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:
from collections import deque
import sys
sys.setrecursionlimit(200000)
#input = sys.stdin.readline
h,w = map(int,input().split())
a = [[j for j in input()] for i in range(h)]
used = [[0]*w for i in range(h)]
def dfs(x,y):
    if used[x][y]:
        return 0
    global go
    used[x][y] = 1
    if x-1 >=0 and a[x-1][y] != a[x][y]:
            go.add((x-1,y))
            dfs(x-1,y)
    if y-1 >=0 and a[x][y-1] != a[x][y]:
            go.add((x,y-1))
            dfs(x,y-1)
    if x+1 <h and a[x+1][y] != a[x][y]:
            go.add((x+1,y))      
            dfs(x+1,y)
    if y+1 <w and a[x][y+1] != a[x][y]:
            go.add((x,y+1))
            dfs(x,y+1)
ans = 0
for i in range(h):
    for j in range(w):
        go = set()
        if used[i][j]:
            continue
        dfs(i,j)
        kuro = 0
        siro = 0
        for k,l in go:
            if a[k][l] == "#":
                kuro += 1
            else:
                siro += 1
        ans += kuro*siro

print(ans)