55},{65,17,56},{65,18,75},{65,19,76},{65,20,77},{65,21,78},{65,22,57},{65,23,58},{65,24,53},{65,25,54},{65,26,79},{65,27,80},{65,28,81},{65,29,82},{65,30,83},{65,31,84},{65,32,85},{65,33,86},{65,34,87},{65,35,88},{65,36,41},{65,37,42},{65,38,39},{65,39,40},{65,40,37},{65,41,38},{65,42,45},{65,43,46},{65,44,31},{65,45,32},{65,46,33},{65,47,34},{65,48,47},{65,49,48},{65,50,51},{65,51,52},{65,52,89},{65,53,90},{65,54,93},{65,55,94},{65,56,95},{65,57,96},{65,58,97},{65,59,98},{65,60,99},{65,61,100},{65,62,101},{65,63,102},{65,64,103},{65,65,104},{65,66,105},{65,67,106},{65,68,91},{65,69,92},{65,70,109},{65,71,110},{65,72,107},{65,73,108},{65,74,111},{65,75,112},{66,0,66},{66,1,65},{66,2,64},{66,3,63},{66,4,62},{66,5,61},{66,6,70},{66,7,69},{66,8,68},{66,9,67},{66,10,60},{66,11,59},{66,12,72},{66,13,71},{66,14,74},{66,15,73},{66,16,56},{66,17,55},{66,18,76},{66,19,75},{66,20,78},{66,21,77},{66,22,58},{66,23,57},{66,24,54},{66,25,53},{66,26,80},{66,27,79},{66,28,82},{66,29,81},{66,30,84},{66,31,83},{66,32,86},{66,33,85},{66,34,88},{66,35,87},{66,36,42},{66,37,41},{66,38,40},{66,39,39},{66,40,38},{66,41,37},{66,42,46},{66,43,45},{66,44,32},{66,45,31},{66,46,34},{66,47,33},{66,48,48},{66,49,47},{66,50,52},{66,51,51},{66,52,90},{66,53,89},{66,54,94},{66,55,93},{66,56,96},{66,57,95},{66,58,98},{66,59,97},{66,60,100},{66,61,99},{66,62,102},{66,63,101},{66,64,104},{66,65,103},{66,66,106},{66,67,105},{66,68,92},{66,69,91},{66,70,110},{66,71,109},{66,72,108},{66,73,107},{66,74,112},{66,75,111},{67,0,67},{67,1,68},{67,2,69},{67,3,70},{67,4,71},{67,5,72},{67,6,63},{67,7,64},{67,8,65},{67,9,66},{67,10,73},{67,11,74},{67,12,61},{67,13,62},{67,14,75},{67,15,76},{67,16,57},{67,17,58},{67,18,77},{67,19,78},{67,20,79},{67,21,80},{67,22,81},{67,23,82},{67,24,55},{67,25,56},{67,26,59},{67,27,60},{67,28,53},{67,29,54},{67,30,85},{67,31,86},{67,32,87},{67,33,88},{67,34,83},{67,35,84},{67,36,45},{67,37,46},{67,38,41},{67,39,42},{67,40,47},{67,41,48},{67,42,37},{67,43,38},{67,44,33},{67,45,34},{67,46,31},{67,47,32},{67,48,39},{67,49,40},{67,50,89},{67,51,90},{67,52,51},{67,53,52},{67,54,95},{67,55,96},{67,56,93},{67,57,94},{67,58,99},{67,59,100},{67,60,97},{67,61,98},{67,62,103},{67,63,104},{67,64,101},{67,65,102},{67,66,107},{67,67,108},{67,68,109},{67,69,110},{67,70,91},{67,71,92},{67,72,111},{67,73,112},{67,74,113},{67,75,114},{68,0,68},{68,1,67},{68,2,70},{68,3,69},{68,4,72},{68,5,71},{68,6,64},{68,7,63},{68,8,66},{68,9,65},{68,10,74},{68,11,73},{68,12,62},{68,13,61},{68,14,76},{68,15,75},{68,16,58},{68,17,57},{68,18,78},{68,19,77},{68,20,80},{68,21,79},{68,22,82},{68,23,81},{68,24,56},{68,25,55},{68,26,60},{68,27,59},{68,28,54},{68,29,53},{68,30,86},{68,31,85},{68,32,88},{68,33,87},{68,34,84},{68,35,83},{68,36,46},{68,37,45},{68,38,42},{68,39,41},{68,40,48},{68,41,47},{68,42,38},{68,43,37},{68,44,34},{68,45,33},{68,46,32},{68,47,31},{68,48,40},{68,49,39},{68,50,90},{68,51,89},{68,52,52},{68,53,51},{68,54,96},{68,55,95},{68,56,94},{68,57,93},{68,58,100},{68,59,99},{68,60,98},{68,61,97},{68,62,104},{68,63,103},{68,64,102},{68,65,101},{68,66,108},{68,67,107},{68,68,110},{68,69,109},{68,70,92},{68,71,91},{68,72,112},{68,73,111},{68,74,114},{68,75,113},{69,0,69},{69,1,70},{69,2,67},{69,3,68},{69,4,73},{69,5,74},{69,6,65},{69,7,66},{69,8,63},{69,9,64},{69,10,71},{69,11,72},{69,12,75},{69,13,76},{69,14,61},{69,15,62},{69,16,59},{69,17,60},{69,18,79},{69,19,80},{69,20,81},{69,21,82},{69,22,77},{69,23,78},{69,24,57},{69,25,58},{69,26,55},{69,27,56},{69,28,83},{69,29,84},{69,30,87},{69,31,88},{69,32,53},{69,33,54},{69,34,89},{69,35,90},{69,36,47},{69,37,48},{69,38,45},{69,39,46},{69,40,41},{69,41,42},{69,42,39},{69,43,40},{69,44,51},{69,45,52},{69,46,37},{69,47,38},{69,48,31},{69,49,32},{69,50,33},{69,51,34},{70,0,70},{70,1,69},{70,2,68},{70,3,67},{70,4,74},{70,5,73},{70,6,66},{70,7,65},{70,8,64},{70,9,63},{70,10,72},{70,11,71},{70,12,76},{70,13,75},{70,14,62},{70,15,61},{70,16,60},{70,17,59},{70,18,80},{70,19,79},{70,20,82},{70,21,81},{70,22,78},{70,23,77},{70,24,58},{70,25,57},{70,26,56},{70,27,55},{70,28,84},{70,29,83},{70,30,88},{70,31,87},{70,32,54},{70,33,53},{70,34,90},{70,35,89},{70,36,48},{70,37,47},{70,38,46},{70,39,45},{70,40,42},{70,41,41},{70,42,40},{70,43,39},{70,44,52},{70,45,51},{70,46,38},{70,47,37},{70,48,32},{70,49,31},{70,50,34},{70,51,33},{71,0,71},{71,1,72},{71,2,73},{71,3,74},{71,4,67},{71,5,68},{71,6,75},{71,7,76},{71,8,77},{71,9,78},{71,10,69},{71,11,70},{71,12,65},{71,13,66},{71,14,79},{71,15,80},{71,16,61},{71,17,62},{71,18,63},{71,19,64},{71,20,83},{71,21,84},{71,22,85},{71,23,86},{71,24,59},{71,25,60},{71,26,57},{71,27,58},{71,28,87},{71,29,88},{71,30,55},{71,31,56},{71,32,89},{71,33,90},{71,34,81},{71,35,82},{71,36,91},{71,37,92},{71,38,47},{71,39,48},{71,40,45},{71,41,46},{71,42,51},{71,43,52},{71,44,41},{71,45,42},{71,46,39},{71,47,40},{71,48,33},{71,49,34},{71,50,31},{71,51,32},{72,0,72},{72,1,71},{72,2,74},{72,3,73},{72,4,68},{72,5,67},{72,6,76},{72,7,75},{72,8,78},{72,9,77},{72,10,70},{72,11,69},{72,12,66},{72,13,65},{72,14,80},{72,15,79},{72,16,62},{72,17,61},{72,18,64},{72,19,63},{72,20,84},{72,21,83},{72,22,86},{72,23,85},{72,24,60},{72,25,59},{72,26,58},{72,27,57},{72,28,88},{72,29,87},{72,30,56},{72,31,55},{72,32,90},{72,33,89},{72,34,82},{72,35,81},{72,36,92},{72,37,91},{72,38,48},{72,39,47},{72,40,46},{72,41,45},{72,42,52},{72,43,51},{72,44,42},{72,45,41},{72,46,40},{72,47,39},{72,48,34},{72,49,33},{72,50,32},{72,51,31},{73,0,73},{73,1,74},{73,2,71},{73,3,72},{73,4,69},{73,5,70},{73,6,77},{73,7,78},{73,8,75},{73,9,76},{73,10,67},{73,11,68},{73,12,79},{73,13,80},{73,14,65},{73,15,66},{73,16,63},{73,17,64},{73,18,81},{73,19,82},{73,20,85},{73,21,86},{73,22,83},{73,23,84},{73,24,61},{73,25,62},{73,26,87},{73,27,88},{73,28,57},{73,29,58},{73,30,59},{73,31,60},{73,32,55},{73,33,56},{73,34,91},{73,35,92},{73,36,89},{73,37,90},{73,38,51},{73,39,52},{73,40,93},{73,41,94},{73,42,47},{73,43,48},{73,44,45},{73,45,46},{73,46,53},{73,47,54},{73,48,37},{73,49,38},{73,50,39},{73,51,40},{73,52,41},{73,53,42},{73,54,97},{73,55,98},{73,56,99},{73,57,100},{73,58,95},{73,59,96},{73,60,101},{73,61,102},{73,62,105},{73,63,106},{73,64,107},{73,65,108},{73,66,103},{73,67,104},{73,68,111},{73,69,112},{73,70,113},{73,71,114},{73,72,109},{73,73,110},{73,74,115},{73,75,116},{74,0,74},{74,1,73},{74,2,72},{74,3,71},{74,4,70},{74,5,69},{74,6,78},{74,7,77},{74,8,76},{74,9,75},{74,10,68},{74,11,67},{74,12,80},{74,13,79},{74,14,66},{74,15,65},{74,16,64},{74,17,63},{74,18,82},{74,19,81},{74,20,86},{74,21,85},{74,22,84},{74,23,83},{74,24,62},{74,25,61},{74,26,88},{74,27,87},{74,28,58},{74,29,57},{74,30,60},{74,31,59},{74,32,56},{74,33,55},{74,34,92},{74,35,91},{74,36,90},{74,37,89},{74,38,52},{74,39,51},{74,40,94},{74,41,93},{74,42,48},{74,43,47},{74,44,46},{74,45,45},{74,46,54},{74,47,53},{74,48,38},{74,49,37},{74,50,40},{74,51,39},{74,52,42},{74,53,41},{74,54,98},{74,55,97},{74,56,100},{74,57,99},{74,58,96},{74,59,95},{74,60,102},{74,61,101},{74,62,106},{74,63,105},{74,64,108},{74,65,107},{74,66,104},{74,67,103},{74,68,112},{74,69,111},{74,70,114},{74,71,113},{74,72,110},{74,73,109},{74,74,116},{74,75,115},{75,0,75},{75,1,76},{75,2,77},{75,3,78},{75,4,79},{75,5,80},{75,6,71},{75,7,72},{75,8,73},{75,9,74},{75,10,81},{75,11,82},{75,12,69},{75,13,70},{75,14,67},{75,15,68},{75,16,83},{75,17,84},{75,18,65},{75,19,66},{75,20,63},{75,21,64},{75,22,87},{75,23,88},{75,24,85},{75,25,86},{75,26,61},{75,27,62},{75,28,59},{75,29,60},{75,30,57},{75,31,58},{75,32,91},{75,33,92},{75,34,93},{75,35,94},{75,36,95},{75,37,96},{75,38,89},{75,39,90},{75,40,51},{75,41,52},{75,42,97},{75,43,98},{75,44,47},{75,45,48},{75,46,99},{75,47,100},{75,48,41},{75,49,42},{75,50,37},{75,51,38},{75,52,39},{75,53,40},{75,54,45},{75,55,46},{75,56,53},{75,57,54},{75,58,55},{75,59,56},{75,60,103},{75,61,104},{75,62,107},{75,63,108},{75,64,105},{75,65,106},{75,66,109},{75,67,110},{75,68,113},{75,69,114},{75,70,111},{75,71,112},{75,72,115},{75,73,116},{75,74,117},{75,75,118}},{{0,0,0},{1,0,1},{2,0,2},{2,1,3},{3,0,3},{3,1,2},{4,0,4},{4,1,5},{4,2,6},{4,3,7},{5,0,5},{5,1,4},{5,2,7},{5,3,6},{6,0,6},{6,1,7},{6,2,4},{6,3,5},{7,0,7},{7,1,6},{7,2,5},{7,3,4},{8,0,8},{8,1,9},{8,2,10},{8,3,11},{8,4,12},{8,5,13},{8,6,14},{8,7,15},{9,0,9},{9,1,8},{9,2,11},{9,3,10},{9,4,13},{9,5,12},{9,6,15},{9,7,14},{10,0,10},{10,1,11},{10,2,8},{10,3,9},{10,4,14},{10,5,15},{10,6,12},{10,7,13},{11,0,11},{11,1,10},{11,2,9},{11,3,8},{11,4,15},{11,5,14},{11,6,13},{11,7,12},{12,0,12},{12,1,13},{12,2,14},{12,3,15},{12,4,8},{12,5,9},{12,6,10},{12,7,11},{13,0,13},{13,1,12},{13,2,15},{13,3,14},{13,4,9},{13,5,8},{13,6,11},{13,7,10},{14,0,14},{14,1,15},{14,2,12},{14,3,13},{14,4,10},{14,5