Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3 3
.#.
..#
#..

Sample Output 1

10

Some of the pairs satisfying the condition are ((1, 2), (3, 3)) and ((3, 1), (3, 2)), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.

Sample Input 2

2 4
....
....

Sample Output 2

0

Sample Input 3

4 3
###
###
...
###

Sample Output 3

6

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep(i,n) for (int i=0; i<(n); ++i)
using namespace std;
typedef long long ll;
typedef pair<int,int> P;

class UnionFind{
    vector<int>p,sz;
public:
    UnionFind(int n){
        p.resize(n,-1);
        sz.resize(n,1);
    }
    int find(int x){
        if(p[x] == -1)return x;
        else return p[x] = find(p[x]);
    }
    void unite(int x, int y){
        x = find(x);
        y = find(y);
        if(x == y)return;
        if(sz[x] > sz[y])swap(x,y);
        p[x] = y;
        sz[y] += sz[x];
    }
    bool same(int x, int y){
        return find(x) == find(y);
    }
    int size(int x){
        return sz[find(x)];
    }
};

int dy[]={-1,0,1,0};
int dx[]={0,-1,0,1};

int main(){
    int h,w;
    cin>>h>>w;
    vector<string>s(h);
    rep(i,h)cin>>s[i];
    UnionFind uf(h*w);
    rep(i,h)rep(j,w){
        rep(dir,4){
            int vy=i+dy[dir];
            int vx=j+dx[dir];
            if(vy<0||vy>=h||vx<0||vx>=w)continue;
            if(s[i][j]!=s[vy][vx])uf.unite(i*w+j,vy*w+vx);
        }
    }
    map<int,int>all,black;
    rep(i,h)rep(j,w){
        all[uf.find(i*w+j)]++;
        if(s[i][j]=='#')black[uf.find(i*w+j)]++;
    }
    ll ans=0;
    for(auto& p:all){
        ans+=(ll)(p.second-black[p.first])*black[p.first];
    }
    cout<<ans<<endl;
}