Problem: There is a grid with H rows and W columns, where each square is painted black or white.

You are given H strings S_1, S_2, ..., S_H, each of length W. If the square at the i-th row from the top and the j-th column from the left is painted black, the j-th character in the string S_i is `#`; if that square is painted white, the j-th character in the string S_i is `.`.

Find the number of pairs of a black square c_1 and a white square c_2 that satisfy the following condition:

* There is a path from the square c_1 to the square c_2 where we repeatedly move to a vertically or horizontally adjacent square through an alternating sequence of black and white squares: black, white, black, white...

Constraints

* 1 \leq H, W \leq 400
* |S_i| = W (1 \leq i \leq H)
* For each i (1 \leq i \leq H), the string S_i consists of characters `#` and `.`.

Input

Input is given from Standard Input in the following format:


H W
S_1
S_2
:
S_H


Output

Print the answer.

Examples

Input

3 3
.#.
..#
#..


Output

10


Input

3 3
.#.
..#
..


Output

10


Input

2 4
....
....


Output

0


Input

4 3


...


Output

6

Solution (in PYTHON):

Solution:
#!/usr/bin/env python
# -*- coding: utf-8 -*-

# AISing Programming Contest 2019：C - Alternating Path
import sys
sys.setrecursionlimit(10000000)

H, W = [int(i) for i in raw_input().strip().split(' ')]
S = []
for _ in range(H):
    S.append(raw_input().strip())
C = '#.'
CR = {'#':0, '.':1}


def find(h, w, sumi):
    while True:
        if sumi[h][w] == False:
            return (h, w)
        w += 1
        if w >= W:
            w = 0
            h += 1
            if h >= H:
                return None
    return None


def chain((h, w), t, c, sumi):
    if 0 <= h < H and 0 <= w < W:
        pass
    else:
        return c
    if sumi[h][w]:
        return c
    if S[h][w] == C[t]:
        sumi[h][w] = True
        c[t] += 1
        for ptr in [(-1, 0), (0, 1), (1, 0), (0, -1)]:
            c = chain((h+ptr[0], w+ptr[1]), 1-t, c, sumi)
        return c
    return c


def main():
    sumi = [[False for _ in range(W)] for _ in range(H)]
    h, w = 0, 0
    n = 0
    while True:
        c = [0, 0]
        # print 'sumi:', sumi
        result = find(h, w, sumi)
        if not result:
            break
        h, w = result[0], result[1]
        # print 'found:', h, w
        c = chain((h, w), CR[S[h][w]], c, sumi)
        # print c
        n += c[0] * c[1]
    print n


if __name__ == '__main__':
    main()