,11},{14,6,8},{14,7,9},{15,0,15},{15,1,14},{15,2,13},{15,3,12},{15,4,11},{15,5,10},{15,6,9},{15,7,8},{16,0,16},{16,1,17},{16,2,18},{16,3,19},{16,4,20},{16,5,21},{16,6,22},{16,7,23},{16,8,24},{16,9,25},{16,10,26},{16,11,27},{16,12,28},{16,13,29},{16,14,30},{16,15,31},{17,0,17},{17,1,16},{17,2,19},{17,3,18},{17,4,21},{17,5,20},{17,6,23},{17,7,22},{17,8,25},{17,9,24},{17,10,27},{17,11,26},{17,12,29},{17,13,28},{17,14,31},{17,15,30},{18,0,18},{18,1,19},{18,2,16},{18,3,17},{18,4,22},{18,5,23},{18,6,20},{18,7,21},{18,8,26},{18,9,27},{18,10,24},{18,11,25},{18,12,30},{18,13,31},{18,14,28},{18,15,29},{19,0,19},{19,1,18},{19,2,17},{19,3,16},{19,4,23},{19,5,22},{19,6,21},{19,7,20},{19,8,27},{19,9,26},{19,10,25},{19,11,24},{19,12,31},{19,13,30},{19,14,29},{19,15,28},{20,0,20},{20,1,21},{20,2,22},{20,3,23},{20,4,16},{20,5,17},{20,6,18},{20,7,19},{20,8,28},{20,9,29},{20,10,30},{20,11,31},{20,12,24},{20,13,25},{20,14,26},{20,15,27},{21,0,21},{21,1,20},{21,2,23},{21,3,22},{21,4,17},{21,5,16},{21,6,19},{21,7,18},{21,8,29},{21,9,28},{21,10,31},{21,11,30},{21,12,25},{21,13,24},{21,14,27},{21,15,26},{22,0,22},{22,1,23},{22,2,20},{22,3,21},{22,4,18},{22,5,19},{22,6,16},{22,7,17},{22,8,30},{22,9,31},{22,10,28},{22,11,29},{22,12,26},{22,13,27},{22,14,24},{22,15,25},{23,0,23},{23,1,22},{23,2,21},{23,3,20},{23,4,19},{23,5,18},{23,6,17},{23,7,16},{23,8,31},{23,9,30},{23,10,29},{23,11,28},{23,12,27},{23,13,26},{23,14,25},{23,15,24},{24,0,24},{24,1,25},{24,2,26},{24,3,27},{24,4,28},{24,5,29},{24,6,30},{24,7,31},{24,8,16},{24,9,17},{24,10,18},{24,11,19},{24,12,20},{24,13,21},{24,14,22},{24,15,23},{25,0,25},{25,1,24},{25,2,27},{25,3,26},{25,4,29},{25,5,28},{25,6,31},{25,7,30},{25,8,17},{25,9,16},{25,10,19},{25,11,18},{25,12,21},{25,13,20},{25,14,23},{25,15,22},{26,0,26},{26,1,27},{26,2,24},{26,3,25},{26,4,30},{26,5,31},{26,6,28},{26,7,29},{26,8,18},{26,9,19},{26,10,16},{26,11,17},{26,12,22},{26,13,23},{26,14,20},{26,15,21},{27,0,27},{27,1,26},{27,2,25},{27,3,24},{27,4,31},{27,5,30},{27,6,29},{27,7,28},{27,8,19},{27,9,18},{27,10,17},{27,11,16},{27,12,23},{27,13,22},{27,14,21},{27,15,20},{28,0,28},{28,1,29},{28,2,30},{28,3,31},{28,4,24},{28,5,25},{28,6,26},{28,7,27},{28,8,20},{28,9,21},{28,10,22},{28,11,23},{28,12,16},{28,13,17},{28,14,18},{28,15,19},{29,0,29},{29,1,28},{29,2,31},{29,3,30},{29,4,25},{29,5,24},{29,6,27},{29,7,26},{29,8,21},{29,9,20},{29,10,23},{29,11,22},{29,12,17},{29,13,16},{29,14,19},{29,15,18},{30,0,30},{30,1,31},{30,2,28},{30,3,29},{30,4,26},{30,5,27},{30,6,24},{30,7,25},{30,8,22},{30,9,23},{30,10,20},{30,11,21},{30,12,18},{30,13,19},{30,14,16},{30,15,17},{31,0,31},{31,1,30},{31,2,29},{31,3,28},{31,4,27},{31,5,26},{31,6,25},{31,7,24},{31,8,23},{31,9,22},{31,10,21},{31,11,20},{31,12,19},{31,13,18},{31,14,17},{31,15,16},{32,0,32},{32,1,33},{32,2,34},{32,3,35},{32,4,36},{32,5,37},{32,6,38},{32,7,39},{32,8,40},{32,9,41},{32,10,42},{32,11,43},{32,12,44},{32,13,45},{32,14,46},{32,15,47},{32,16,48},{32,17,49},{32,18,50},{32,19,51},{32,20,52},{32,21,53},{32,22,54},{32,23,55},{32,24,56},{32,25,57},{32,26,58},{32,27,59},{32,28,60},{32,29,61},{32,30,62},{32,31,63},{33,0,33},{33,1,32},{33,2,35},{33,3,34},{33,4,37},{33,5,36},{33,6,39},{33,7,38},{33,8,41},{33,9,40},{33,10,43},{33,11,42},{33,12,45},{33,13,44},{33,14,47},{33,15,46},{33,16,49},{33,17,48},{33,18,51},{33,19,50},{33,20,53},{33,21,52},{33,22,55},{33,23,54},{33,24,57},{33,25,56},{33,26,59},{33,27,58},{33,28,61},{33,29,60},{33,30,63},{33,31,62},{34,0,34},{34,1,35},{34,2,32},{34,3,33},{34,4,38},{34,5,39},{34,6,36},{34,7,37},{34,8,42},{34,9,43},{34,10,40},{34,11,41},{34,12,46},{34,13,47},{34,14,44},{34,15,45},{34,16,50},{34,17,51},{34,18,48},{34,19,49},{34,20,54},{34,21,55},{34,22,52},{34,23,53},{34,24,58},{34,25,59},{34,26,56},{34,27,57},{34,28,62},{34,29,63},{34,30,60},{34,31,61},{35,0,35},{35,1,34},{35,2,33},{35,3,32},{35,4,39},{35,5,38},{35,6,37},{35,7,36},{35,8,43},{35,9,42},{35,10,41},{35,11,40},{35,12,47},{35,13,46},{35,14,45},{35,15,44},{35,16,51},{35,17,50},{35,18,49},{35,19,48},{35,20,55},{35,21,54},{35,22,53},{35,23,52},{35,24,59},{35,25,58},{35,26,57},{35,27,56},{35,28,63},{35,29,62},{35,30,61},{35,31,60},{36,0,36},{36,1,37},{36,2,38},{36,3,39},{36,4,32},{36,5,33},{36,6,34},{36,7,35},{36,8,44},{36,9,45},{36,10,46},{36,11,47},{36,12,40},{36,13,41},{36,14,42},{36,15,43},{36,16,52},{36,17,53},{36,18,54},{36,19,55},{36,20,48},{36,21,49},{36,22,50},{36,23,51},{36,24,60},{36,25,61},{36,26,62},{36,27,63},{36,28,56},{36,29,57},{36,30,58},{36,31,59},{37,0,37},{37,1,36},{37,2,39},{37,3,38},{37,4,33},{37,5,32},{37,6,35},{37,7,34},{37,8,45},{37,9,44},{37,10,47},{37,11,46},{37,12,41},{37,13,40},{37,14,43},{37,15,42},{37,16,53},{37,17,52},{37,18,55},{37,19,54},{37,20,49},{37,21,48},{37,22,51},{37,23,50},{37,24,61},{37,25,60},{37,26,63},{37,27,62},{37,28,57},{37,29,56},{37,30,59},{37,31,58},{38,0,38},{38,1,39},{38,2,36},{38,3,37},{38,4,34},{38,5,35},{38,6,32},{38,7,33},{38,8,46},{38,9,47},{38,10,44},{38,11,45},{38,12,42},{38,13,43},{38,14,40},{38,15,41},{38,16,54},{38,17,55},{38,18,52},{38,19,53},{38,20,50},{38,21,51},{38,22,48},{38,23,49},{38,24,62},{38,25,63},{38,26,60},{38,27,61},{38,28,58},{38,29,59},{38,30,56},{38,31,57},{39,0,39},{39,1,38},{39,2,37},{39,3,36},{39,4,35},{39,5,34},{39,6,33},{39,7,32},{39,8,47},{39,9,46},{39,10,45},{39,11,44},{39,12,43},{39,13,42},{39,14,41},{39,15,40},{39,16,55},{39,17,54},{39,18,53},{39,19,52},{39,20,51},{39,21,50},{39,22,49},{39,23,48},{39,24,63},{39,25,62},{39,26,61},{39,27,60},{39,28,59},{39,29,58},{39,30,57},{39,31,56},{40,0,40},{40,1,41},{40,2,42},{40,3,43},{40,4,44},{40,5,45},{40,6,46},{40,7,47},{40,8,32},{40,9,33},{40,10,34},{40,11,35},{40,12,36},{40,13,37},{40,14,38},{40,15,39},{40,16,56},{40,17,57},{40,18,58},{40,19,59},{40,20,60},{40,21,61},{40,22,62},{40,23,63},{40,24,48},{40,25,49},{40,26,50},{40,27,51},{40,28,52},{40,29,53},{40,30,54},{40,31,55},{41,0,41},{41,1,40},{41,2,43},{41,3,42},{41,4,45},{41,5,44},{41,6,47},{41,7,46},{41,8,33},{41,9,32},{41,10,35},{41,11,34},{41,12,37},{41,13,36},{41,14,39},{41,15,38},{41,16,57},{41,17,56},{41,18,59},{41,19,58},{41,20,61},{41,21,60},{41,22,63},{41,23,62},{41,24,49},{41,25,48},{41,26,51},{41,27,50},{41,28,53},{41,29,52},{41,30,55},{41,31,54},{42,0,42},{42,1,43},{42,2,40},{42,3,41},{42,4,46},{42,5,47},{42,6,44},{42,7,45},{42,8,34},{42,9,35},{42,10,32},{42,11,33},{42,12,38},{42,13,39},{42,14,36},{42,15,37},{42,16,58},{42,17,59},{42,18,56},{42,19,57},{42,20,62},{42,21,63},{42,22,60},{42,23,61},{42,24,50},{42,25,51},{42,26,48},{42,27,49},{42,28,54},{42,29,55},{42,30,52},{42,31,53},{43,0,43},{43,1,42},{43,2,41},{43,3,40},{43,4,47},{43,5,46},{43,6,45},{43,7,44},{43,8,35},{43,9,34},{43,10,33},{43,11,32},{43,12,39},{43,13,38},{43,14,37},{43,15,36},{43,16,59},{43,17,58},{43,18,57},{43,19,56},{43,20,63},{43,21,62},{43,22,61},{43,23,60},{43,24,51},{43,25,50},{43,26,49},{43,27,48},{43,28,55},{43,29,54},{43,30,53},{43,31,52},{44,0,44},{44,1,45},{44,2,46},{44,3,47},{44,4,40},{44,5,41},{44,6,42},{44,7,43},{44,8,36},{44,9,37},{44,10,38},{44,11,39},{44,12,32},{44,13,33},{44,14,34},{44,15,35},{44,16,60},{44,17,61},{44,18,62},{44,19,63},{44,20,56},{44,21,57},{44,22,58},{44,23,59},{44,24,52},{44,25,53},{44,26,54},{44,27,55},{44,28,48},{44,29,49},{44,30,50},{44,31,51},{45,0,45},{45,1,44},{45,2,47},{45,3,46},{45,4,41},{45,5,40},{45,6,43},{45,7,42},{45,8,37},{45,9,36},{45,10,39},{45,11,38},{45,12,33},{45,13,32},{45,14,35},{45,15,34},{45,16,61},{45,17,60},{45,18,63},{45,19,62},{45,20,57},{45,21,56},{45,22,59},{45,23,58},{45,24,53},{45,25,52},{45,26,55},{45,27,54},{45,28,49},{45,29,48},{45,30,51},{45,31,50},{46,0,46},{46,1,47},{46,2,44},{46,3,45},{46,4,42},{46,5,43},{46,6,40},{46,7,41},{46,8,38},{46,9,39},{46,10,36},{46,11,37},{46,12,34},{46,13,35},{46,14,32},{46,15,33},{46,16,62},{46,17,63},{46,18,60},{46,19,61},{46,20,58},{46,21,59},{46,22,56},{46,23,57},{46,24,54},{46,25,55},{46,26,52},{46,27,53},{46,28,50},{46,29,51},{46,30,48},{46,31,49},{47,0,47},{47,1,46},{47,2,45},{47,3,44},{47,4,43},{47,5,42},{47,6,41},{47,7,40},{47,8,39},{47,9,38},{47,10,37},{47,11,36},{47,12,35},{47,13,34},{47,14,33},{47,15,32},{47,16,63},{47,17,62},{47,18,61},{47,19,60},{47,20,59},{47,21,58},{47,22,57},{47,23,56},{47,24,55},{47,25,54},{47,26,53},{47,27,52},{47,28,51},{47,29,50},{47,30,49},{47,31,48},{48,0,48},{48,1,49},{48,2,50},{48,3,51},{48,4,52},{48,5,53},{48,6,54},{48,7,55},{48,8,56},{48,9,57},{48,10,58},{48,11,59},{48,12,60},{48,13,61},{48,14,62},{48,15,63},{48,16,32},{48,17,33},{48,18,34},{48,19,35},{48,20,36},{48,21,37},{48,22,38},{48,23,39},{48,24,40},{48,25,41},{48,26,42},{48,27,43},{48,28,44},{48,29,45},{48,30,46},{48,31,47},{49,0,49},{49,1,48},{49,2,51},{49,3,50},{49,4,53},{49,5,52},{49,6,55},{49,