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 = sys.stdin.readline
sys.setrecursionlimit(10**7)
h, w = map(int, input().split())
n = h*w
fld = ''.join([input().rstrip()for _ in range(h)])
edges = [set() for _ in range(n)]


def to_v(i, j):
    return i*w+j


for i in range(h):
    for j in range(w):
        v = to_v(i, j)
        dirc = [(-1, 0), (0, 1), (1, 0), (0, -1)]
        for di, dj in dirc:
            x, y = i+di, j+dj
            if x < 0 or h <= x or y < 0 or w <= y:
                continue
            v2 = to_v(x, y)
            if fld[v] != fld[v2]:
                edges[v].add(v2)
                edges[v2].add(v)


def dfs(v, c=0):
    if visited[v]:
        return
    visited[v] = 1
    cnt[c] += 1
    for v2 in edges[v]:
        dfs(v2, c ^ 1)


visited = [0]*n
ans = 0
for v in range(n):
    if visited[v]:
        continue
    cnt = [0, 0]
    dfs(v)
    ans += cnt[0]*cnt[1]
print(ans)