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
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")

from collections import defaultdict
rows, cols = map(int, input().split())
n = rows*cols
ns = defaultdict(set)
ss = [None] * rows
color = [None] * n
for i in range(rows):
    s = input()
    ss[i] = s
    for j,c in enumerate(s):
        u = i*cols+j
        color[u] = c
        if i>0:
            if c!=ss[i-1][j]:
                v = u - cols
                ns[u].add(v)
                ns[v].add(u)
        if j>0:
            if c!=s[j-1]:
                v = u - 1
                ns[u].add(v)
                ns[v].add(u)
seen = [False] * n
ans = 0
for u in range(n):
    if seen[u]:
        continue
    q = [u]
    s = set([u])
    while q:
        u = q.pop()
        for v in ns[u]:
            if seen[v]:
                continue
            seen[v] = True
            s.add(v)
            q.append(v)
    ans += sum(color[item]=="#" for item in s) * sum(color[item]=="." for item in s)
print(ans)