7,54},{49,8,57},{49,9,56},{49,10,59},{49,11,58},{49,12,61},{49,13,60},{49,14,63},{49,15,62},{49,16,33},{49,17,32},{49,18,35},{49,19,34},{49,20,37},{49,21,36},{49,22,39},{49,23,38},{49,24,41},{49,25,40},{49,26,43},{49,27,42},{49,28,45},{49,29,44},{49,30,47},{49,31,46},{50,0,50},{50,1,51},{50,2,48},{50,3,49},{50,4,54},{50,5,55},{50,6,52},{50,7,53},{50,8,58},{50,9,59},{50,10,56},{50,11,57},{50,12,62},{50,13,63},{50,14,60},{50,15,61},{50,16,34},{50,17,35},{50,18,32},{50,19,33},{50,20,38},{50,21,39},{50,22,36},{50,23,37},{50,24,42},{50,25,43},{50,26,40},{50,27,41},{50,28,46},{50,29,47},{50,30,44},{50,31,45},{51,0,51},{51,1,50},{51,2,49},{51,3,48},{51,4,55},{51,5,54},{51,6,53},{51,7,52},{51,8,59},{51,9,58},{51,10,57},{51,11,56},{51,12,63},{51,13,62},{51,14,61},{51,15,60},{51,16,35},{51,17,34},{51,18,33},{51,19,32},{51,20,39},{51,21,38},{51,22,37},{51,23,36},{51,24,43},{51,25,42},{51,26,41},{51,27,40},{51,28,47},{51,29,46},{51,30,45},{51,31,44},{52,0,52},{52,1,53},{52,2,54},{52,3,55},{52,4,48},{52,5,49},{52,6,50},{52,7,51},{52,8,60},{52,9,61},{52,10,62},{52,11,63},{52,12,56},{52,13,57},{52,14,58},{52,15,59},{52,16,36},{52,17,37},{52,18,38},{52,19,39},{52,20,32},{52,21,33},{52,22,34},{52,23,35},{52,24,44},{52,25,45},{52,26,46},{52,27,47},{52,28,40},{52,29,41},{52,30,42},{52,31,43},{53,0,53},{53,1,52},{53,2,55},{53,3,54},{53,4,49},{53,5,48},{53,6,51},{53,7,50},{53,8,61},{53,9,60},{53,10,63},{53,11,62},{53,12,57},{53,13,56},{53,14,59},{53,15,58},{53,16,37},{53,17,36},{53,18,39},{53,19,38},{53,20,33},{53,21,32},{53,22,35},{53,23,34},{53,24,45},{53,25,44},{53,26,47},{53,27,46},{53,28,41},{53,29,40},{53,30,43},{53,31,42},{54,0,54},{54,1,55},{54,2,52},{54,3,53},{54,4,50},{54,5,51},{54,6,48},{54,7,49},{54,8,62},{54,9,63},{54,10,60},{54,11,61},{54,12,58},{54,13,59},{54,14,56},{54,15,57},{54,16,38},{54,17,39},{54,18,36},{54,19,37},{54,20,34},{54,21,35},{54,22,32},{54,23,33},{54,24,46},{54,25,47},{54,26,44},{54,27,45},{54,28,42},{54,29,43},{54,30,40},{54,31,41},{55,0,55},{55,1,54},{55,2,53},{55,3,52},{55,4,51},{55,5,50},{55,6,49},{55,7,48},{55,8,63},{55,9,62},{55,10,61},{55,11,60},{55,12,59},{55,13,58},{55,14,57},{55,15,56},{55,16,39},{55,17,38},{55,18,37},{55,19,36},{55,20,35},{55,21,34},{55,22,33},{55,23,32},{55,24,47},{55,25,46},{55,26,45},{55,27,44},{55,28,43},{55,29,42},{55,30,41},{55,31,40},{56,0,56},{56,1,57},{56,2,58},{56,3,59},{56,4,60},{56,5,61},{56,6,62},{56,7,63},{56,8,48},{56,9,49},{56,10,50},{56,11,51},{56,12,52},{56,13,53},{56,14,54},{56,15,55},{56,16,40},{56,17,41},{56,18,42},{56,19,43},{56,20,44},{56,21,45},{56,22,46},{56,23,47},{56,24,32},{56,25,33},{56,26,34},{56,27,35},{56,28,36},{56,29,37},{56,30,38},{56,31,39},{57,0,57},{57,1,56},{57,2,59},{57,3,58},{57,4,61},{57,5,60},{57,6,63},{57,7,62},{57,8,49},{57,9,48},{57,10,51},{57,11,50},{57,12,53},{57,13,52},{57,14,55},{57,15,54},{57,16,41},{57,17,40},{57,18,43},{57,19,42},{57,20,45},{57,21,44},{57,22,47},{57,23,46},{57,24,33},{57,25,32},{57,26,35},{57,27,34},{57,28,37},{57,29,36},{57,30,39},{57,31,38},{58,0,58},{58,1,59},{58,2,56},{58,3,57},{58,4,62},{58,5,63},{58,6,60},{58,7,61},{58,8,50},{58,9,51},{58,10,48},{58,11,49},{58,12,54},{58,13,55},{58,14,52},{58,15,53},{58,16,42},{58,17,43},{58,18,40},{58,19,41},{58,20,46},{58,21,47},{58,22,44},{58,23,45},{58,24,34},{58,25,35},{58,26,32},{58,27,33},{58,28,38},{58,29,39},{58,30,36},{58,31,37},{59,0,59},{59,1,58},{59,2,57},{59,3,56},{59,4,63},{59,5,62},{59,6,61},{59,7,60},{59,8,51},{59,9,50},{59,10,49},{59,11,48},{59,12,55},{59,13,54},{59,14,53},{59,15,52},{59,16,43},{59,17,42},{59,18,41},{59,19,40},{59,20,47},{59,21,46},{59,22,45},{59,23,44},{59,24,35},{59,25,34},{59,26,33},{59,27,32},{59,28,39},{59,29,38},{59,30,37},{59,31,36},{60,0,60},{60,1,61},{60,2,62},{60,3,63},{60,4,56},{60,5,57},{60,6,58},{60,7,59},{60,8,52},{60,9,53},{60,10,54},{60,11,55},{60,12,48},{60,13,49},{60,14,50},{60,15,51},{60,16,44},{60,17,45},{60,18,46},{60,19,47},{60,20,40},{60,21,41},{60,22,42},{60,23,43},{60,24,36},{60,25,37},{60,26,38},{60,27,39},{60,28,32},{60,29,33},{60,30,34},{60,31,35},{61,0,61},{61,1,60},{61,2,63},{61,3,62},{61,4,57},{61,5,56},{61,6,59},{61,7,58},{61,8,53},{61,9,52},{61,10,55},{61,11,54},{61,12,49},{61,13,48},{61,14,51},{61,15,50},{61,16,45},{61,17,44},{61,18,47},{61,19,46},{61,20,41},{61,21,40},{61,22,43},{61,23,42},{61,24,37},{61,25,36},{61,26,39},{61,27,38},{61,28,33},{61,29,32},{61,30,35},{61,31,34},{62,0,62},{62,1,63},{62,2,60},{62,3,61},{62,4,58},{62,5,59},{62,6,56},{62,7,57},{62,8,54},{62,9,55},{62,10,52},{62,11,53},{62,12,50},{62,13,51},{62,14,48},{62,15,49},{62,16,46},{62,17,47},{62,18,44},{62,19,45},{62,20,42},{62,21,43},{62,22,40},{62,23,41},{62,24,38},{62,25,39},{62,26,36},{62,27,37},{62,28,34},{62,29,35},{62,30,32},{62,31,33},{63,0,63},{63,1,62},{63,2,61},{63,3,60},{63,4,59},{63,5,58},{63,6,57},{63,7,56},{63,8,55},{63,9,54},{63,10,53},{63,11,52},{63,12,51},{63,13,50},{63,14,49},{63,15,48},{63,16,47},{63,17,46},{63,18,45},{63,19,44},{63,20,43},{63,21,42},{63,22,41},{63,23,40},{63,24,39},{63,25,38},{63,26,37},{63,27,36},{63,28,35},{63,29,34},{63,30,33},{63,31,32},{64,0,64},{64,1,65},{64,2,66},{64,3,67},{64,4,68},{64,5,69},{64,6,70},{64,7,71},{64,8,72},{64,9,73},{64,10,74},{64,11,75},{64,12,76},{64,13,77},{64,14,78},{64,15,79},{64,16,80},{64,17,81},{64,18,82},{64,19,83},{64,20,84},{64,21,85},{64,22,86},{64,23,87},{64,24,88},{64,25,89},{64,26,90},{64,27,91},{64,28,92},{64,29,93},{64,30,94},{64,31,95},{64,32,96},{64,33,97},{64,34,98},{64,35,99},{64,36,100},{64,37,101},{64,38,102},{64,39,103},{64,40,104},{64,41,105},{64,42,106},{64,43,107},{64,44,108},{64,45,109},{64,46,110},{64,47,111},{64,48,112},{64,49,113},{64,50,114},{64,51,115},{64,52,116},{64,53,117},{64,54,118},{64,55,119},{64,56,120},{64,57,121},{64,58,122},{64,59,123},{64,60,124},{64,61,125},{64,62,126},{64,63,127},{65,0,65},{65,1,64},{65,2,67},{65,3,66},{65,4,69},{65,5,68},{65,6,71},{65,7,70},{65,8,73},{65,9,72},{65,10,75},{65,11,74},{65,12,77},{65,13,76},{65,14,79},{65,15,78},{65,16,81},{65,17,80},{65,18,83},{65,19,82},{65,20,85},{65,21,84},{65,22,87},{65,23,86},{65,24,89},{65,25,88},{65,26,91},{65,27,90},{65,28,93},{65,29,92},{65,30,95},{65,31,94},{65,32,97},{65,33,96},{65,34,99},{65,35,98},{65,36,101},{65,37,100},{65,38,103},{65,39,102},{65,40,105},{65,41,104},{65,42,107},{65,43,106},{65,44,109},{65,45,108},{65,46,111},{65,47,110},{65,48,113},{65,49,112},{65,50,115},{65,51,114},{65,52,117},{65,53,116},{65,54,119},{65,55,118},{65,56,121},{65,57,120},{65,58,123},{65,59,122},{65,60,125},{65,61,124},{65,62,127},{65,63,126},{66,0,66},{66,1,67},{66,2,64},{66,3,65},{66,4,70},{66,5,71},{66,6,68},{66,7,69},{66,8,74},{66,9,75},{66,10,72},{66,11,73},{66,12,78},{66,13,79},{66,14,76},{66,15,77},{66,16,82},{66,17,83},{66,18,80},{66,19,81},{66,20,86},{66,21,87},{66,22,84},{66,23,85},{66,24,90},{66,25,91},{66,26,88},{66,27,89},{66,28,94},{66,29,95},{66,30,92},{66,31,93},{66,32,98},{66,33,99},{66,34,96},{66,35,97},{66,36,102},{66,37,103},{66,38,100},{66,39,101},{66,40,106},{66,41,107},{66,42,104},{66,43,105},{66,44,110},{66,45,111},{66,46,108},{66,47,109},{66,48,114},{66,49,115},{66,50,112},{66,51,113},{66,52,118},{66,53,119},{66,54,116},{66,55,117},{66,56,122},{66,57,123},{66,58,120},{66,59,121},{66,60,126},{66,61,127},{66,62,124},{66,63,125},{67,0,67},{67,1,66},{67,2,65},{67,3,64},{67,4,71},{67,5,70},{67,6,69},{67,7,68},{67,8,75},{67,9,74},{67,10,73},{67,11,72},{67,12,79},{67,13,78},{67,14,77},{67,15,76},{67,16,83},{67,17,82},{67,18,81},{67,19,80},{67,20,87},{67,21,86},{67,22,85},{67,23,84},{67,24,91},{67,25,90},{67,26,89},{67,27,88},{67,28,95},{67,29,94},{67,30,93},{67,31,92},{67,32,99},{67,33,98},{67,34,97},{67,35,96},{67,36,103},{67,37,102},{67,38,101},{67,39,100},{67,40,107},{67,41,106},{67,42,105},{67,43,104},{67,44,111},{67,45,110},{67,46,109},{67,47,108},{67,48,115},{67,49,114},{67,50,113},{67,51,112},{67,52,119},{67,53,118},{67,54,117},{67,55,116},{67,56,123},{67,57,122},{67,58,121},{67,59,120},{67,60,127},{67,61,126},{67,62,125},{67,63,124},{68,0,68},{68,1,69},{68,2,70},{68,3,71},{68,4,64},{68,5,65},{68,6,66},{68,7,67},{68,8,76},{68,9,77},{68,10,78},{68,11,79},{68,12,72},{68,13,73},{68,14,74},{68,15,75},{68,16,84},{68,17,85},{68,18,86},{68,19,87},{68,20,80},{68,21,81},{68,22,82},{68,23,83},{68,24,92},{68,25,93},{68,26,94},{68,27,95},{68,28,88},{68,29,89},{68,30,90},{68,31,91},{68,32,100},{68,33,101},{68,34,102},{68,35,103},{68,36,96},{68,37,97},{68,38,98},{68,39,99},{68,40,108},{68,41,109},{68,42,110},{68,43,111},{68,44,104},{68,45,105},{68,46,106},{68,47,107},{68,48,116},{68,49,117},{68,50,118},{68,51,119},{68,52,112},{68,53,113},{68,54,114},{68,55,115},{68,56,124},{68,57,125},{68,58,126},{68,59,127},{68,60,120},{68,61,121},{68