Tetris revisited

题意翻译

**题目描述** 给定一个 $n \times m$ 的游戏盘，盘内有一些格子已被填充，要求用一些图形将剩余空格填满。 可用图形都以2~5个单元格组成，包含了将2~5个单元格共边连接的所有情况，填充时可以旋转和翻转。 **输入格式** 第一行两个整数 $n$ 和 $m$ 。 接下来 $n$ 行，每行 $m$ 个字符，表示该行游戏盘的情况。其中"#" 代表初始填充格，"."代空格。 **输出格式** 如果无法用上述图形将游戏盘填满，输出 $-1$ 。 否则，输出一种填充方式，用不同的数字代表不同的图形，"#" 代表初始填充格。

题目描述

Physicist Woll likes to play one relaxing game in between his search of the theory of everything. Game interface consists of a rectangular $ n×m $ playing field and a dashboard. Initially some cells of the playing field are filled while others are empty. Dashboard contains images of all various connected (we mean connectivity by side) figures of 2, 3, 4 and 5 cells, with all their rotations and reflections. Player can copy any figure from the dashboard and place it anywhere at the still empty cells of the playing field. Of course any figure can be used as many times as needed. Woll's aim is to fill the whole field in such a way that there are no empty cells left, and also... just have some fun. Every initially empty cell should be filled with exactly one cell of some figure. Every figure should be entirely inside the board. In the picture black cells stand for initially filled cells of the field, and one-colour regions represent the figures.

输入输出格式

输入格式

First line contains integers $ n $ and $ m $ ( $ 1<=n,m<=1000 $ ) — the height and the width of the field correspondingly. Next $ n $ lines contain $ m $ symbols each. They represent the field in a natural way: $ j $ -th character of the $ i $ -th line is "\#" if the corresponding cell is filled, and "." if it is empty.

输出格式

If there is no chance to win the game output the only number "-1" (without the quotes). Otherwise output any filling of the field by the figures in the following format: each figure should be represented by some digit and figures that touch each other by side should be represented by distinct digits. Every initially filled cell should be represented by "\#".

输入输出样例

输入样例 #1

2 3
...
#.#

输出样例 #1

000
#0#

输入样例 #2

3 3
.#.
...
..#

输出样例 #2

5#1
511
55#

输入样例 #3

3 3
...
.##
.#.

输出样例 #3

-1

输入样例 #4

1 2
##

输出样例 #4

##

说明

In the third sample, there is no way to fill a cell with no empty neighbours. In the forth sample, Woll does not have to fill anything, so we should output the field from the input.