よく調べないままAck関数を組んでえらいめにあった話 - 音楽室と化学室と美術室とPC室の融合部屋　所謂自由室

追記：4/8　15:52　プログラム書き直しました

なんとなくTwitterのタイムラインを見てると $Ack(2,2)$ って関数を計算してる人いたから調べてみた．

関数の挙動の仕様としては

$Ack(m,n)$ について

$m=0$ のとき $Ack(0,n) = n+1$

$n=0$ のとき $Ack(m,0) = Ack(m-1,1)$

その他のとき $Ack(m,n) = Ack(m-1,Ack(m.n-1))$

なんだ簡単そうじゃん！ってとりあえず再帰関数で組んでみたら $Ack(4,4)$ でスタックオーバーフロー

よくわからないまま「うん？」って思ってとりあえず実装を見直す．

とりあえず再帰が深いところまで行ってるんだろうなーって思って配列を使って実装をした．

int Ack(int m, int n) {

std::string FileName = "Ack(" + std::to_string(m) + "," + std::to_string(n) + ").txt";

std::ofstream WF;

WF.open(FileName, std::ios::out);

std::vector<int> List;

List.push_back(m);

List.push_back(n);

WF << "Ack(" + std::to_string(m) + "," + std::to_string(n) + ")" << std::endl;

while (List.size() != 1) {

std::vector<int> TList;

int Size = List.size();

for (int i = 0; i < Size - 2; i++)TList.push_back(List[i]);

if (List[Size - 2] == 0)TList.push_back(List[Size - 1] + 1);

else if (List[Size - 1] == 0) {

TList.push_back(List[Size - 2] - 1);

TList.push_back(1);

} else {

TList.push_back(List[Size - 2] - 1);

TList.push_back(List[Size - 2]);

TList.push_back(List[Size - 1] - 1);

}

List = TList;

Size = List.size();

WF << "=";

if (List.size() >= 2) {

for (int i = 0; i < Size - 2; i++) {

WF << "Ack(" + std::to_string(List[i]) + ",";

}

WF << "Ack(" + std::to_string(List[Size-2]) + "," + std::to_string(List[Size-1]) + ")";

for (int i = 0; i < Size - 2; i++) { WF << ")";

}

} else {

WF << std::to_string(List[0]);

}

WF << std::endl;

}

WF << "∴Ack(" + std::to_string(m) + ", " + std::to_string(n) + ") = " + std::to_string(List[0]);

WF.close();

return List[0];

