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 ** 7)
h, w = map(int, input().split())
s = [input() for i in range(h)]
t = [[None] * w for i in range(h)]
d = [(1, 0), (0, 1), (-1, 0), (0, -1)]
def dfs(i, j, bw):
    global h, w
    if not (0 <= i < h and 0 <= j < w) or s[i][j] == bw or t[i][j]:
        return 0, 0
    t[i][j] = True
    W, b = 0, 0
    if s[i][j] == "#":
        b += 1
    else:
        W += 1
    for k in d:
        n, m = dfs(i + k[0], j + k[1], s[i][j])
        W += n
        b += m
    return W, b
ans = 0
for i in range(h):
    for j in range(w):
        X, Y = dfs(i, j, "u shi ta pu ni chi a ku n wara")
        ans += X * Y
print(ans)