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

1. The letters on these cells form a permutation of the set {$a,b,c,d$}.
2. The cell marked b is directly reachable from cell marked a.
3. The cell marked c is directly reachable from the cell marked b.
4. 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

$1 \le n,m \le 20$