}

とりあえずこんな実装でいいかな？って $Ack(4,4)$ を動かしてみると計算時間がすこぶる長い長い．

どんな値になるんだ？？って思ってぐぐってみると

$Ack(4,4) = 2^{2^{2^{65536}}} - 3$

うん！無理ｗ！

$Ack(3,3)=61$ としょぼい数字っぽいなーって思ってネタ要員だと思ってたけど4,4でこんなことなるんかこれ・・・

とりあえずリサーチはちゃんとやろうね！って感じたありゅさんだった．

申し訳程度の出力（Ack(3,3)を貼ろうとしたらブログが止まったのでAck(3,2)をペタリ）

Ack(3,2)
=Ack(2,Ack(3,1))
=Ack(2,Ack(2,Ack(3,0)))
=Ack(2,Ack(2,Ack(2,1)))
=Ack(2,Ack(2,Ack(1,Ack(2,0))))
=Ack(2,Ack(2,Ack(1,Ack(1,1))))
=Ack(2,Ack(2,Ack(1,Ack(0,Ack(1,0)))))
=Ack(2,Ack(2,Ack(1,Ack(0,Ack(0,1)))))
=Ack(2,Ack(2,Ack(1,Ack(0,2))))
=Ack(2,Ack(2,Ack(1,3)))
=Ack(2,Ack(2,Ack(0,Ack(1,2))))
=Ack(2,Ack(2,Ack(0,Ack(0,Ack(1,1)))))
=Ack(2,Ack(2,Ack(0,Ack(0,Ack(0,Ack(1,0))))))
=Ack(2,Ack(2,Ack(0,Ack(0,Ack(0,Ack(0,1))))))
=Ack(2,Ack(2,Ack(0,Ack(0,Ack(0,2)))))
=Ack(2,Ack(2,Ack(0,Ack(0,3))))
=Ack(2,Ack(2,Ack(0,4)))
=Ack(2,Ack(2,5))
=Ack(2,Ack(1,Ack(2,4)))
=Ack(2,Ack(1,Ack(1,Ack(2,3))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(2,2)))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(1,Ack(2,1))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(2,0)))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,1)))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(1,0))))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,1))))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,2)))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,3))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(1,2)))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(1,1))))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(1,0)))))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,1)))))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,2))))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,3)))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,4))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(1,5)))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(0,Ack(1,4))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(1,3)))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(1,2))))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,1)))))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,0))))))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,1))))))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,2)))))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,3))))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,4)))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,5))))))
=Ack(2,Ack(1,Ack(1,Ack(1,Ack(0,6)))))
=Ack(2,Ack(1,Ack(1,Ack(1,7))))
=Ack(2,Ack(1,Ack(1,Ack(0,Ack(1,6)))))
=Ack(2,Ack(1,Ack(1,Ack(0,Ack(0,Ack(1,5))))))
=Ack(2,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(1,4)))))))
=Ack(2,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,3))))))))
=Ack(2,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,2)))))))))
=Ack(2,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,1))))))))))
=Ack(2,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,0)))))))))))
=Ack(2,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,1)))))))))))
=Ack(2,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,2))))))))))
=Ack(2,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,3)))))))))
=Ack(2,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,4))))))))
=Ack(2,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,5)))))))
=Ack(2,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,6))))))
=Ack(2,Ack(1,Ack(1,Ack(0,Ack(0,7)))))
=Ack(2,Ack(1,Ack(1,Ack(0,8))))
=Ack(2,Ack(1,Ack(1,9)))
=Ack(2,Ack(1,Ack(0,Ack(1,8))))
=Ack(2,Ack(1,Ack(0,Ack(0,Ack(1,7)))))
=Ack(2,Ack(1,Ack(0,Ack(0,Ack(0,Ack(1,6))))))
=Ack(2,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,5)))))))
=Ack(2,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,4))))))))
=Ack(2,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,3)))))))))
=Ack(2,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,2))))))))))
=Ack(2,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,1)))))))))))
=Ack(2,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,0))))))))))))
=Ack(2,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,1))))))))))))
=Ack(2,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,2)))))))))))
=Ack(2,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,3))))))))))
=Ack(2,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,4)))))))))
=Ack(2,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,5))))))))
=Ack(2,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,6)))))))
=Ack(2,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,7))))))
=Ack(2,Ack(1,Ack(0,Ack(0,Ack(0,8)))))
=Ack(2,Ack(1,Ack(0,Ack(0,9))))
=Ack(2,Ack(1,Ack(0,10)))
=Ack(2,Ack(1,11))
=Ack(2,Ack(0,Ack(1,10)))
=Ack(2,Ack(0,Ack(0,Ack(1,9))))
=Ack(2,Ack(0,Ack(0,Ack(0,Ack(1,8)))))
=Ack(2,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,7))))))
=Ack(2,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,6)))))))
=Ack(2,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,5))))))))
=Ack(2,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,4)))))))))
=Ack(2,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,3))))))))))
=Ack(2,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,2)))))))))))
=Ack(2,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,1))))))))))))
=Ack(2,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,0)))))))))))))
=Ack(2,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,1)))))))))))))
=Ack(2,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,2))))))))))))
=Ack(2,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,3)))))))))))
=Ack(2,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,4))))))))))
=Ack(2,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,5)))))))))
=Ack(2,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,6))))))))
=Ack(2,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,7)))))))
=Ack(2,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,8))))))
=Ack(2,Ack(0,Ack(0,Ack(0,Ack(0,9)))))
=Ack(2,Ack(0,Ack(0,Ack(0,10))))
=Ack(2,Ack(0,Ack(0,11)))
=Ack(2,Ack(0,12))
=Ack(2,13)
=Ack(1,Ack(2,12))
=Ack(1,Ack(1,Ack(2,11)))
=Ack(1,Ack(1,Ack(1,Ack(2,10))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(2,9)))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(2,8))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(2,7)))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(2,6))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(2,5)))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(2,4))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(2,3)))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(2,2))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(2,1)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(2,0))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,1))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(1,0)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,1)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,2))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,3)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(1,2))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(1,1)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(1,0))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,1))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,2)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,3))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,4)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,5))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(1,4)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(1,3))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(1,2)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,1))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,0)))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,1)))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,2))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,3)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,4))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,5)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,6))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,7)))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(1,6))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(1,5)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(1,4))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,3)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,2))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,1)))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,0))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,1))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,2)))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,3))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,4)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,5))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,6)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,7))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,8)))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,9))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(1,8)))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(1,7))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(1,6)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,5))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,4)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,3))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,2)))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,1))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,0)))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,1)))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,2))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,3)))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,4))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,5)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,6))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,7)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,8))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,9)))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,10))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,11)))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(1,10))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(1,9)))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(1,8))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,7)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,6))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,5)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,4))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,3)))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,2))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,1)))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,0))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,1))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,2)))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,3))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,4)))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,5))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,6)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,7))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,8)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,9))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,10)))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,11))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,12)))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,13))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(1,12)))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(1,11))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(1,10)))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,9))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,8)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,7))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,6)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,5))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,4)))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,3))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,2)))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,1))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,0)))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,1)))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,2))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,3)))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,4))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,5)))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,6))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,7)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,8))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,9)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,10))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,11)))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,12))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,13)))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,14))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,15)))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(1,14))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(1,13)))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(1,12))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,11)))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,10))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,9)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,8))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,7)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,6))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,5)))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,4))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,3)))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,2))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,1)))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,0))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,1))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,2)))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,3))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,4)))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,5))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,6)))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,7))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,8)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,9))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,10)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,11))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,12)))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,13))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,14)))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,15))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,16)))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,17))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(1,16)))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(1,15))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(1,14)))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,13))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