,62,122},{68,63,123},{69,0,69},{69,1,68},{69,2,71},{69,3,70},{69,4,65},{69,5,64},{69,6,67},{69,7,66},{69,8,77},{69,9,76},{69,10,79},{69,11,78},{69,12,73},{69,13,72},{69,14,75},{69,15,74},{69,16,85},{69,17,84},{69,18,87},{69,19,86},{69,20,81},{69,21,80},{69,22,83},{69,23,82},{69,24,93},{69,25,92},{69,26,95},{69,27,94},{69,28,89},{69,29,88},{69,30,91},{69,31,90},{69,32,101},{69,33,100},{69,34,103},{69,35,102},{69,36,97},{69,37,96},{69,38,99},{69,39,98},{69,40,109},{69,41,108},{69,42,111},{69,43,110},{69,44,105},{69,45,104},{69,46,107},{69,47,106},{69,48,117},{69,49,116},{69,50,119},{69,51,118},{69,52,113},{69,53,112},{69,54,115},{69,55,114},{69,56,125},{69,57,124},{69,58,127},{69,59,126},{69,60,121},{69,61,120},{69,62,123},{69,63,122},{70,0,70},{70,1,71},{70,2,68},{70,3,69},{70,4,66},{70,5,67},{70,6,64},{70,7,65},{70,8,78},{70,9,79},{70,10,76},{70,11,77},{70,12,74},{70,13,75},{70,14,72},{70,15,73},{70,16,86},{70,17,87},{70,18,84},{70,19,85},{70,20,82},{70,21,83},{70,22,80},{70,23,81},{70,24,94},{70,25,95},{70,26,92},{70,27,93},{70,28,90},{70,29,91},{70,30,88},{70,31,89},{70,32,102},{70,33,103},{70,34,100},{70,35,101},{70,36,98},{70,37,99},{70,38,96},{70,39,97},{70,40,110},{70,41,111},{70,42,108},{70,43,109},{70,44,106},{70,45,107},{70,46,104},{70,47,105},{70,48,118},{70,49,119},{70,50,116},{70,51,117},{70,52,114},{70,53,115},{70,54,112},{70,55,113},{70,56,126},{70,57,127},{70,58,124},{70,59,125},{70,60,122},{70,61,123},{70,62,120},{70,63,121},{71,0,71},{71,1,70},{71,2,69},{71,3,68},{71,4,67},{71,5,66},{71,6,65},{71,7,64},{71,8,79},{71,9,78},{71,10,77},{71,11,76},{71,12,75},{71,13,74},{71,14,73},{71,15,72},{71,16,87},{71,17,86},{71,18,85},{71,19,84},{71,20,83},{71,21,82},{71,22,81},{71,23,80},{71,24,95},{71,25,94},{71,26,93},{71,27,92},{71,28,91},{71,29,90},{71,30,89},{71,31,88},{71,32,103},{71,33,102},{71,34,101},{71,35,100},{71,36,99},{71,37,98},{71,38,97},{71,39,96},{71,40,111},{71,41,110},{71,42,109},{71,43,108},{71,44,107},{71,45,106},{71,46,105},{71,47,104},{71,48,119},{71,49,118},{71,50,117},{71,51,116},{71,52,115},{71,53,114},{71,54,113},{71,55,112},{71,56,127},{71,57,126},{71,58,125},{71,59,124},{71,60,123},{71,61,122},{71,62,121},{71,63,120},{72,0,72},{72,1,73},{72,2,74},{72,3,75},{72,4,76},{72,5,77},{72,6,78},{72,7,79},{72,8,64},{72,9,65},{72,10,66},{72,11,67},{72,12,68},{72,13,69},{72,14,70},{72,15,71},{72,16,88},{72,17,89},{72,18,90},{72,19,91},{72,20,92},{72,21,93},{72,22,94},{72,23,95},{72,24,80},{72,25,81},{72,26,82},{72,27,83},{72,28,84},{72,29,85},{72,30,86},{72,31,87},{72,32,104},{72,33,105},{72,34,106},{72,35,107},{72,36,108},{72,37,109},{72,38,110},{72,39,111},{72,40,96},{72,41,97},{72,42,98},{72,43,99},{72,44,100},{72,45,101},{72,46,102},{72,47,103},{72,48,120},{72,49,121},{72,50,122},{72,51,123},{72,52,124},{72,53,125},{72,54,126},{72,55,127},{72,56,112},{72,57,113},{72,58,114},{72,59,115},{72,60,116},{72,61,117},{72,62,118},{72,63,119},{73,0,73},{73,1,72},{73,2,75},{73,3,74},{73,4,77},{73,5,76},{73,6,79},{73,7,78},{73,8,65},{73,9,64},{73,10,67},{73,11,66},{73,12,69},{73,13,68},{73,14,71},{73,15,70},{73,16,89},{73,17,88},{73,18,91},{73,19,90},{73,20,93},{73,21,92},{73,22,95},{73,23,94},{73,24,81},{73,25,80},{73,26,83},{73,27,82},{73,28,85},{73,29,84},{73,30,87},{73,31,86},{73,32,105},{73,33,104},{73,34,107},{73,35,106},{73,36,109},{73,37,108},{73,38,111},{73,39,110},{73,40,97},{73,41,96},{73,42,99},{73,43,98},{73,44,101},{73,45,100},{73,46,103},{73,47,102},{73,48,121},{73,49,120},{73,50,123},{73,51,122},{73,52,125},{73,53,124},{73,54,127},{73,55,126},{73,56,113},{73,57,112},{73,58,115},{73,59,114},{73,60,117},{73,61,116},{73,62,119},{73,63,118},{74,0,74},{74,1,75},{74,2,72},{74,3,73},{74,4,78},{74,5,79},{74,6,76},{74,7,77},{74,8,66},{74,9,67},{74,10,64},{74,11,65},{74,12,70},{74,13,71},{74,14,68},{74,15,69},{74,16,90},{74,17,91},{74,18,88},{74,19,89},{74,20,94},{74,21,95},{74,22,92},{74,23,93},{74,24,82},{74,25,83},{74,26,80},{74,27,81},{74,28,86},{74,29,87},{74,30,84},{74,31,85},{74,32,106},{74,33,107},{74,34,104},{74,35,105},{74,36,110},{74,37,111},{74,38,108},{74,39,109},{74,40,98},{74,41,99},{74,42,96},{74,43,97},{74,44,102},{74,45,103},{74,46,100},{74,47,101},{74,48,122},{74,49,123},{74,50,120},{74,51,121},{74,52,126},{74,53,127},{74,54,124},{74,55,125},{74,56,114},{74,57,115},{74,58,112},{74,59,113},{74,60,118},{74,61,119},{74,62,116},{74,63,117},{75,0,75},{75,1,74},{75,2,73},{75,3,72},{75,4,79},{75,5,78},{75,6,77},{75,7,76},{75,8,67},{75,9,66},{75,10,65},{75,11,64},{75,12,71},{75,13,70},{75,14,69},{75,15,68},{75,16,91},{75,17,90},{75,18,89},{75,19,88},{75,20,95},{75,21,94},{75,22,93},{75,23,92},{75,24,83},{75,25,82},{75,26,81},{75,27,80},{75,28,87},{75,29,86},{75,30,85},{75,31,84},{75,32,107},{75,33,106},{75,34,105},{75,35,104},{75,36,111},{75,37,110},{75,38,109},{75,39,108},{75,40,99},{75,41,98},{75,42,97},{75,43,96},{75,44,103},{75,45,102},{75,46,101},{75,47,100},{75,48,123},{75,49,122},{75,50,121},{75,51,120},{75,52,127},{75,53,126},{75,54,125},{75,55,124},{75,56,115},{75,57,114},{75,58,113},{75,59,112},{75,60,119},{75,61,118},{75,62,117},{75,63,116}},{{0,0,0},{1,0,1},{2,0,2},{2,1,3},{3,0,3},{3,1,2},{4,0,4},{4,1,5},{4,2,6},{5,0,5},{5,1,4},{5,2,7},{5,3,8},{6,0,6},{6,1,7},{6,2,4},{7,0,7},{7,1,6},{7,2,5},{7,3,9},{7,4,10},{8,0,8},{8,1,9},{8,2,10},{8,3,5},{9,0,9},{9,1,8},{9,2,11},{9,3,7},{9,4,12},{9,5,13},{10,0,10},{10,1,11},{10,2,8},{10,3,12},{10,4,7},{11,0,11},{11,1,10},{11,2,9},{11,3,13},{11,4,14},{11,5,12},{12,0,12},{12,1,13},{12,2,14},{12,3,10},{12,4,9},{12,5,11},{13,0,13},{13,1,12},{13,2,15},{13,3,11},{13,4,16},{13,5,9},{14,0,14},{14,1,15},{14,2,12},{14,3,16},{14,4,11},{14,5,17},{14,6,18},{14,7,19},{14,8,20},{15,0,15},{15,1,14},{15,2,13},{15,3,17},{15,4,18},{15,5,16},{15,6,19},{15,7,20},{15,8,21},{15,9,22},{16,0,16},{16,1,17},{16,2,18},{16,3,14},{16,4,13},{16,5,15},{16,6,20},{16,7,21},{16,8,19},{17,0,17},{17,1,16},{17,2,19},{17,3,15},{17,4,20},{17,5,14},{17,6,21},{17,7,18},{17,8,22},{17,9,23},{17,10,24},{18,0,18},{18,1,19},{18,2,16},{18,3,20},{18,4,15},{18,5,21},{18,6,14},{18,7,17},{18,8,23},{18,9,24},{18,10,25},{19,0,19},{19,1,18},{19,2,17},{19,3,21},{19,4,22},{19,5,20},{19,6,15},{19,7,14},{19,8,16},{20,0,20},{20,1,21},{20,2,22},{20,3,18},{20,4,17},{20,5,19},{20,6,16},{20,7,15},{20,8,14},{21,0,21},{21,1,20},{21,2,23},{21,3,19},{21,4,24},{21,5,18},{21,6,17},{21,7,16},{21,8,15},{21,9,25},{21,10,26},{21,11,27},{21,12,28},{22,0,22},{22,1,23},{22,2,20},{22,3,24},{22,4,19},{22,5,25},{22,6,26},{22,7,27},{22,8,17},{22,9,15},{23,0,23},{23,1,22},{23,2,21},{23,3,25},{23,4,26},{23,5,24},{23,6,27},{23,7,28},{23,8,18},{23,9,17},{23,10,29},{23,11,30},{23,12,31},{23,13,32},{24,0,24},{24,1,25},{24,2,26},{24,3,22},{24,4,21},{24,5,23},{24,6,28},{24,7,29},{24,8,27},{24,9,18},{24,10,17},{25,0,25},{25,1,24},{25,2,27},{25,3,23},{25,4,28},{25,5,22},{25,6,29},{25,7,26},{25,8,30},{25,9,21},{25,10,18},{26,0,26},{26,1,27},{26,2,24},{26,3,28},{26,4,23},{26,5,29},{26,6,22},{26,7,25},{26,8,31},{26,9,30},{26,10,21},{26,11,32},{26,12,33},{26,13,34},{26,14,35},{26,15,36},{27,0,27},{27,1,26},{27,2,25},{27,3,29},{27,4,30},{27,5,28},{27,6,23},{27,7,22},{27,8,24},{27,9,31},{27,10,32},{27,11,21},{27,12,34},{27,13,33},{27,14,36},{27,15,35},{28,0,28},{28,1,29},{28,2,30},{28,3,26},{28,4,25},{28,5,27},{28,6,24},{28,7,23},{28,8,32},{28,9,33},{28,10,31},{28,11,34},{28,12,21},{29,0,29},{29,1,28},{29,2,31},{29,3,27},{29,4,32},{29,5,26},{29,6,25},{29,7,24},{29,8,33},{29,9,34},{29,10,23},{29,11,35},{29,12,30},{29,13,36},{29,14,37},{29,15,38},{29,16,39},{29,17,40},{30,0,30},{30,1,31},{30,2,28},{30,3,32},{30,4,27},{30,5,33},{30,6,34},{30,7,35},{30,8,25},{30,9,26},{30,10,36},{30,11,23},{30,12,29},{30,13,37},{30,14,38},{30,15,39},{30,16,40},{30,17,41},{31,0,31},{31,1,30},{31,2,29},{31,3,33},{31,4,34},{31,5,32},{31,6,35},{31,7,36},{31,8,26},{31,9,27},{31,10,28},{31,11,37},{31,12,23},{31,13,38},{31,14,39},{31,15,40},{31,16,41},{31,17,42},{31,18,43},{32,0,32},{32,1,33},{32,2,34},{32,3,30},{32,4,29},{32,5,31},{32,6,36},{32,7,37},{32,8,28},{32,9,35},{32,10,27},{32,11,26},{32,12,38},{32,13,23},{33,0,33},{33,1,32},{33,2,35},{33,3,31},{33,4,36},{33,5,30},{33,6,37},{33,7,34},{33,8,29},{33,9,28},{33,10,38},{33,11,39},{33,12,26},{33,13,27},{33,14,40},{33,15,41},{33,16,42},{33,17,43},{33,18,44},{33,19,45},{34,0,34},{34,1,35},{34,2,32},{34,3,36},{34,4,31},{34,5,37},{34,6,30},{34,7,33},{34,8,38},{34,9,29},{34,10,39},{34,11,28},{34,12,27},{34,13,26},{34,14,41},{34,15,42},{34,16,43},{34,17,44},{34,18,45},{34,19,46},{34,20,47},{35,0,35},{35,1,34},{35,2,33},{35,3,37},{35,4,38},{35,5,36},{35,6,31},{35,7,30},{35,8,39},{35,9,32},{35,10,40},{35,11,29},{35,12,41},{35,13,42},{35,14,26},{35,15,27},{36,0,36},{36,1,37},{36,2,38