Problem Statement

There is a town represented as a two-dimensional grid with $H$ horizontal rows and $W$ vertical columns. A character $a_{i,j}$ describes the square at the $i$-th row from the top and $j$-th column from the left. Here, $a_{i,j}$ is one of the following: S , G , . , # , a, ..., and z. # represents a square that cannot be entered, and a, ..., z represent squares with teleporters.

Takahashi is initially at the square represented as S. In each second, he will make one of the following moves:

• Go to a non-# square that is horizontally or vertically adjacent to his current position.
• Choose a square with the same character as that of his current position, and teleport to that square. He can only use this move when he is at a square represented as a, ..., or z.

Find the shortest time Takahashi needs to reach the square represented as G from the one represented as S. If the destination is unreachable, report -1 instead.

Constraints

• $1 \le H, W \le 2000$
• $a_{i,j}$ is S, G, ., #, or a lowercase English letter.
• There is exactly one square represented as S and one square represented as G.

Input

Input is given from Standard Input in the following format:

H W
a_{1,1}\dots a_{1,W}
\vdots
a_{H,1}\dots a_{H,W}

Output

Print the shortest time Takahashi needs to reach the square represented as G from the one represented as S. If the destination is unreachable from the initial position, print -1 instead.