Casper is designing an electronic circuit on a NxM rectangular grid plate. There are NxM square tiles that are aligned to the grid on the plate. Two (out of four) opposite corners of each tile are connected by a wire.

A power source is connected to the top left corner of the plate. A lamp is connected to the bottom right corner of the plate. The lamp is on only if there is a path of wires connecting power source to lamp. In order to switch the lamp on, any number of tiles can be turned by 90 (in both directions).

In the picture above the lamp is off. If any one of the tiles in the second column from the right is turned by 90 , power source and lamp get connected, and the lamp is on.

Write a program to find out the minimal number of tiles that have to be turned by 90 to switch the lamp on.

입력

• The first line of input contains two integer numbers N and M, the dimensions of the plate. In each of
• the following N lines there are M symbols fi either \ or / fi which indicate the direction of the wire connecting the opposite vertices of the corresponding tile.

출력

it is not possible, output the string: NO SOLUTION

Constraints

입출력 예

입력

3 5
\\/\\
\\///
/\\\\

출력

1

출처:BOI 2011 day1 3/4