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## Statement

## Goal

You are given a sliding puzzle containing`W`×

`H`- 1 pieces. You need to find how many times you have to slide these pieces to reorder them from 1 at the top left to

`W`×

`H`- 1 just at the left of the bottom right corner (with the empty space at the bottom right).

For example, only one move is needed to solve the following puzzle (slide 7 to the left) :

1 2 3 4

5 6 . 7

2 moves are needed to solve the following puzzle (slide 3 to the left then 4 to the left) :

1 2 . 3 4

Input

**Line 1 :**The height

`H`and width

`W`of the puzzle.

**Next**A row of the puzzle (

`H`Lines :`W`numbers separated by a space). The empty space is marked with a dot .

Output

**Line 1 :**The number of moves needed to solve the puzzle.

Constraints

1 ≤

0 ≤ Answer ≤ 10

`W`,`H`≤ 100 ≤ Answer ≤ 10

Example

Input

2 2 2 3 1 .

Output

4

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