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 ** 9)
H, W = map(int, input().split())
G = [list(input()) for i in range(H)]
C = [[0] * W for i in range(H)]


def dfs(nh, nw, color):
    direction = [(1, 0), (0, 1), (-1, 0), (0, -1)]
    C[nh][nw] = color
    for dh, dw in direction:
        if not ((0 <= nh + dh < H) and (0 <= nw + dw < W)):
            continue
        if C[nh + dh][nw + dw] != 0:
            continue
        if G[nh][nw] == G[nh + dh][nw + dw]:
            continue
        C[nh + dh][nw + dw] = color
        dfs(nh + dh, nw + dw, -color)


Color = 1
for h in range(H):
    for w in range(W):
        if C[h][w] == 0:
            dfs(h, w, Color)
            Color += 1


Count = {}
for h in range(H):
    for w in range(W):
        Count[C[h][w]] = 0
        Count[-C[h][w]] = 0


for h in range(H):
    for w in range(W):
        Count[C[h][w]] += 1


ans = 0
for key in Count.keys():
    ans += Count[key] * Count[-key]

print(ans // 2)