You are given a square matrix $A$ of size $n \times n$ whose elements are integers. We will denote the element on the intersection of the $i$-th row and the $j$-th column as $A_{i,j}$.

You can perform operations on the matrix. In each operation, you can choose an integer $k$, then for each index $i$ ($1 \leq i \leq n$), swap $A_{i, k}$ with $A_{k, i}$. Note that cell $A_{k, k}$ remains unchanged.

For example, for $n = 4$ and $k = 3$, this matrix will be transformed like this:

The operation $k = 3$ swaps the blue row with the green column.

You can perform this operation any number of times. Find the lexicographically smallest matrix$^\dagger$ you can obtain after performing arbitrary number of operations.

${}^\dagger$ For two matrices $A$ and $B$ of size $n \times n$, let $a_{(i-1) \cdot n + j} = A_{i,j}$ and $b_{(i-1) \cdot n + j} = B_{i,j}$. Then, the matrix $A$ is lexicographically smaller than the matrix $B$ when there exists an index $i$ ($1 \leq i \leq n^2$) such that a_i < b_i and for all indices $j$ such that 1 \leq j < i, $a_j = b_j$.