},{36,3,34},{36,4,33},{36,5,35},{36,6,32},{36,7,31},{36,8,40},{36,9,39},{36,10,30},{36,11,41},{36,12,42},{36,13,29},{36,14,27},{36,15,26},{37,0,37},{37,1,36},{37,2,39},{37,3,35},{37,4,40},{37,5,34},{37,6,33},{37,7,32},{37,8,41},{37,9,38},{37,10,42},{37,11,31},{37,12,43},{37,13,30},{37,14,29},{37,15,44},{37,16,45},{37,17,46},{37,18,47},{37,19,48},{37,20,49},{37,21,50},{38,0,38},{38,1,39},{38,2,36},{38,3,40},{38,4,35},{38,5,41},{38,6,42},{38,7,43},{38,8,34},{38,9,37},{38,10,33},{38,11,44},{38,12,32},{38,13,31},{38,14,30},{38,15,29},{38,16,46},{38,17,45},{38,18,48},{38,19,47},{38,20,50},{38,21,49},{39,0,39},{39,1,38},{39,2,37},{39,3,41},{39,4,42},{39,5,40},{39,6,43},{39,7,44},{39,8,35},{39,9,36},{39,10,34},{39,11,33},{39,12,45},{39,13,46},{39,14,31},{39,15,30},{39,16,29},{39,17,47},{39,18,49},{39,19,50},{39,20,48},{39,21,51},{39,22,52},{40,0,40},{40,1,41},{40,2,42},{40,3,38},{40,4,37},{40,5,39},{40,6,44},{40,7,45},{40,8,36},{40,9,43},{40,10,35},{40,11,46},{40,12,47},{40,13,48},{40,14,33},{40,15,31},{40,16,30},{40,17,29},{41,0,41},{41,1,40},{41,2,43},{41,3,39},{41,4,44},{41,5,38},{41,6,45},{41,7,42},{41,8,37},{41,9,46},{41,10,47},{41,11,36},{41,12,35},{41,13,49},{41,14,34},{41,15,33},{41,16,31},{41,17,30},{42,0,42},{42,1,43},{42,2,40},{42,3,44},{42,4,39},{42,5,45},{42,6,38},{42,7,41},{42,8,46},{42,9,47},{42,10,37},{42,11,48},{42,12,36},{42,13,35},{42,14,49},{42,15,34},{42,16,33},{42,17,31},{42,18,50},{42,19,51},{42,20,52},{42,21,53},{42,22,54},{42,23,55},{42,24,56},{43,0,43},{43,1,42},{43,2,41},{43,3,45},{43,4,46},{43,5,44},{43,6,39},{43,7,38},{43,8,47},{43,9,40},{43,10,48},{43,11,49},{43,12,37},{43,13,50},{43,14,51},{43,15,52},{43,16,34},{43,17,33},{43,18,31},{44,0,44},{44,1,45},{44,2,46},{44,3,42},{44,4,41},{44,5,43},{44,6,40},{44,7,39},{44,8,48},{44,9,49},{44,10,50},{44,11,38},{44,12,51},{44,13,47},{44,14,52},{44,15,37},{44,16,53},{44,17,34},{44,18,33},{44,19,54},{44,20,55},{44,21,56},{44,22,57},{44,23,58},{44,24,59},{44,25,60},{44,26,61},{45,0,45},{45,1,44},{45,2,47},{45,3,43},{45,4,48},{45,5,42},{45,6,41},{45,7,40},{45,8,49},{45,9,50},{45,10,46},{45,11,51},{45,12,39},{45,13,52},{45,14,53},{45,15,54},{45,16,37},{45,17,38},{45,18,34},{45,19,33},{46,0,46},{46,1,47},{46,2,44},{46,3,48},{46,4,43},{46,5,49},{46,6,50},{46,7,51},{46,8,42},{46,9,41},{46,10,45},{46,11,40},{46,12,52},{46,13,39},{46,14,54},{46,15,53},{46,16,38},{46,17,37},{46,18,55},{46,19,34},{46,20,56},{46,21,57},{46,22,58},{46,23,59},{46,24,60},{46,25,61},{46,26,62},{46,27,63},{47,0,47},{47,1,46},{47,2,45},{47,3,49},{47,4,50},{47,5,48},{47,6,51},{47,7,52},{47,8,43},{47,9,42},{47,10,41},{47,11,53},{47,12,40},{47,13,44},{47,14,55},{47,15,56},{47,16,54},{47,17,39},{47,18,37},{47,19,38},{47,20,34},{48,0,48},{48,1,49},{48,2,50},{48,3,46},{48,4,45},{48,5,47},{48,6,52},{48,7,53},{48,8,44},{48,9,51},{48,10,43},{48,11,42},{48,12,54},{48,13,40},{48,14,56},{48,15,55},{48,16,57},{48,17,58},{48,18,38},{48,19,37},{48,20,39},{48,21,59},{48,22,60},{48,23,61},{48,24,62},{48,25,63},{48,26,64},{48,27,65},{48,28,66},{49,0,49},{49,1,48},{49,2,51},{49,3,47},{49,4,52},{49,5,46},{49,6,53},{49,7,50},{49,8,45},{49,9,44},{49,10,54},{49,11,43},{49,12,55},{49,13,41},{49,14,42},{49,15,57},{49,16,56},{49,17,59},{49,18,39},{49,19,58},{49,20,37},{49,21,38},{50,0,50},{50,1,51},{50,2,48},{50,3,52},{50,4,47},{50,5,53},{50,6,46},{50,7,49},{50,8,54},{50,9,45},{50,10,44},{50,11,55},{50,12,56},{50,13,43},{50,14,57},{50,15,58},{50,16,59},{50,17,60},{50,18,42},{50,19,39},{50,20,38},{50,21,37},{51,0,51},{51,1,50},{51,2,49},{51,3,53},{51,4,54},{51,5,52},{51,6,47},{51,7,46},{51,8,55},{51,9,48},{51,10,56},{51,11,45},{51,12,44},{51,13,57},{51,14,43},{51,15,59},{51,16,58},{51,17,61},{51,18,60},{51,19,42},{51,20,62},{51,21,39},{51,22,63},{51,23,64},{51,24,65},{51,25,66},{51,26,67},{51,27,68},{51,28,69},{51,29,70},{51,30,71},{52,0,52},{52,1,53},{52,2,54},{52,3,50},{52,4,49},{52,5,51},{52,6,48},{52,7,47},{52,8,56},{52,9,55},{52,10,57},{52,11,58},{52,12,46},{52,13,45},{52,14,44},{52,15,43},{52,16,60},{52,17,62},{52,18,59},{52,19,61},{52,20,42},{52,21,63},{52,22,39},{53,0,53},{53,1,52},{53,2,55},{53,3,51},{53,4,56},{53,5,50},{53,6,49},{53,7,48},{53,8,57},{53,9,54},{53,10,58},{53,11,47},{53,12,59},{53,13,60},{53,14,45},{53,15,46},{53,16,44},{53,17,63},{53,18,61},{53,19,62},{53,20,64},{53,21,42},{53,22,65},{53,23,66},{53,24,67},{53,25,68},{53,26,69},{53,27,70},{53,28,71},{53,29,72},{53,30,73},{53,31,74},{54,0,54},{54,1,55},{54,2,52},{54,3,56},{54,4,51},{54,5,57},{54,6,58},{54,7,59},{54,8,50},{54,9,53},{54,10,49},{54,11,60},{54,12,48},{54,13,61},{54,14,46},{54,15,45},{54,16,47},{54,17,64},{54,18,62},{54,19,44},{54,20,63},{54,21,65},{54,22,42},{54,23,67},{54,24,66},{54,25,69},{54,26,68},{54,27,71},{54,28,70},{54,29,73},{54,30,72},{54,31,75},{54,32,76},{55,0,55},{55,1,54},{55,2,53},{55,3,57},{55,4,58},{55,5,56},{55,6,59},{55,7,60},{55,8,51},{55,9,52},{55,10,61},{55,11,50},{55,12,49},{55,13,62},{55,14,47},{55,15,48},{55,16,63},{55,17,65},{55,18,46},{55,19,64},{55,20,44},{55,21,66},{55,22,67},{55,23,42},{55,24,68},{55,25,70},{55,26,71},{55,27,69},{55,28,72},{55,29,74},{55,30,75},{55,31,73},{55,32,77},{55,33,78},{56,0,56},{56,1,57},{56,2,58},{56,3,54},{56,4,53},{56,5,55},{56,6,60},{56,7,61},{56,8,52},{56,9,59},{56,10,51},{56,11,62},{56,12,50},{56,13,63},{56,14,48},{56,15,47},{56,16,49},{56,17,66},{56,18,64},{56,19,65},{56,20,46},{56,21,44},{56,22,68},{56,23,69},{56,24,42},{57,0,57},{57,1,56},{57,2,59},{57,3,55},{57,4,60},{57,5,54},{57,6,61},{57,7,58},{57,8,53},{57,9,62},{57,10,52},{57,11,63},{57,12,64},{57,13,51},{57,14,50},{57,15,49},{57,16,48},{57,17,67},{57,18,65},{57,19,66},{57,20,68},{57,21,46},{57,22,44},{57,23,70},{57,24,69},{57,25,71},{57,26,72},{57,27,73},{57,28,74},{57,29,75},{57,30,76},{57,31,77},{57,32,78},{57,33,79},{57,34,80},{58,0,58},{58,1,59},{58,2,56},{58,3,60},{58,4,55},{58,5,61},{58,6,54},{58,7,57},{58,8,62},{58,9,63},{58,10,53},{58,11,52},{58,12,65},{58,13,64},{58,14,66},{58,15,50},{58,16,51},{58,17,48},{58,18,67},{58,19,49},{58,20,69},{58,21,68},{58,22,46},{58,23,44},{58,24,70},{58,25,72},{58,26,73},{58,27,74},{58,28,75},{58,29,71},{58,30,77},{58,31,76},{58,32,79},{58,33,80},{58,34,81},{59,0,59},{59,1,58},{59,2,57},{59,3,61},{59,4,62},{59,5,60},{59,6,55},{59,7,54},{59,8,63},{59,9,56},{59,10,64},{59,11,65},{59,12,53},{59,13,66},{59,14,67},{59,15,51},{59,16,50},{59,17,49},{59,18,52},{59,19,68},{59,20,70},{59,21,48},{59,22,69},{59,23,46},{59,24,44},{59,25,73},{59,26,74},{59,27,72},{59,28,76},{59,29,77},{59,30,78},{59,31,79},{59,32,75},{59,33,81},{59,34,82},{59,35,83},{60,0,60},{60,1,61},{60,2,62},{60,3,58},{60,4,57},{60,5,59},{60,6,56},{60,7,55},{60,8,64},{60,9,65},{60,10,63},{60,11,54},{60,12,66},{60,13,53},{60,14,68},{60,15,67},{60,16,52},{60,17,50},{60,18,51},{60,19,69},{60,20,71},{60,21,70},{60,22,48},{60,23,72},{60,24,46},{60,25,44},{60,26,75},{60,27,76},{60,28,73},{60,29,78},{60,30,74},{60,31,80},{60,32,81},{60,33,77},{60,34,79},{61,0,61},{61,1,60},{61,2,63},{61,3,59},{61,4,64},{61,5,58},{61,6,57},{61,7,56},{61,8,65},{61,9,66},{61,10,55},{61,11,67},{61,12,62},{61,13,54},{61,14,69},{61,15,68},{61,16,70},{61,17,51},{61,18,53},{61,19,52},{61,20,72},{61,21,71},{61,22,73},{61,23,48},{61,24,74},{61,25,46},{61,26,44},{62,0,62},{62,1,63},{62,2,60},{62,3,64},{62,4,59},{62,5,65},{62,6,66},{62,7,67},{62,8,58},{62,9,57},{62,10,68},{62,11,56},{62,12,61},{62,13,55},{62,14,70},{62,15,69},{62,16,71},{62,17,52},{62,18,54},{62,19,53},{62,20,51},{62,21,72},{62,22,74},{62,23,73},{62,24,48},{62,25,75},{62,26,46},{62,27,77},{62,28,78},{62,29,76},{62,30,79},{62,31,81},{62,32,80},{62,33,82},{62,34,83},{62,35,84},{62,36,85},{63,0,63},{63,1,62},{63,2,61},{63,3,65},{63,4,66},{63,5,64},{63,6,67},{63,7,68},{63,8,59},{63,9,58},{63,10,60},{63,11,57},{63,12,69},{63,13,56},{63,14,71},{63,15,70},{63,16,55},{63,17,53},{63,18,72},{63,19,73},{63,20,54},{63,21,52},{63,22,51},{63,23,74},{63,24,75},{63,25,48},{63,26,76},{63,27,46},{64,0,64},{64,1,65},{64,2,66},{64,3,62},{64,4,61},{64,5,63},{64,6,68},{64,7,69},{64,8,60},{64,9,67},{64,10,59},{64,11,70},{64,12,57},{64,13,58},{64,14,72},{64,15,71},{64,16,73},{64,17,54},{64,18,56},{64,19,55},{64,20,53},{64,21,74},{64,22,75},{64,23,51},{64,24,76},{64,25,77},{64,26,48},{64,27,78},{64,28,79},{64,29,80},{64,30,81},{64,31,82},{64,32,83},{64,33,84},{64,34,85},{64,35,86},{64,36,87},{64,37,88},{64,38,89},{65,0,65},{65,1,64},{65,2,67},{65,3,63},{65,4,68},{65,5,62},{65,6,69},{65,7,66},{65,8,61},{65,9,60},{65,10,70},{65,11,59},{65,12,58},{65,13,71},{65,14,73},{65,15,72},{65,16,74},{65,17,55},{65,18,57},{65,19,56},{65,20,75},{65,21,54},{65,22,53},{65,23,76},{65,24,51},{65,25,78},{65,26,77},{65,27,48},{65,28,80},{65,29,79},{65,30,82},{65,31,83},{65,32,84},{65,33,