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(10**6)

H, W = map(int, input().split())
S = [input() for _ in range(H)]
check = [[0]*W for _ in range(H)]
di = [-1, 0, 1, 0]
dj = [ 0,-1, 0, 1]
black, white = 0, 0

def dfs(i, j):
    global check, black, white
    if check[i][j]:
        return
    else:
        check[i][j] = 1
    if S[i][j] == '#':
        black += 1
    else:
        white += 1
    for dir in range(4):
        ni = i + di[dir]
        nj = j + dj[dir]
        if ni < 0 or ni >= H or nj < 0 or nj >= W: continue
        if S[i][j] == S[ni][nj]: continue
        dfs(ni, nj)
    return

ans = 0
for i in range(H):
    for j in range(W):
        black, white = 0, 0
        dfs(i, j)
        ans += black * white

print(ans)