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#1027. 「一本通 1.4 例 1」电路维修

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题目描述

译自 BalticOI 2011 Day1 T3「Switch the Lamp On」
有一种正方形的电路元件,在它的两组相对顶点中,有一组会用导线连接起来,另一组则不会。
有 $N\times M$ 个这样的元件,你想将其排列成 $N$ 行 $M$ 列放在电路板上。电路板的左上角连接电源,右下角连接灯泡。

试求:至少要旋转多少个正方形元件才能让电源与灯泡连通,若无解则输出 $\texttt{NO SOLUTION}$。

Casper is designing an electronic circuit on a $N ×M$ rectangular grid plate. There are $N ×M$ square tiles that are aligned to the grid on the plate. Two (out of four) opposite corners of each tile are connected by a wire.
A power source is connected to the top left corner of the plate. A lamp is connected to the bottom right corner of the plate. The lamp is on only if there is a path of wires connecting power source to lamp. In order to switch the lamp on, any number of tiles can be turned by $90°$ (in both directions).
In the picture above the lamp is off. If any one of the tiles in the second column from the right is turned by $90°$ , power source and lamp get connected, and the lamp is on.
Write a program to find out the minimal number of tiles that have to be turned by $90°$ to switch the lamp on.

输入格式

第一行有两个整数 $N$ 和 $M$。
在接下来的 $N$ 行中,每行有 $M$ 个字符。每个字符均为 \/,表示正方形元件上导线的连接方向。

The first line of input contains two integer numbers $N$ and $M$, the dimensions of the plate. In each of the following $N$ lines there are $M$ symbols – either \ or / – which indicate the direction of the wire connecting the opposite vertices of the corresponding tile.

输出格式

输出共一行,若有解则输出一个整数,表示至少要旋转多少个正方形元件才能让电源与灯泡连通;若无解则输出 NO SOLUTION

There must be exactly one line of output. If it is possible to switch the lamp on, this line must contain only one integer number: the minimal number of tiles that have to be turned to switch on the lamp. If it is not possible, output the string: NO SOLUTION

样例

样例输入

3 5
\\/\\
\\///
/\\\\

样例输出

1

数据范围与提示

对于 $40\%$ 的数据,$1 ≤ N ≤ 4, 1 ≤ M ≤ 5$。
对于所有数据,$1 ≤ N,M ≤ 500$。


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