p03157 AISing Programming Contest 2019 - Alternating Path
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
```python
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
h,w = map(int,input().split())
S = [input() for _ in range(h)]


avail = [[True]*w for _ in range(h)]


def search(i,j,data):
    if S[i][j] == "#":
        data[0] += 1
    else:
        data[1] += 1
    avail[i][j] = False

    if i+1 < h and S[i+1][j] != S[i][j] and avail[i+1][j]:
        search(i+1,j,data)
    if j+1 < w and S[i][j+1] != S[i][j] and avail[i][j+1]:
        search(i,j+1,data)
    if i > 0 and S[i][j] != S[i-1][j] and avail[i-1][j]:
        search(i-1,j,data)
    if j > 0 and S[i][j] != S[i][j-1] and avail[i][j-1]:
        search(i,j-1,data)

ans = 0
for i in range(h):
    for j in range(w):
        if avail[i][j]:
            data = [0,0]
            search(i,j,data)
            ans+= data[0]*data[1]
            #print(data,i,j)

print(ans)
```