Problem Statement

There is an $N \times N$ grid. Let $(i,j)$ denote the cell at the $i$-th row from the top and $j$-th column from the left.

You are given $N \times N$ characters $S_{1,1}, \dots , S_{N,N}$. Each character is a digit (0 to 9) or ?. Determine if it is possible to replace each ? with a digit to satisfy the following condition, and if possible, output one such way of replacement.

For each $1 \le i,j \le N$, write $S_{i,j}$ as an integer in cell $(i,j)$. For a path from cell $(1,1)$ to cell $(N,N)$ by repeating moves only to adjacent cells to the right or down, let the score of the path be the sum of the integers written in the cells on the path (including the start and end points). Then, for all $\binom{2N-2}{N-1}$ possible paths, the scores are all equal.

Constraints

• $2 \le N \le 100$
• $S_{i,j}$ is a digit (0 to 9) or ?.

Input

The input is given from Standard Input in the following format:

N
S_{1,1}S_{1,2}\ldotsS_{1,N}
S_{2,1}S_{2,2}\ldotsS_{2,N}
\vdots
S_{N,1}S_{N,2}\ldotsS_{N,N}

Output

If it is impossible to make a replacement that satisfies the condition, output -1. If possible, output $S_{1,1}, \dots , S_{N,N}$ after the replacement in the following format:

S_{1,1}S_{1,2}\ldotsS_{1,N}
S_{2,1}S_{2,2}\ldotsS_{2,N}
\vdots
S_{N,1}S_{N,2}\ldotsS_{N,N}

If there are multiple solutions, any of them will be accepted.