CF984B.Minesweeper

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).

有一天，Alex 决定回忆童年时光——那时计算机性能还不太强大，许多人只玩系统自带的默认游戏。Alex 当时很喜欢玩扫雷游戏。他想象自己正在拯救世界，拆除恐怖分子埋设的炸弹，但很少获胜。

自那以后，Alex 已经长大，如今他能轻松通关最难的关卡。这很快让他感到厌烦，于是他想：如果童年时电脑给他生成的是无效的棋盘，而 Alex 当时无法获胜，会不会正是因为这个原因呢？

他需要你的帮助来验证这一点。

扫雷棋盘是一个 $n \times m$ 的矩形，其中每个格子要么为空，要么包含一个从 $1$ 到 $8$ 的数字，要么是一颗地雷。当且仅当满足以下条件时，该棋盘是有效的：

• 若某格子中有一个数字 $k$，则其恰好有 $k$ 个相邻格子含有地雷；
• 若某格子为空，则其所有相邻格子均不含地雷。

两个格子被称为相邻，当且仅当它们有一条公共边或一个公共角（即：一个格子最多有 $8$ 个相邻格子）。

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.

第一行包含两个整数 $n$ 和 $m$（$1 \le n, m \le 100$）—— 表示场地的尺寸。

接下来的 $n$ 行描述该场地。每行包含 $m$ 个字符，每个字符为：.（表示该格子为空）、*（表示该格子中有一颗炸弹），或一个从 $1$ 到 $8$（含）的数字。

Print "YES", if the field is valid and "NO" otherwise.

You can choose the case (lower or upper) for each letter arbitrarily.

如果该字段有效，则输出 "YES"，否则输出 "NO"。

对于每个字母，你可以任意选择其大小写（小写或大写）。

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 Wikipedia's article.

在第二个例子中，答案为“NO”，因为如果炸弹的位置保持不变，则场地的第一行应为 *2*1。

您可以在 维基百科的文章 中了解有关扫雷游戏的更多信息。