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())
board = [[int(j=="#") for j in input()] for i in range(h)]
dxdy = [(0,1), (0,-1), (1,0), (-1,0)]

def dfs(i, j, k, prev):
    if used[i][j] or board[i][j] == prev:
        return
    used[i][j] = 1
    k[board[i][j]] += 1
    for dx, dy in dxdy:
        nx, ny = i+dx, j+dy
        if 0 <= nx < h and 0 <= ny < w and not used[nx][ny] and board[nx][ny] != board[i][j]:
            dfs(nx,ny,k,board[i][j])

used = [[0]*w for i in range(h)]
ans = 0
for i in range(h):
    for j in range(w):
        if used[i][j]:
            continue
        k = [0]*2
        dfs(i,j,k, -1)
        ans += k[0]*k[1]
print(ans)