85},{65,34,86},{65,35,87},{65,36,88},{65,37,89},{65,38,90},{66,0,66},{66,1,67},{66,2,64},{66,3,68},{66,4,63},{66,5,69},{66,6,62},{66,7,65},{66,8,70},{66,9,61},{66,10,71},{66,11,72},{66,12,60},{66,13,59},{66,14,58},{66,15,73},{66,16,75},{66,17,56},{66,18,74},{66,19,57},{66,20,76},{66,21,55},{66,22,77},{66,23,53},{66,24,54},{66,25,51},{66,26,78},{66,27,79},{66,28,48},{67,0,67},{67,1,66},{67,2,65},{67,3,69},{67,4,70},{67,5,68},{67,6,63},{67,7,62},{67,8,71},{67,9,64},{67,10,72},{67,11,61},{67,12,73},{67,13,74},{67,14,59},{67,15,60},{67,16,76},{67,17,57},{67,18,58},{67,19,75},{67,20,77},{67,21,78},{67,22,55},{67,23,54},{67,24,53},{67,25,79},{67,26,51},{67,27,80},{67,28,81},{67,29,82},{67,30,83},{67,31,84},{67,32,85},{67,33,86},{67,34,87},{67,35,88},{67,36,89},{67,37,90},{67,38,91},{67,39,92},{68,0,68},{68,1,69},{68,2,70},{68,3,66},{68,4,65},{68,5,67},{68,6,64},{68,7,63},{68,8,72},{68,9,71},{68,10,62},{68,11,73},{68,12,74},{68,13,75},{68,14,60},{68,15,61},{68,16,77},{68,17,76},{68,18,78},{68,19,59},{68,20,57},{68,21,58},{68,22,56},{68,23,79},{68,24,55},{68,25,53},{68,26,54},{68,27,51},{68,28,82},{68,29,81},{68,30,80},{68,31,85},{68,32,86},{68,33,83},{68,34,84},{68,35,89},{68,36,90},{68,37,87},{68,38,88},{68,39,91},{69,0,69},{69,1,68},{69,2,71},{69,3,67},{69,4,72},{69,5,66},{69,6,65},{69,7,64},{69,8,73},{69,9,70},{69,10,74},{69,11,75},{69,12,63},{69,13,76},{69,14,61},{69,15,62},{69,16,78},{69,17,77},{69,18,79},{69,19,60},{69,20,58},{69,21,80},{69,22,59},{69,23,56},{69,24,57},{69,25,54},{69,26,53},{69,27,55},{69,28,51},{69,29,83},{69,30,84},{69,31,86},{69,32,82},{69,33,87},{69,34,88},{69,35,85},{69,36,91},{69,37,92},{69,38,93},{69,39,94},{69,40,95},{69,41,96},{70,0,70},{70,1,71},{70,2,68},{70,3,72},{70,4,67},{70,5,73},{70,6,74},{70,7,75},{70,8,66},{70,9,69},{70,10,65},{70,11,64},{70,12,76},{70,13,77},{70,14,62},{70,15,63},{70,16,61},{70,17,78},{70,18,80},{70,19,79},{70,20,59},{70,21,60},{70,22,81},{70,23,57},{70,24,58},{70,25,55},{70,26,82},{70,27,53},{70,28,54},{70,29,51},{70,30,85},{70,31,87},{70,32,88},{70,33,89},{70,34,90},{70,35,91},{70,36,84},{70,37,86},{70,38,92},{70,39,93},{70,40,94},{70,41,95},{71,0,71},{71,1,70},{71,2,69},{71,3,73},{71,4,74},{71,5,72},{71,6,75},{71,7,76},{71,8,67},{71,9,68},{71,10,66},{71,11,77},{71,12,78},{71,13,65},{71,14,63},{71,15,64},{71,16,62},{71,17,79},{71,18,81},{71,19,80},{71,20,60},{71,21,61},{71,22,82},{71,23,83},{71,24,84},{71,25,57},{71,26,55},{71,27,54},{71,28,53},{71,29,58},{71,30,51},{72,0,72},{72,1,73},{72,2,74},{72,3,70},{72,4,69},{72,5,71},{72,6,76},{72,7,77},{72,8,68},{72,9,75},{72,10,67},{72,11,66},{72,12,79},{72,13,78},{72,14,64},{72,15,65},{72,16,80},{72,17,81},{72,18,63},{72,19,82},{72,20,61},{72,21,62},{72,22,83},{72,23,60},{72,24,85},{72,25,58},{72,26,57},{72,27,59},{72,28,55},{72,29,53},{72,30,54},{72,31,88},{72,32,87},{72,33,90},{72,34,89},{72,35,92},{72,36,86},{72,37,84},{72,38,94},{72,39,95},{72,40,93},{72,41,97},{72,42,98},{73,0,73},{73,1,72},{73,2,75},{73,3,71},{73,4,76},{73,5,70},{73,6,77},{73,7,74},{73,8,69},{73,9,78},{73,10,79},{73,11,68},{73,12,67},{73,13,80},{73,14,65},{73,15,66},{73,16,64},{73,17,82},{73,18,83},{73,19,63},{73,20,81},{73,21,84},{73,22,61},{73,23,62},{73,24,86},{73,25,59},{73,26,58},{73,27,57},{73,28,60},{73,29,54},{73,30,53},{73,31,55},{73,32,89},{73,33,88},{73,34,91},{73,35,90},{73,36,92},{73,37,93},{73,38,87},{73,39,96},{73,40,97},{73,41,94},{74,0,74},{74,1,75},{74,2,72},{74,3,76},{74,4,71},{74,5,77},{74,6,70},{74,7,73},{74,8,78},{74,9,79},{74,10,69},{74,11,80},{74,12,68},{74,13,67},{74,14,81},{74,15,82},{74,16,65},{74,17,83},{74,18,66},{74,19,84},{74,20,85},{74,21,64},{74,22,62},{74,23,63},{74,24,61},{74,25,86},{74,26,59},{74,27,58},{74,28,57},{74,29,55},{74,30,60},{74,31,53},{75,0,75},{75,1,74},{75,2,73},{75,3,77},{75,4,78},{75,5,76},{75,6,71},{75,7,70},{75,8,79},{75,9,72},{75,10,80},{75,11,69},{75,12,81},{75,13,68},{75,14,82},{75,15,83},{75,16,66},{75,17,84},{75,18,85},{75,19,67},{75,20,65},{75,21,86},{75,22,64},{75,23,87},{75,24,63},{75,25,62},{75,26,60},{75,27,88},{75,28,58},{75,29,57},{75,30,55},{75,31,54},{75,32,59},{75,33,91},{75,34,92},{75,35,93},{75,36,94},{75,37,95},{75,38,96},{75,39,97},{75,40,98},{75,41,99},{75,42,100},{75,43,101},{75,44,102}},{{0,0,0},{1,0,1},{2,0,2},{3,0,3},{3,1,4},{4,0,4},{4,1,3},{5,0,5},{5,1,6},{5,2,7},{6,0,6},{6,1,5},{6,2,8},{7,0,7},{7,1,8},{7,2,5},{8,0,8},{8,1,7},{8,2,6},{9,0,9},{9,1,10},{9,2,11},{9,3,12},{9,4,13},{10,0,10},{10,1,9},{10,2,12},{10,3,11},{10,4,14},{11,0,11},{11,1,12},{11,2,9},{11,3,10},{11,4,15},{11,5,16},{12,0,12},{12,1,11},{12,2,10},{12,3,9},{12,4,16},{12,5,15},{13,0,13},{13,1,14},{13,2,15},{13,3,16},{13,4,9},{14,0,14},{14,1,13},{14,2,16},{14,3,15},{14,4,10},{15,0,15},{15,1,16},{15,2,13},{15,3,14},{15,4,11},{15,5,12},{16,0,16},{16,1,15},{16,2,14},{16,3,13},{16,4,12},{16,5,11},{17,0,17},{17,1,18},{17,2,19},{17,3,20},{17,4,21},{17,5,22},{17,6,23},{17,7,24},{17,8,25},{18,0,18},{18,1,17},{18,2,20},{18,3,19},{18,4,22},{18,5,21},{18,6,24},{18,7,23},{18,8,26},{19,0,19},{19,1,20},{19,2,17},{19,3,18},{19,4,23},{19,5,24},{19,6,21},{19,7,22},{19,8,27},{19,9,28},{20,0,20},{20,1,19},{20,2,18},{20,3,17},{20,4,24},{20,5,23},{20,6,22},{20,7,21},{20,8,28},{20,9,27},{21,0,21},{21,1,22},{21,2,23},{21,3,24},{21,4,17},{21,5,18},{21,6,19},{21,7,20},{21,8,29},{21,9,30},{21,10,31},{22,0,22},{22,1,21},{22,2,24},{22,3,23},{22,4,18},{22,5,17},{22,6,20},{22,7,19},{22,8,30},{22,9,29},{22,10,32},{23,0,23},{23,1,24},{23,2,21},{23,3,22},{23,4,19},{23,5,20},{23,6,17},{23,7,18},{23,8,31},{23,9,32},{23,10,29},{24,0,24},{24,1,23},{24,2,22},{24,3,21},{24,4,20},{24,5,19},{24,6,18},{24,7,17},{24,8,32},{24,9,31},{24,10,30},{25,0,25},{25,1,26},{25,2,27},{25,3,28},{25,4,29},{25,5,30},{25,6,31},{25,7,32},{25,8,17},{26,0,26},{26,1,25},{26,2,28},{26,3,27},{26,4,30},{26,5,29},{26,6,32},{26,7,31},{26,8,18},{27,0,27},{27,1,28},{27,2,25},{27,3,26},{27,4,31},{27,5,32},{27,6,29},{27,7,30},{27,8,19},{27,9,20},{28,0,28},{28,1,27},{28,2,26},{28,3,25},{28,4,32},{28,5,31},{28,6,30},{28,7,29},{28,8,20},{28,9,19},{29,0,29},{29,1,30},{29,2,31},{29,3,32},{29,4,25},{29,5,26},{29,6,27},{29,7,28},{29,8,21},{29,9,22},{29,10,23},{30,0,30},{30,1,29},{30,2,32},{30,3,31},{30,4,26},{30,5,25},{30,6,28},{30,7,27},{30,8,22},{30,9,21},{30,10,24},{31,0,31},{31,1,32},{31,2,29},{31,3,30},{31,4,27},{31,5,28},{31,6,25},{31,7,26},{31,8,23},{31,9,24},{31,10,21},{32,0,32},{32,1,31},{32,2,30},{32,3,29},{32,4,28},{32,5,27},{32,6,26},{32,7,25},{32,8,24},{32,9,23},{32,10,22},{33,0,33},{33,1,34},{33,2,35},{33,3,36},{33,4,37},{33,5,38},{33,6,39},{33,7,40},{33,8,41},{33,9,42},{33,10,43},{33,11,44},{33,12,45},{33,13,46},{33,14,47},{33,15,48},{33,16,49},{34,0,34},{34,1,33},{34,2,36},{34,3,35},{34,4,38},{34,5,37},{34,6,40},{34,7,39},{34,8,42},{34,9,41},{34,10,44},{34,11,43},{34,12,46},{34,13,45},{34,14,48},{34,15,47},{34,16,50},{35,0,35},{35,1,36},{35,2,33},{35,3,34},{35,4,39},{35,5,40},{35,6,37},{35,7,38},{35,8,43},{35,9,44},{35,10,41},{35,11,42},{35,12,47},{35,13,48},{35,14,45},{35,15,46},{35,16,51},{35,17,52},{36,0,36},{36,1,35},{36,2,34},{36,3,33},{36,4,40},{36,5,39},{36,6,38},{36,7,37},{36,8,44},{36,9,43},{36,10,42},{36,11,41},{36,12,48},{36,13,47},{36,14,46},{36,15,45},{36,16,52},{36,17,51},{37,0,37},{37,1,38},{37,2,39},{37,3,40},{37,4,33},{37,5,34},{37,6,35},{37,7,36},{37,8,45},{37,9,46},{37,10,47},{37,11,48},{37,12,41},{37,13,42},{37,14,43},{37,15,44},{37,16,53},{37,17,54},{37,18,55},{38,0,38},{38,1,37},{38,2,40},{38,3,39},{38,4,34},{38,5,33},{38,6,36},{38,7,35},{38,8,46},{38,9,45},{38,10,48},{38,11,47},{38,12,42},{38,13,41},{38,14,44},{38,15,43},{38,16,54},{38,17,53},{38,18,56},{39,0,39},{39,1,40},{39,2,37},{39,3,38},{39,4,35},{39,5,36},{39,6,33},{39,7,34},{39,8,47},{39,9,48},{39,10,45},{39,11,46},{39,12,43},{39,13,44},{39,14,41},{39,15,42},{39,16,55},{39,17,56},{39,18,53},{40,0,40},{40,1,39},{40,2,38},{40,3,37},{40,4,36},{40,5,35},{40,6,34},{40,7,33},{40,8,48},{40,9,47},{40,10,46},{40,11,45},{40,12,44},{40,13,43},{40,14,42},{40,15,41},{40,16,56},{40,17,55},{40,18,54},{41,0,41},{41,1,42},{41,2,43},{41,3,44},{41,4,45},{41,5,46},{41,6,47},{41,7,48},{41,8,33},{41,9,34},{41,10,35},{41,11,36},{41,12,37},{41,13,38},{41,14,39},{41,15,40},{41,16,57},{41,17,58},{41,18,59},{41,19,60},{41,20,61},{42,0,42},{42,1,41},{42,2,44},{42,3,43},{42,4,46},{42,5,45},{42,6,48},{42,7,47},{42,8,34},{42,9,33},{42,10,36},{42,11,35},{42,12,38},{42,13,37},{42,14,40},{42,15,39},{42,16,58},{42,17,57},{42,18,60},{42,19,59},{42,20,62},{43,0,43},{43,1,44},{43,2,41},{43,3,42},{43,4,47},{43,5,48},{43,6,45},{43,7,46},{43,8,35},{43,9,36},{43,10,33},{43,11,34},{43,12,39},{43,13,40},{43,14,37},{43,15,38},{43,16,59},{43,17,60},{43,18,57},{43,19,58},{43,20,63},{43,21,64},{44,0