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 defaultdict as dd

n, mm = [int(i) for i in input().split()]
c = 0
A = []

m = dd(tuple)

for i in range(n):
    B = input()
    for j in range(mm):
        m[(i, j)]=c
        c+=1
    A.append([i=='#' for i in B])

par = [i for i in range(c)]

def find(a):
    if par[a] == a:
        return a
    par[a] = find(par[a])
    return par[a]

def unite(a, b):
    if a < b:
        a, b = b, a
    par[find(a)] = find(b)

def issafe(x,y):
    return x>=0 and x<n and y>=0 and y<mm

for i in range(n):
    for j in range(mm):
        dx = [[-1, 0], [0, 1], [0, -1], [1, 0]]
        for k in range(len(dx)):
            if issafe(i+dx[k][0], j+dx[k][1]) and A[i][j] != A[i+dx[k][0]][j+dx[k][1]]:
                unite(m[(i, j)], m[(i+dx[k][0], j+dx[k][1])])
                
bl = [0]*c
wh = [0]*c

for i in range(n):
    for j in range(mm):
        if A[i][j] == 1:
            bl[find(m[i, j])]+=1
        else:
            wh[find(m[i, j])]+=1

ans = 0
for i in range(c):
    ans += bl[i]*wh[i]

print(ans)