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문제

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?

Consider the following grid, with N=5 and M=6:

            ###=##
#.W.##
#.####
#.@W##
######

A single slide has endpoints denoted by an uppercase W. Her optimal strategy is to move right to the slide endpoint in 1 time, take the slide in 0 time to the other endpoint, and move right and up in 2 more time to end on the exit.  This requires a total of 3 time, the minimum.

입력

• Line 1: Two space separated integers: N and M
• Lines 2..N+1: Line i+1 describes row i of the maze: M characters (no spaces)

출력

• Line 1: An integer, corresponding to the shortest time that Bessie needs to exit the maze.

예제 입력 1

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


예제 출력 1

3