,44},{44,1,43},{44,2,42},{44,3,41},{44,4,48},{44,5,47},{44,6,46},{44,7,45},{44,8,36},{44,9,35},{44,10,34},{44,11,33},{44,12,40},{44,13,39},{44,14,38},{44,15,37},{44,16,60},{44,17,59},{44,18,58},{44,19,57},{44,20,64},{44,21,63},{45,0,45},{45,1,46},{45,2,47},{45,3,48},{45,4,41},{45,5,42},{45,6,43},{45,7,44},{45,8,37},{45,9,38},{45,10,39},{45,11,40},{45,12,33},{45,13,34},{45,14,35},{45,15,36},{45,16,61},{45,17,62},{45,18,63},{45,19,64},{45,20,57},{46,0,46},{46,1,45},{46,2,48},{46,3,47},{46,4,42},{46,5,41},{46,6,44},{46,7,43},{46,8,38},{46,9,37},{46,10,40},{46,11,39},{46,12,34},{46,13,33},{46,14,36},{46,15,35},{46,16,62},{46,17,61},{46,18,64},{46,19,63},{46,20,58},{47,0,47},{47,1,48},{47,2,45},{47,3,46},{47,4,43},{47,5,44},{47,6,41},{47,7,42},{47,8,39},{47,9,40},{47,10,37},{47,11,38},{47,12,35},{47,13,36},{47,14,33},{47,15,34},{47,16,63},{47,17,64},{47,18,61},{47,19,62},{47,20,59},{47,21,60},{48,0,48},{48,1,47},{48,2,46},{48,3,45},{48,4,44},{48,5,43},{48,6,42},{48,7,41},{48,8,40},{48,9,39},{48,10,38},{48,11,37},{48,12,36},{48,13,35},{48,14,34},{48,15,33},{48,16,64},{48,17,63},{48,18,62},{48,19,61},{48,20,60},{48,21,59},{49,0,49},{49,1,50},{49,2,51},{49,3,52},{49,4,53},{49,5,54},{49,6,55},{49,7,56},{49,8,57},{49,9,58},{49,10,59},{49,11,60},{49,12,61},{49,13,62},{49,14,63},{49,15,64},{49,16,33},{50,0,50},{50,1,49},{50,2,52},{50,3,51},{50,4,54},{50,5,53},{50,6,56},{50,7,55},{50,8,58},{50,9,57},{50,10,60},{50,11,59},{50,12,62},{50,13,61},{50,14,64},{50,15,63},{50,16,34},{51,0,51},{51,1,52},{51,2,49},{51,3,50},{51,4,55},{51,5,56},{51,6,53},{51,7,54},{51,8,59},{51,9,60},{51,10,57},{51,11,58},{51,12,63},{51,13,64},{51,14,61},{51,15,62},{51,16,35},{51,17,36},{52,0,52},{52,1,51},{52,2,50},{52,3,49},{52,4,56},{52,5,55},{52,6,54},{52,7,53},{52,8,60},{52,9,59},{52,10,58},{52,11,57},{52,12,64},{52,13,63},{52,14,62},{52,15,61},{52,16,36},{52,17,35},{53,0,53},{53,1,54},{53,2,55},{53,3,56},{53,4,49},{53,5,50},{53,6,51},{53,7,52},{53,8,61},{53,9,62},{53,10,63},{53,11,64},{53,12,57},{53,13,58},{53,14,59},{53,15,60},{53,16,37},{53,17,38},{53,18,39},{54,0,54},{54,1,53},{54,2,56},{54,3,55},{54,4,50},{54,5,49},{54,6,52},{54,7,51},{54,8,62},{54,9,61},{54,10,64},{54,11,63},{54,12,58},{54,13,57},{54,14,60},{54,15,59},{54,16,38},{54,17,37},{54,18,40},{55,0,55},{55,1,56},{55,2,53},{55,3,54},{55,4,51},{55,5,52},{55,6,49},{55,7,50},{55,8,63},{55,9,64},{55,10,61},{55,11,62},{55,12,59},{55,13,60},{55,14,57},{55,15,58},{55,16,39},{55,17,40},{55,18,37},{56,0,56},{56,1,55},{56,2,54},{56,3,53},{56,4,52},{56,5,51},{56,6,50},{56,7,49},{56,8,64},{56,9,63},{56,10,62},{56,11,61},{56,12,60},{56,13,59},{56,14,58},{56,15,57},{56,16,40},{56,17,39},{56,18,38},{57,0,57},{57,1,58},{57,2,59},{57,3,60},{57,4,61},{57,5,62},{57,6,63},{57,7,64},{57,8,49},{57,9,50},{57,10,51},{57,11,52},{57,12,53},{57,13,54},{57,14,55},{57,15,56},{57,16,41},{57,17,42},{57,18,43},{57,19,44},{57,20,45},{58,0,58},{58,1,57},{58,2,60},{58,3,59},{58,4,62},{58,5,61},{58,6,64},{58,7,63},{58,8,50},{58,9,49},{58,10,52},{58,11,51},{58,12,54},{58,13,53},{58,14,56},{58,15,55},{58,16,42},{58,17,41},{58,18,44},{58,19,43},{58,20,46},{59,0,59},{59,1,60},{59,2,57},{59,3,58},{59,4,63},{59,5,64},{59,6,61},{59,7,62},{59,8,51},{59,9,52},{59,10,49},{59,11,50},{59,12,55},{59,13,56},{59,14,53},{59,15,54},{59,16,43},{59,17,44},{59,18,41},{59,19,42},{59,20,47},{59,21,48},{60,0,60},{60,1,59},{60,2,58},{60,3,57},{60,4,64},{60,5,63},{60,6,62},{60,7,61},{60,8,52},{60,9,51},{60,10,50},{60,11,49},{60,12,56},{60,13,55},{60,14,54},{60,15,53},{60,16,44},{60,17,43},{60,18,42},{60,19,41},{60,20,48},{60,21,47},{61,0,61},{61,1,62},{61,2,63},{61,3,64},{61,4,57},{61,5,58},{61,6,59},{61,7,60},{61,8,53},{61,9,54},{61,10,55},{61,11,56},{61,12,49},{61,13,50},{61,14,51},{61,15,52},{61,16,45},{61,17,46},{61,18,47},{61,19,48},{61,20,41},{62,0,62},{62,1,61},{62,2,64},{62,3,63},{62,4,58},{62,5,57},{62,6,60},{62,7,59},{62,8,54},{62,9,53},{62,10,56},{62,11,55},{62,12,50},{62,13,49},{62,14,52},{62,15,51},{62,16,46},{62,17,45},{62,18,48},{62,19,47},{62,20,42},{63,0,63},{63,1,64},{63,2,61},{63,3,62},{63,4,59},{63,5,60},{63,6,57},{63,7,58},{63,8,55},{63,9,56},{63,10,53},{63,11,54},{63,12,51},{63,13,52},{63,14,49},{63,15,50},{63,16,47},{63,17,48},{63,18,45},{63,19,46},{63,20,43},{63,21,44},{64,0,64},{64,1,63},{64,2,62},{64,3,61},{64,4,60},{64,5,59},{64,6,58},{64,7,57},{64,8,56},{64,9,55},{64,10,54},{64,11,53},{64,12,52},{64,13,51},{64,14,50},{64,15,49},{64,16,48},{64,17,47},{64,18,46},{64,19,45},{64,20,44},{64,21,43},{65,0,65},{65,1,66},{65,2,67},{65,3,68},{65,4,69},{65,5,70},{65,6,71},{65,7,72},{65,8,73},{65,9,74},{65,10,75},{65,11,76},{65,12,77},{65,13,78},{65,14,79},{65,15,80},{65,16,81},{65,17,82},{65,18,83},{65,19,84},{65,20,85},{65,21,86},{65,22,87},{65,23,88},{65,24,89},{65,25,90},{65,26,91},{65,27,92},{65,28,93},{65,29,94},{65,30,95},{65,31,96},{65,32,97},{66,0,66},{66,1,65},{66,2,68},{66,3,67},{66,4,70},{66,5,69},{66,6,72},{66,7,71},{66,8,74},{66,9,73},{66,10,76},{66,11,75},{66,12,78},{66,13,77},{66,14,80},{66,15,79},{66,16,82},{66,17,81},{66,18,84},{66,19,83},{66,20,86},{66,21,85},{66,22,88},{66,23,87},{66,24,90},{66,25,89},{66,26,92},{66,27,91},{66,28,94},{66,29,93},{66,30,96},{66,31,95},{66,32,98},{67,0,67},{67,1,68},{67,2,65},{67,3,66},{67,4,71},{67,5,72},{67,6,69},{67,7,70},{67,8,75},{67,9,76},{67,10,73},{67,11,74},{67,12,79},{67,13,80},{67,14,77},{67,15,78},{67,16,83},{67,17,84},{67,18,81},{67,19,82},{67,20,87},{67,21,88},{67,22,85},{67,23,86},{67,24,91},{67,25,92},{67,26,89},{67,27,90},{67,28,95},{67,29,96},{67,30,93},{67,31,94},{67,32,99},{67,33,100},{68,0,68},{68,1,67},{68,2,66},{68,3,65},{68,4,72},{68,5,71},{68,6,70},{68,7,69},{68,8,76},{68,9,75},{68,10,74},{68,11,73},{68,12,80},{68,13,79},{68,14,78},{68,15,77},{68,16,84},{68,17,83},{68,18,82},{68,19,81},{68,20,88},{68,21,87},{68,22,86},{68,23,85},{68,24,92},{68,25,91},{68,26,90},{68,27,89},{68,28,96},{68,29,95},{68,30,94},{68,31,93},{68,32,100},{68,33,99},{69,0,69},{69,1,70},{69,2,71},{69,3,72},{69,4,65},{69,5,66},{69,6,67},{69,7,68},{69,8,77},{69,9,78},{69,10,79},{69,11,80},{69,12,73},{69,13,74},{69,14,75},{69,15,76},{69,16,85},{69,17,86},{69,18,87},{69,19,88},{69,20,81},{69,21,82},{69,22,83},{69,23,84},{69,24,93},{69,25,94},{69,26,95},{69,27,96},{69,28,89},{69,29,90},{69,30,91},{69,31,92},{69,32,101},{69,33,102},{69,34,103},{70,0,70},{70,1,69},{70,2,72},{70,3,71},{70,4,66},{70,5,65},{70,6,68},{70,7,67},{70,8,78},{70,9,77},{70,10,80},{70,11,79},{70,12,74},{70,13,73},{70,14,76},{70,15,75},{70,16,86},{70,17,85},{70,18,88},{70,19,87},{70,20,82},{70,21,81},{70,22,84},{70,23,83},{70,24,94},{70,25,93},{70,26,96},{70,27,95},{70,28,90},{70,29,89},{70,30,92},{70,31,91},{70,32,102},{70,33,101},{70,34,104},{71,0,71},{71,1,72},{71,2,69},{71,3,70},{71,4,67},{71,5,68},{71,6,65},{71,7,66},{71,8,79},{71,9,80},{71,10,77},{71,11,78},{71,12,75},{71,13,76},{71,14,73},{71,15,74},{71,16,87},{71,17,88},{71,18,85},{71,19,86},{71,20,83},{71,21,84},{71,22,81},{71,23,82},{71,24,95},{71,25,96},{71,26,93},{71,27,94},{71,28,91},{71,29,92},{71,30,89},{71,31,90},{71,32,103},{71,33,104},{71,34,101},{72,0,72},{72,1,71},{72,2,70},{72,3,69},{72,4,68},{72,5,67},{72,6,66},{72,7,65},{72,8,80},{72,9,79},{72,10,78},{72,11,77},{72,12,76},{72,13,75},{72,14,74},{72,15,73},{72,16,88},{72,17,87},{72,18,86},{72,19,85},{72,20,84},{72,21,83},{72,22,82},{72,23,81},{72,24,96},{72,25,95},{72,26,94},{72,27,93},{72,28,92},{72,29,91},{72,30,90},{72,31,89},{72,32,104},{72,33,103},{72,34,102},{73,0,73},{73,1,74},{73,2,75},{73,3,76},{73,4,77},{73,5,78},{73,6,79},{73,7,80},{73,8,65},{73,9,66},{73,10,67},{73,11,68},{73,12,69},{73,13,70},{73,14,71},{73,15,72},{73,16,89},{73,17,90},{73,18,91},{73,19,92},{73,20,93},{73,21,94},{73,22,95},{73,23,96},{73,24,81},{73,25,82},{73,26,83},{73,27,84},{73,28,85},{73,29,86},{73,30,87},{73,31,88},{73,32,105},{73,33,106},{73,34,107},{73,35,108},{73,36,109},{74,0,74},{74,1,73},{74,2,76},{74,3,75},{74,4,78},{74,5,77},{74,6,80},{74,7,79},{74,8,66},{74,9,65},{74,10,68},{74,11,67},{74,12,70},{74,13,69},{74,14,72},{74,15,71},{74,16,90},{74,17,89},{74,18,92},{74,19,91},{74,20,94},{74,21,93},{74,22,96},{74,23,95},{74,24,82},{74,25,81},{74,26,84},{74,27,83},{74,28,86},{74,29,85},{74,30,88},{74,31,87},{74,32,106},{74,33,105},{74,34,108},{74,35,107},{74,36,110},{75,0,75},{75,1,76},{75,2,73},{75,3,74},{75,4,79},{75,5,80},{75,6,77},{75,7,78},{75,8,67},{75,9,68},{75,10,65},{75,11,66},{75,12,71},{75,13,72},{75,14,69},{75,15,70},{75,16,91},{75,17,92},{75,18,89},{75,19,90},{75,20,95},{75,21,96},{75,22,93},{75,23,94},{75,24,83},{75,25,84},{75,26,81},{75,27,82},{75,28,87},{75,29,88},{75,30,85},{75,31,86},{75,32,107},{75,33,108},{75,34,105},{75,35,106},{75,36,111},{75,37,112}}};
)
]

