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(200000)
input = sys.stdin.readline

H, W = map(int, input().split())
S = []
for i in [0]*H:
    l = input()
    S.append([1 if x == "#" else -1 for x in l])

bk = 0
wh = 0
def check(S, x, y):
    global bk, wh
    n = S[y][x]
    if n == 0:
        return 
    elif n == 1:
        bk += 1
    elif n == -1:
        wh += 1
    S[y][x] = 0
    if 0 < y and S[y-1][x] == -n:
        check(S, x, y-1)
    if 0 < x and S[y][x-1] == -n:
        check(S, x-1, y)
    if y < H-1 and S[y+1][x] == -n:
        check(S, x, y+1)
    if x < W-1 and S[y][x+1] == -n:
        check(S, x+1, y)
    return 

cnt = 0
for y in range(H):
    for x in range(W):
        if S[y][x] == 1:
            check(S, x, y)
            cnt += wh*bk
            wh = 0
            bk = 0
            
print(cnt)