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 PYTHON3):

Solution:
# https://atcoder.jp/contests/aising2019/submissions/3986315
# 解説のように 連結成分を求めてから、bfsする
import sys
sys.setrecursionlimit(2 * 10 ** 5)

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

ans = 0

dx = [0, 0, 1, -1]
dy = [1, -1, 0, 0]

un_reached = [[True for i in range(W)] for j in range(H)]


def isIn(x, y):
    return 0 <= x < H and 0 <= y < W


def dfs(x, y):
    un_reached[x][y] = False
    if s[x][y] == '#':
        cc[1] += 1
    else:
        cc[0] += 1

    for i in range(4):
        nx = x+dx[i]
        ny = y+dy[i]
        if isIn(nx, ny) and s[nx][ny] != s[x][y] and un_reached[nx][ny]:
            dfs(nx, ny)


for i in range(H):
    for j in range(W):
        if un_reached[i][j]:
            cc = [0 for _ in range(2)]
            dfs(i, j)
            ans += cc[1]*cc[0]
print(ans)