Other Chocolate Games

We can study many kinds of inequalities. For example, the chocolate games that satisfy the inequalities y≤⌊((z+h)/k)⌋ or y≤h⌊(z/k)⌋ are interesting, when k is even and h is a non-negative integer. The authors are studying these games.

High School Mathematical Research Project

How High School Students Discovered New Chocolate Games

Dr. Miyadera taught the rectangular chocolate games presented in [] to his students and encouraged them to make new chocolate games. Students were very good at proposing new types of chocolate games, including the ones in Figures –. These students were the first people who studied chocolate games that satisfy inequalities.

As for the triangular chocolate game applications on smart phones, see [], [], and [].

The fact that high school students could discover new theorems using computer algebra systems is very important for mathematics education. There are many teachers around the world who make students rediscover formulas in the classroom. In so-called “learning by doing,” students are supposed to rediscover formulas and theorems, while teachers know these formulas and theorems. In the authors’ high school research projects, students discover new things! The difference between discovery and rediscovery is very big, and the method the authors introduced can change mathematics education greatly.

The method used in the group is as follows.

First Dr. Ryohei Miyadera introduces some problems to the high school students, and after that students are required to create new problems by changing the conditions of the original problems. Sometimes they make a problem that is a little bit different from the original problem. At other times they propose a completely new problem. When the proposed problem seems to be very promising to Dr. Miyadera, he and his students begin to research it. They make computer programs using Mathematica and try to find interesting facts by calculation. Once they discover a new fact, they begin to prove it. Even if the proposed problem does not seem to be interesting enough, Dr. Miyadera encourages students to study it. It is often the case that a problem that seems to be trivial to him turns out to be a good problem. Some students have a kind of intuition that is beyond the imagination of Dr. Miyadera, who is an active mathematician himself. This method of research looks simple, but it is very effective.

In the history of this research group, more than 60 students have participated. Dr. Miyadera discovered that some students are very good at proposing new ideas while others are good at proving formulas and theorems. According to some researchers of mathematics education, there has never been a group of high school students that have been constantly discovering new formulas and theorems.

This group of students won the first prize in the Canada Wide Virtual Science Fair 2007, 2008, 2009, 2010, 2011, 2012, and 2013. They won the Imai Isao Award in 2007, which is the first prize in the Japan Wide High School Research Contest supported by Kogakuin University in Japan. They won the first prize in the Japan Science & Engineering Challenge 2008, and represented Japan in the International Science and Engineering Fair. (Japan declined to send them to the fair because of the epidemic of swine influenza.) They became finalists in the Japan Science & Engineering Challenge in 2011, 2012, and 2013. They became Google Science Fair Regional Finalists in 2012 and became semifinalists in the Yau High School Mathematics Awards in 2012 and 2013.

For a detailed explanation about the authors’ high school mathematics research project, see [], [], [], [], [], [], and []. The authors have presented their research at the International Mathematica Symposium in [], [], and [].

They have also presented their research in the Mathematica Demonstrations Project, and Ryohei Miyadera was selected as a featured contributor. See [], [], and [].

Dr. Miyadera received the Excellent Teacher Award from the Ministry of Education of Japan in 2012, and he received the Wolfram Innovator Award in 2012 for his research with high school students.

If you are interested in doing a high school or undergraduate mathematics research project, one of the best books to use is by Cowen and Kennedy [].

Conclusion

If students use Mathematica freely with an experienced mathematician, they can discover a lot of new and interesting facts of mathematics. The difference between a true discovery and rediscovery is great. We think that the best way to learn how to be creative is to create new and interesting things.

Acknowledgments

We would like to thank Professor Robert Cowen of the City University of New York for his encouragement when we met []; he gave his book [] to us. We learned how to use Mathematica in our research by using his book. We also would like to thank Ed Pegg Jr of Wolfram Research and Professor Tadashi Takahashi for giving us valuable advice.

References

Wikipedia. “Chomp.” (Dec 4, 2013) en.wikipedia.org/wiki/Chomp.

A. C. Robin, “A Poisoned Chocolate Problem,” Problem Corner, The Mathematical Gazette, 73(466), 1989 pp. 341–343. (An answer for the above problem is in 74(468), 1990 pp. 171–173.)

R. Miyadera, S. Nakamura, and R. Hanafusa, “New Chocolate Games—Variants of the Game of Nim,” Proceedings of the Annual International Conference on Computational Mathematics, Computational Geometry & Statistics, Singapore, 2012 pp. 122–128. dl4.globalstf.org/?wpsc-product=new-chocolate-game-variants-of-the-game-of-nim.

R. Miyadera, S. Nakamura, and R. Hanafusa, “New Chocolate Games,” GSTF Journal of Mathematics, Statistics and Operations Research, 1(1), 2012 pp. 111–116. dl4.globalstf.org/?wpsc-product=new-chocolate-games.

S. Nakamura, Y. Naito, R. Miyadera et al., “Chocolate Games That Are Variants of Nim and Interesting Graphs Made by These Games,” Visual Mathematics, 14(2), 2012. www.mi.sanu.ac.rs/vismath/miyaderasept2012/index.html.

T. Yamauchi, T. Inoue, and Y. Tomari, “Variants of the Game of Nim That Have Inequalities as Conditions,” Rose-Hulman Institute of Technology, Undergraduate Math Journal, 10(2), 2009. www.rose-hulman.edu/mathjournal/archives/2009/vol10-n2/paper12/v10n2-12pd.pdf.

R. Miyadera and S. Nakamura, “A Chocolate Game,” Mathematics of Puzzles, Journal of Information Processing (special issue), 53(6), 2012 pp. 1582–1591 (in Japanese).

M. Naito, T. Yamauchi, T. Inoue et al., “Discrete Mathematics and Computer Algebra System,” Proceedings of the 9th Asian Symposium on Computer Mathematics-Mathematical Aspects of Computer and Information Sciences Joint Conference (ASCM-MACIS), Fukuoka, Japan: Kyushu University, 2009 pp. 127–136. gcoe-mi.jp/temp/publish/a2019bae287f4628e4bfc9d273150000.pdf.

MathPuzzle.com. “The Bitter Chocolate Problem.” Material added 8 Jan 06 (Happy New Year). www.mathpuzzle.com/26Feb2006.html.

T. Nakaoka, R. Miyadera et al., “Combinatorial Games and Beautiful Graphs Produced by Them,” Visual Mathematics, 11(3), 2009. www.mi.sanu.ac.rs/vismath/miyaderasept2009/index.html.

R. Cowen and J. Kennedy, Discovering Mathematics with Mathematica, Erudition Books, 2001.

M. Fukui, “Bitter Chocolate Games 1.” itunes.apple.com/jp/app/bitter-chocolate-games-1/id495880660?mt=8.

M. Fukui, “Bitter Chocolate Games 2.” itunes.apple.com/jp/app/bitter-chocolate-games-2/id502476677?mt=8.

S. Nakamura, “Poison Chocolate Game.” market.android.com/details?id=com.kgshmathclub.chocoapp.

R. Miyadera, T. Inoue, and S. Nakamura, “High School Mathematics Research Project Using Computer Algebra System,” Proceedings of the 16th International Seminar on Education of Gifted Students in Mathematics, The Korean Society of Mathematical Education, Chungnam National University, Daejeon, Korea, 2011 pp. 303–316.

S. Hashiba, D. Minematsu, H. Shimoda, and R. Miyadera, “How High School Students Can Discover Original Ideas of Mathematics Using Mathematica,” Mathematica in Education and Research 11(3), 2006.

H. Matsui, D. Minematsu, T. Yamauchi, and R. Miyadera, “Pascal-Like Triangles and Fibonacci-Like Sequences,” Mathematical Gazette, 94(529), 2010 pp. 27–41.

R. Miyadera, T. Hashiba, Y. Nakagawa, T. Yamauchi, H. Matsui, S. Hashiba, D. Minematsu, and M. Sakaguchi, “Pascal-Like Triangles and Sierpinski-Like Gaskets,” Visual Mathematics, 9(1), 2007. www.mi.sanu.ac.rs/vismath/miyad/pascalliketriangle.html.

H. Matsui and T. Yamauchi, “Formulas for Fibonacci-Like Sequences Produced by Pascal-Like Triangles,” Rose-Hulman Institute of Technology Undergraduate Math Journal, 9(2), 2008. www.rose-hulman.edu/mathjournal/archives/2008/vol9-n2/paper11/v9n2-11p.pdf.

H. Matsui, N. Saita, K. Kawata, Y. Sakurama, and R. Miyadera, “Elementary Problems, B-1019,” Fibonacci Quarterly, 44(3), 2006. www.fq.math.ca/Problems/August2006elementary.pdf.

R. Miyadera, “General Theory of Russian Roulette.” library.wolfram.com/infocenter/MathSource/5710.

R. Miyadera, K. Fujii et al., “How High School Students Could Present Original Math Research Using Mathematica,” The International Mathematica Symposium, 2003. library.wolfram.com/infocenter/Conferences/4983.

R. Miyadera and D. Minematsu, “Curious Properties of an Iterative Process: How Could High School Students Present Original Mathematics Research Using Mathematica?,” The International Mathematica Symposium, 2004. library.wolfram.com/infocenter/Conferences/6055.

R. Miyadera, “Using Mathematica in Doing the Research of Mathematics with High School Students,” Proceedings of the Fourth International Mathematica Symposium (IMS2001), Tokyo, 2001.

H. Matsui, T. Yamauchi, D. Minematsu, and R. Miyadera. “Pascal-Like Triangles Made from a Game” from the Wolfram Demonstrations Project—A Wolfram Web Resource. demonstrations.wolfram.com/PascalLikeTrianglesMadeFromAGame.

H. Matsui, T. Yamauchi, D. Minematsu, and R. Miyadera. “Pascal-Like Triangles Mod k” from the Wolfram Demonstrations Project—A Wolfram Web Resource. demonstrations.wolfram.com/PascalLikeTrianglesModK.

T. Inoue, T. Nakaoka, and R. Miyadera. “A Bitter Chocolate Problem That Satisfies an Inequality” from the Wolfram Demonstrations Project—A Wolfram Web Resource. demonstrations.wolfram.com/ABitterChocolateProblemThatSatisfiesAnInequality.