One-Four Overload

### 题目描述 Alice 有一个 $n$ 行 $m$ 列的矩阵，矩阵中有些单元格被标记了，而有的没有。在与矩阵边缘相邻的单元格总是没有被标记的。（当且仅当两个单元格共边时，我们称这两个单元格式相邻的）。 Alice 想往每个单元格里填入一个数字，使得该矩阵满足以下条件： - 每个没标记的格子只能填入 $1$ 或者 $4$； - 每个标记的格子的数字必须为**与它相邻的没有被标记的格子之和**； - 每个标记的单元格的数字必须为 $5$ 的倍数。 Alice 是蒟蒻，做不出来，于是找你来帮忙 ~~（实际上是找的 Bob 然后让你来帮忙，但不如你直接帮 Alice）~~。 ### 输入格式 第一行 $n$ 与 $m$（$1 \le n,m \le 500$）。 接下来 $n$ 行每行 $m$ 列，为一个字符 `X` 或 `.`，分别表示标记过的格子（`X`）与没标记过的格子（`.`）。 ### 输出格式 第一行输出 `YES` 或 `NO`，表示是否存在一个合法的矩阵以满足 Alice 的要求。 如果输出的是 `YES`，则输出一个矩阵，表示合法的矩阵。 翻译 @[XiaoQuQu](https://www.luogu.com.cn/user/427623)

Alice has an empty grid with $ n $ rows and $ m $ columns. Some of the cells are marked, and no marked cells are adjacent to the edge of the grid. (Two squares are adjacent if they share a side.) Alice wants to fill each cell with a number such that the following statements are true: - every unmarked cell contains either the number $ 1 $ or $ 4 $ ; - every marked cell contains the sum of the numbers in all unmarked cells adjacent to it (if a marked cell is not adjacent to any unmarked cell, this sum is $ 0 $ ); - every marked cell contains a multiple of $ 5 $ . Alice couldn't figure it out, so she asks Bob to help her. Help Bob find any such grid, or state that no such grid exists.

The first line of input contains two integers $ n $ and $ m $ ( $ 1 \leq n, m \leq 500 $ ) — the number of rows and the number of columns in the grid, respectively. Then $ n $ lines follow, each containing $ m $ characters. Each of these characters is either '.' or 'X' — an unmarked and a marked cell, respectively. No marked cells are adjacent to the edge of the grid.

Output "'NO" if no suitable grid exists. Otherwise, output "'YES"'. Then output $ n $ lines of $ m $ space-separated integers — the integers in the grid.

5 5
.....
.XXX.
.X.X.
.XXX.
.....

YES
4 1 4 4 1
4 5 5 5 1
4 5 1 5 4
1 5 5 5 4
1 4 4 1 4

5 5
.....
.XXX.
.XXX.
.XXX.
.....

NO

3 2
..
..
..

YES
4 1
4 1
1 4

9 9
.........
.XXXXX.X.
.X...X...
.X.XXXXX.
.X.X.X.X.
.X.XXX.X.
.X.....X.
.XXXXXXX.
.........

YES
4 4 4 1 4 1 4 1 4
1 5 5 5 5 5 4 10 1
4 5 1 4 1 5 4 4 4
4 5 1 5 5 0 5 5 1
4 5 1 5 4 5 1 5 4
4 5 1 5 5 5 4 5 1
1 5 4 4 1 1 4 5 1
4 5 5 5 5 5 5 5 4
1 1 1 1 4 4 1 1 4

It can be shown that no such grid exists for the second test.