[USACO11OPEN]Corn Maze S

题意翻译

奶牛们去一个 $N\times M$ 玉米迷宫,$2 \leq N \leq 300,2 \leq M \leq300$。 迷宫里有一些传送装置,可以将奶牛从一点到另一点进行瞬间转移。这些装置可以双向使用。 如果一头奶牛处在这个装置的起点或者终点,这头奶牛就**必须**使用这个装置。 玉米迷宫除了唯一的一个出口都被玉米包围。 迷宫中的每个元素都由以下项目中的一项组成: 1. 玉米,`#` 表示,这些格子是不可以通过的。 1. 草地,`.` 表示,可以简单的通过。 1. 传送装置,每一对大写字母 $\tt{A}$ 到 $\tt{Z}$ 表示。 1. 出口,`=` 表示。 1. 起点, `@` 表示 奶牛能在一格草地上可能存在的四个相邻的格子移动,花费 $1$ 个单位时间。从装置的一个结点到另一个结点不花时间。

题目描述

This past fall, Farmer John took the cows to visit a corn maze. But this wasn't just any corn maze: it featured several gravity-powered teleporter slides, which cause cows to teleport instantly from one point in the maze to another. The slides work in both directions: a cow can slide from the slide's start to the end instantly, or from the end to the start. If a cow steps on a space that hosts either end of a slide, she must use the slide. The outside of the corn maze is entirely corn except for a single exit. The maze can be represented by an N x M (2 <= N <= 300; 2 <= M <= 300) grid. Each grid element contains one of these items: \* Corn (corn grid elements are impassable) \* Grass (easy to pass through!) \* A slide endpoint (which will transport a cow to the other endpoint) \* The exit A cow can only move from one space to the next if they are adjacent and neither contains corn. Each grassy space has four potential neighbors to which a cow can travel. It takes 1 unit of time to move from a grassy space to an adjacent space; it takes 0 units of time to move from one slide endpoint to the other. Corn-filled spaces are denoted with an octothorpe (#). Grassy spaces are denoted with a period (.). Pairs of slide endpoints are denoted with the same uppercase letter (A-Z), and no two different slides have endpoints denoted with the same letter. The exit is denoted with the equals sign (=). Bessie got lost. She knows where she is on the grid, and marked her current grassy space with the 'at' symbol (@). What is the minimum time she needs to move to the exit space?

输入输出格式

输入格式


第一行:两个用空格隔开的整数 $N$ 和 $M$。 第 $2\sim N+1$ 行:第 $i+1$ 行描述了迷宫中的第 $i$ 行的情况(共有$M$个字符,每个字符中间没有空格)。

输出格式


一个整数,表示起点到出口所需的最短时间。

输入输出样例

输入样例 #1

5 6
###=##
#.W.##
#.####
#.@W##
######

输出样例 #1

3

说明

例如以下矩阵,$N=5,M=6$。 ```plain ###=## #.W.## #.#### #.@W## ###### ``` 唯一的一个装置的结点用大写字母 $\tt{W}$ 表示。 最优方案为:先向右走到装置的结点,花费一个单位时间,再到装置的另一个结点上,花费 $0$ 个单位时间,然后再向右走一个,再向上走一个,到达出口处,总共花费了 $3$ 个单位时间。