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:
# Mar 11, 12:14-
def inpl(): return list(map(int,input().split()))

H,W = inpl()
S = ''
for i in range(H):
    S += input()

N = H*W
parent = [-1]*N
white = [0]*N
black = [0]*N

def group(n):
    if parent[n] < 0:
        return n
    else:
        g = group(parent[n])
        parent[n] = g
        return g

def merge(m,n):
    gm = group(m)
    gn = group(n)
    if gm != gn:
        parent[gn] = gm
        white[gm] += white[gn]
        black[gm] += black[gn]
    return gm

def groupsize(n):
    g = group(n)
    return white[g]*black[g]

def place(n):
    return divmod(n,W)

def index(h,w):
    return h*W + w

for n in range(N):
    if S[n] == '.':
        white[n] = 1
    else:
        black[n] = 1

    h, w = place(n)
    if h > 0 and S[n] != S[n-W]:
        merge(n-W,n)
    if w > 0 and S[n] != S[n-1]:
        merge(n-1,n)    

groupset = set()
for n in range(N):
    groupset.add(group(n))

sizes = [ groupsize(p) for p in groupset ]
ans = sum(sizes)

print(ans)