Big Hexagons

Tokens of several colors have been placed on a hex grid.

Your task is count the number of regular hexagons whose all vertices are of the same color.

Input

The first line contains two numbers $X,Y$ , $2 \leq X,Y \leq 100$ . $X$ is the number of grid points in the first row, and $Y$ is the number of rows. Odd-numbered rows contain $X$ grid points and even-numbered rows contain $X-1$ grid points.

The following $Y$ lines contain a description of a board. A dot denotes an empty grid points, and colors are denoted by lowercase characters (’a’-’z’). See the example.

Output

Output the number of regular hexagons.

Problem information

Author: Eryk Kopczynski

Generation: 2026-01-25T14:44:12.323Z