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 CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,a) FOR(i,0,a)
const int MAX_W=400,MAX_H=400;
int H,W;
string S[MAX_H];	
bool flg[MAX_H][MAX_W];
typedef pair<int,int> P;
int dx[4]={1,0,-1,0},dy[4]={0,1,0,-1};
int main(){
	cin>>H>>W;
	REP(i,H)cin>>S[i];
	ll ans=0;
	REP(h,H){
		REP(w,W){
			if (!flg[h][w] && S[h][w]=='#'){
				queue<P> que;
				que.push(P(h,w));
				flg[h][w]=true;
				ll bc=0,wc=0;
				while(!que.empty()){
					P p=que.front();
					que.pop();
					if (S[p.first][p.second]=='#'){
						bc++;
					}else{
						wc++;
					}
					REP(t,4){
						int h2=p.first+dy[t],w2=p.second+dx[t];
						if (0<=h2 && h2<H && 0<=w2 && w2<W && S[h2][w2]!=S[p.first][p.second] && !flg[h2][w2]){
							que.push(P(h2,w2));
							flg[h2][w2]=true;
						}
					}
				}
				ans+=wc*bc;
			}
		}
	}
	cout<<ans<<endl;
	return 0;
}