Submatrices
Description
You are given matrix $s$ that contains $n$ rows and $m$ columns. Each element of a matrix is one of the $5$ first Latin letters (in upper case).
For each $k$ ($1 \le k \le 5$) calculate the number of submatrices that contain exactly $k$ different letters. Recall that a submatrix of matrix $s$ is a matrix that can be obtained from $s$ after removing several (possibly zero) first rows, several (possibly zero) last rows, several (possibly zero) first columns, and several (possibly zero) last columns. If some submatrix can be obtained from $s$ in two or more ways, you have to count this submatrix the corresponding number of times.
The first line contains two integers $n$ and $m$ ($1 \le n, m \le 800$).
Then $n$ lines follow, each containing the string $s_i$ ($|s_i| = m$) — $i$-th row of the matrix.
For each $k$ ($1 \le k \le 5$) print one integer — the number of submatrices that contain exactly $k$ different letters.
Input
The first line contains two integers $n$ and $m$ ($1 \le n, m \le 800$).
Then $n$ lines follow, each containing the string $s_i$ ($|s_i| = m$) — $i$-th row of the matrix.
Output
For each $k$ ($1 \le k \le 5$) print one integer — the number of submatrices that contain exactly $k$ different letters.
Samples
2 3
ABB
ABA
9 9 0 0 0
6 6
EDCECE
EDDCEB
ACCECC
BAEEDC
DDDDEC
DDAEAD
56 94 131 103 57
3 10
AEAAEEEEEC
CEEAAEEEEE
CEEEEAACAA
78 153 99 0 0