P5461 Pardoning Prisoners of War

With the help of the anti-cheating system, some contestants who copied or cheated in the monthly contest have been caught.

There are $2^n \times 2^n$ cheaters $(n \le 10)$ standing in a square matrix, waiting for kkksc03's decision. kkksc03 decides to pardon some of them. He splits the square matrix evenly into $4$ smaller square matrices, and each smaller matrix has side length half of the original matrix. All cheaters in the upper-left matrix will be pardoned. In the remaining $3$ smaller matrices, each matrix is split into $4$ even smaller matrices, and cheaters are pardoned in the same way... until the matrix can no longer be split. All cheaters who are not pardoned will receive the brown-name penalty. Given $n$, output the fate of each cheater, where $0$ means pardoned and $1$ means not pardoned.

An integer $n$.

A $2^n \times 2^n$ 01 matrix representing whether each person is pardoned. There is one space between numbers.

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