You are given a 2D grid with each cell containing a letter, you have to start at any point and move either up, down, left and right to create the word "ALCATRAZ" by picking up letters in order. After choosing a letter, it gets removed and leaves the cell empty. You have to determine the minimum number of moves needed to do so.

Input

2 space separated integers N, M (number of rows and columns respectively.)

1 <= N, M <= 500

Then next N lines gives the details of the maze.

Output

The shortest path as described in the above problem.

Print "IMPOSSIBLE" (without quotes) if you can't make that word.

Example

Input:
4 5
AZCLT
AARAL
SJATC
LARAZ
Output:
9

Path is as follows: 2,4 → 2,5 → 3,5 → 3,4 → 3,3 → 3,4 → 4,4 → 4,3 → 4,4 → 4,5