Minesweeper

题意翻译

给出一个扫雷地图（大家肯定都玩过），让你求这个地图是否合法。 对于地图是否合法有两个规则： - 对应点的数字周围必须有对应数字个雷 - 空的地方周围没有雷 感谢@liyifeng 提供翻译

题目描述

One day Alex decided to remember childhood when computers were not too powerful and lots of people played only default games. Alex enjoyed playing Minesweeper that time. He imagined that he saved world from bombs planted by terrorists, but he rarely won. Alex has grown up since then, so he easily wins the most difficult levels. This quickly bored him, and he thought: what if the computer gave him invalid fields in the childhood and Alex could not win because of it? He needs your help to check it. A Minesweeper field is a rectangle $ n \times m $ , where each cell is either empty, or contains a digit from $ 1 $ to $ 8 $ , or a bomb. The field is valid if for each cell: - if there is a digit $ k $ in the cell, then exactly $ k $ neighboring cells have bombs. - if the cell is empty, then all neighboring cells have no bombs. Two cells are neighbors if they have a common side or a corner (i. e. a cell has at most $ 8 $ neighboring cells).

输入输出格式

输入格式

The first line contains two integers $ n $ and $ m $ ( $ 1 \le n, m \le 100 $ ) — the sizes of the field. The next $ n $ lines contain the description of the field. Each line contains $ m $ characters, each of them is "." (if this cell is empty), "\*" (if there is bomb in this cell), or a digit from $ 1 $ to $ 8 $ , inclusive.

输出格式

Print "YES", if the field is valid and "NO" otherwise. You can choose the case (lower or upper) for each letter arbitrarily.

输入输出样例

输入样例 #1

3 3
111
1*1
111

输出样例 #1

YES

输入样例 #2

2 4
*.*.
1211

输出样例 #2

NO

说明

In the second example the answer is "NO" because, if the positions of the bombs are preserved, the first line of the field should be \*2\*1. You can read more about Minesweeper in <a>Wikipedia's article</a>.