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

from collections import deque
import itertools as it
import sys
import math

sys.setrecursionlimit(1000000)

INF = 10 ** 18

H, W = map(int, raw_input().split())
S = [raw_input() for _ in range(H)]

used = [[False] * W for _ in range(H)]

def func(y, x, c):
    if y < 0 or x < 0 or y >= H or x >= W:
        return 0, 0
    if used[y][x] or S[y][x] == c:
        return 0, 0

    used[y][x] = True

    rw, rb = 0, 0
    if S[y][x] == '.':
        rw = 1
    else:
        rb = 1
    ret = func(y - 1, x, S[y][x])
    rw += ret[0]
    rb += ret[1]
    ret = func(y + 1, x, S[y][x])
    rw += ret[0]
    rb += ret[1]
    ret = func(y, x - 1, S[y][x])
    rw += ret[0]
    rb += ret[1]
    ret = func(y, x + 1, S[y][x])
    rw += ret[0]
    rb += ret[1]
    return rw, rb

ans = 0

for i in range(H):
    for j in range(W):
        ret = func(i, j, ' ')
        ans += ret[0] * ret[1]

print ans