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:
import sys
sys.setrecursionlimit(200000)

H, W = map(int, input().split())
S = []
for i in range(H):
    S.append(input())


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

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


def dfs(x, y):
    global nb, nw
    if S[y][x] == '#':
        nb += 1
    if S[y][x] == '.':
        nw += 1
    for i in range(4):
        nx = x + dx[i]
        ny = y + dy[i]
        if nx < 0 or nx >= W or ny < 0 or ny >= H:
            continue
        if used[ny][nx]:
            continue
        if S[y][x] == '#' and S[ny][nx] == '#':
            continue
        if S[y][x] == '.' and S[ny][nx] == '.':
            continue
        used[ny][nx] = True
        dfs(nx, ny)

ans = 0
for i in range(H):
    for j in range(W):
        if not used[i][j]:
            used[i][j] = True
            nb = 0
            nw = 0
            dfs(j, i)
            ans += nb*nw
print(ans)