H. Submatricestime limit per test3.5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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. OutputFor each k (1 \le k \le 5) print one integer — the number of submatrices that contain exactly k different letters.ExamplesInput
2 3
ABB
ABA
Output
9 9 0 0 0 Input
6 6
EDCECE
EDDCEB
ACCECC
BAEEDC
DDDDEC
DDAEAD
Output
56 94 131 103 57 Input
3 10
AEAAEEEEEC
CEEAAEEEEE
CEEEEAACAA
Output
78 153 99 0 0 
2 3
ABB
ABA

9 9 0 0 0 
['*special problem', 'bitmasks', 'data structures', 'dp']