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(10000000)
H, W = map(int, input().split())
S = [input() for _ in range(H)]
seen = [[0]*W for _ in range(H)]


def rec(h,w,seen):
	if S[h][w] == '.':
		res = [1, 0]
	else:
		res = [0, 1]
	dh = [-1, 1, 0, 0]
	dw = [0, 0, -1, 1] 
	seen[h][w] = 1
	for i in range(4):
		nh = h+dh[i]
		nw = w+dw[i]
		if 0 <= nh <= H-1 and 0 <= nw <= W-1:
			if seen[nh][nw] == 0 and S[nh][nw] != S[h][w]:
				r0, r1 = rec(nh, nw, seen)
				res[0] += r0
				res[1] += r1
					
	return res

ans = 0
for h in range(H):
	for w in range(W):
		if seen[h][w] != 1:
			t0, t1 = rec(h, w, seen)
			ans += t0 * t1
print(ans)