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(1000000)


H,W=map(int,input().split())
S=[]
for i in range(H):
    S.append(input())

def DFS(h,w,black,white,m):
    black,white=BorW(h,w,black,white)
    step=[[0,1],[0,-1],[1,0],[-1,0]]
    seen[h][w]=1
    for dh,dw in step:
        nh=h+dh
        nw=w+dw
        if 0<=nh<H and 0<=nw<W:
            if seen[nh][nw]==0 and m!=S[nh][nw]:
                seen[nh][nw]=1
                black,white=DFS(nh,nw,black,white,S[nh][nw])
    return black,white


def BorW(h,w,black,white):
    if S[h][w]=="#":
        black+=1
    else:
        white+=1
    return black,white


seen=[[0]*W for _ in range(H)]

L=[]
for h in range(H):
    for w in range(W):
        black=0
        white=0
        if seen[h][w]==0:
            black,white=DFS(h,w,black,white,S[h][w])
            L.append([black,white])
ans=0
for b,w in L:
     ans+=b*w

print(ans)