,12)))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,11))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,10)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,9))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,8)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,7))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,6)))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,5))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,4)))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,3))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,2)))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,1))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,0)))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,1)))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,2))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,3)))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,4))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,5)))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,6))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,7)))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,8))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,9)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,10))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,11)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,12))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,13)))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,14))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,15)))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,16))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,17)))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,18))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(1,19)))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(1,18))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(1,17)))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(1,16))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,15)))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,14))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,13)))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,12))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,11)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,10))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,9)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,8))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,7)))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,6))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,5)))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,4))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,3)))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,2))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,1)))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,0))))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,1))))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,2)))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,3))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,4)))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,5))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,6)))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,7))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,8)))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,9))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,10)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,11))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,12)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,13))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,14)))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,15))))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,16)))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,17))))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,18)))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,19))))))
=Ack(1,Ack(1,Ack(1,Ack(1,Ack(0,20)))))
=Ack(1,Ack(1,Ack(1,Ack(1,21))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(1,20)))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(1,19))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(1,18)))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,17))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,16)))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,15))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,14)))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,13))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,12)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,11))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,10)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,9))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,8)))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,7))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,6)))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,5))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,4)))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,3))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,2)))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,1))))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,0)))))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,1)))))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,2))))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,3)))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,4))))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,5)))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,6))))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,7)))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,8))))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,9)))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,10))))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,11)))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,12))))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,13)))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,14))))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,15)))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,16))))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,17)))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,18))))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,19)))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,20))))))
=Ack(1,Ack(1,Ack(1,Ack(0,Ack(0,21)))))
=Ack(1,Ack(1,Ack(1,Ack(0,22))))
=Ack(1,Ack(1,Ack(1,23)))
=Ack(1,Ack(1,Ack(0,Ack(1,22))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(1,21)))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(1,20))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,19)))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,18))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,17)))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,16))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,15)))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,14))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,13)))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,12))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,11)))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,10))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,9)))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,8))))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,7)))))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,6))))))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,5)))))))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,4))))))))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,3)))))))))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,2))))))))))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,1)))))))))))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,0))))))))))))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,1))))))))))))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,2)))))))))))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,3))))))))))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,4)))))))))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,5))))))))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,6)))))))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,7))))))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,8)))))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,9))))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,10)))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,11))))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,12)))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,13))))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,14)))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,15))))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,16)))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,17))))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,18)))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,19))))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,20)))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,21))))))
=Ack(1,Ack(1,Ack(0,Ack(0,Ack(0,22)))))
=Ack(1,Ack(1,Ack(0,Ack(0,23))))
=Ack(1,Ack(1,Ack(0,24)))
=Ack(1,Ack(1,25))
=Ack(1,Ack(0,Ack(1,24)))
=Ack(1,Ack(0,Ack(0,Ack(1,23))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(1,22)))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,21))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,20)))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,19))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,18)))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,17))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,16)))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,15))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,14)))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,13))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,12)))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,11))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,10)))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,9))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,8)))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,7))))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,6)))))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,5))))))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,4)))))))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,3))))))))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,2)))))))))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,1))))))))))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,0)))))))))))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,1)))))))))))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,2))))))))))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,3)))))))))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,4))))))))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,5)))))))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,6))))))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,7)))))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,8))))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,9)))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,10))))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,11)))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,12))))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,13)))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,14))))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,15)))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,16))))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,17)))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,18))))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,19)))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,20))))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,21)))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,22))))))
=Ack(1,Ack(0,Ack(0,Ack(0,Ack(0,23)))))
=Ack(1,Ack(0,Ack(0,Ack(0,24))))
=Ack(1,Ack(0,Ack(0,25)))
=Ack(1,Ack(0,26))
=Ack(1,27)
=Ack(0,Ack(1,26))
=Ack(0,Ack(0,Ack(1,25)))
=Ack(0,Ack(0,Ack(0,Ack(1,24))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,23)))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,22))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,21)))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,20))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,19)))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,18))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,17)))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,16))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,15)))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,14))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,13)))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,12))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,11)))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,10))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,9)))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,8))))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,7)))))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,6))))))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,5)))))))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,4))))))))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,3)))))))))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,2))))))))))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,1)))))))))))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(1,0))))))))))))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,1))))))))))))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,2)))))))))))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,3))))))))))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,4)))))))))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,5))))))))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,6)))))))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,7))))))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,8)))))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,9))))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,10)))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,11))))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,12)))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,13))))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,14)))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,15))))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,16)))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,17))))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,18)))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,19))))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,20)))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,21))))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,22)))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,23))))))
=Ack(0,Ack(0,Ack(0,Ack(0,Ack(0,24)))))
=Ack(0,Ack(0,Ack(0,Ack(0,25))))
=Ack(0,Ack(0,Ack(0,26)))
=Ack(0,Ack(0,27))
=Ack(0,28)
=29
∴Ack(3, 2) = 29