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/tasks/aising2019_c

import sys
sys.setrecursionlimit(10 ** 7)

H, W = map(int, input().split())
M = [list(input()) for _ in range(H)]
seen = [[False for _ in range(W)] for _ in range(H)]


def dfs(h, w, ph, pw):
    if M[h][w] == '.':
        bc, wc = 0, 1
    else:
        bc, wc = 1, 0
    for (dh, dw) in [(0, 1), (0, -1), (1, 0), (-1, 0)]:
        nh, nw = h + dh, w + dw
        if nh < 0 or H <= nh or nw < 0 or W <= nw:
            continue
        if nh == ph and nw == pw:
            continue
        if seen[nh][nw]:
            continue
        if M[nh][nw] == M[h][w]:
            continue
        seen[nh][nw] = True
        b_add, w_add = dfs(nh, nw, h, w)
        bc += b_add
        wc += w_add
    return bc, wc

ans = 0
for h in range(H):
    for w in range(W):
        if seen[h][w] == False:
            seen[h][w] = True
            b, w = dfs(h, w, -1, -1)
            ans += b * w
print(ans)