You are given a grid of letters. Your task is to calculate, for each letter, the number of rectangular subgrids whose border consists of that letter.

Input

The first line has two integers $n$ and $k$: the size of the grid and the number of letters. The letters are the first $k$ uppercase letters.

After this, there are $n$ lines that describe the grid. Each line has $n$ letters.

Output

Print $k$ lines: for each letter, the number of subgrids.

Constraints

• $1 \le n \le 500$
• $1 \le k \le 26$

Example

Input:

5 3
ABBBC
ABABC
ABBBC
ABBBC
CCCCC

Output:

11
38
29