You are given a grid of n rows and m columns consisting of lowercase English letters a, b, c, and d.

We say 4 cells form a "nice-quadruple" if and only if

The letters on these cells form a permutation of the set {\(a,b,c,d\)}.
The cell marked b is directly reachable from cell marked a.
The cell marked c is directly reachable from the cell marked b.
The cell marked d is directly reachable from the cell marked c.

A cell \((x2,y2)\) is said to be directly reachable from cell \((x1,y1)\) if and only if \((x2,y2)\) is one of these 4 cells { \((x1-1,y1)\), \((x1+1,y1)\), \((x1,y1-1)\) and \((x1,y1+1)\)}).

Given the constraint that each cell can be part of at most 1 "nice-quadruple", what's the maximum number of "nice-quadruples" you can select?

Input format

First line: Two space-separated integers n and m
Next n lines: Each contains m space separated lowercase letters from the set {\(a,b,c,d\)} denoting the grid cells.

Output format

Output the maximum number of "nice-quadruple" you can select.

Constraints

\(1 \le n,m \le 20\)