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:
H,W = map(int, input().split())
fields = [list(input()) for i in range(H)]
# print(fields)

# seen = [False] * (H*W+1)
seen = [[False] * W for i in range(H)]
mv = [(0,1),(0,-1),(1,0),(-1,0)]
from collections import deque
from collections import defaultdict
ans  = 0
for i in range(H):
    for j in range(W):
        if seen[i][j]: continue
        # print("i,j",i,j)
        d = defaultdict(int)
        q = deque()
        q.append((i,j))
        # d[fields[i][j]] += 1
        while len(q) > 0:
            h,w = q.popleft()
            s = fields[h][w] #そこの文字列
            for dh, dw in mv:
                if 0 <= h + dh < H and 0 <= w + dw < W:
                    if seen[h+dh][w+dw]:continue
                    t = fields[h+dh][w+dw] #隣接セルの文字
                    if t == s:continue #同じ場合は加算せず
                    # print(s,t,h,w,h+dh,w+dw,"debug")
                    d[s] += 1
                    q.append((h+dh,w+dw))
                    seen[h+dh][w+dw] = True
        ans += d["#"]*d["."]
# print(seen)
print(ans)