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<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define rep(i,l,r) for (int i=(l); i<=(r); i++)
typedef long long ll;
using namespace std;

const int N=410;
const int dx[4]={-1,1,0,0},dy[4]={0,0,-1,1};
ll ans;
char mp[N][N];
int n,m,co,bel[N][N],s1[N*N],s2[N*N];
struct P{ int x,y; }q[N*N];

void bfs(int sx,int sy){
	int st=0,ed=1; q[1]=(P){sx,sy}; co++; bel[sx][sy]=co;
	if (mp[sx][sy]=='#') s1[co]++; else s2[co]++;
	while (st<ed){
		st++; int x=q[st].x,y=q[st].y;
		rep(i,0,3){
			int x1=x+dx[i],y1=y+dy[i];
			if (x1<1 || x1>n || y1<1 || y1>m || mp[x1][y1]==mp[x][y]) continue;
			if (!bel[x1][y1]){
				bel[x1][y1]=co; q[++ed]=(P){x1,y1};
				if (mp[x1][y1]=='#') s1[co]++; else s2[co]++;
			}
		}
	}
}

int main(){
	scanf("%d%d",&n,&m);
	rep(i,1,n) scanf("%s",mp[i]+1);
	rep(i,1,n) rep(j,1,m) if (!bel[i][j]) bfs(i,j);
	rep(i,1,co) ans+=1ll*s1[i]*s2[i];
	printf("%lld\n",ans);
	return 0;
}