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())
S = [list(input()) for _ in range(H)]

cntblack, cntwhite = 0, 0
visited = [[False] * W for _ in range(H)]

def count(h, w):
    global cntblack, cntwhite
    if visited[h][w]: return
    visited[h][w] = True
    if S[h][w] == ".": cntwhite += 1
    else: cntblack += 1
    for ny, nx in ((1,0),(0,1),(-1,0),(0,-1)):
        ny += h
        nx += w
        if not (0 <= ny < H and 0 <= nx < W): continue
        if S[ny][nx] == S[h][w]: continue
        count(ny, nx)


ans = 0
for h in range(H):
    for w in range(W):
        cntblack, cntwhite = 0, 0
        count(h, w)
        ans += cntblack * cntwhite

print(ans)