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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> iint;
typedef pair<ll,ll> llll;
#define ALL(x) (x).begin(),(x).end()
const ll zero = 0;
const ll INF = 3000000000000000000; //10^18
const int inINF = 1000000000; //10^9
const ll MOD = 1000000007; //10^9+7
const ll MOD2 = 998244353;

int black, white;
void dfs(vector<vector<char>> S, vector<vector<int>> &used, int sh, int sw, int H, int W){
    if(sh < H-1 && used[sh+1][sw] == 0 && S[sh+1][sw] == S[sh][sw]){
        if((sh + sw) % 2 == 1){
            black++;
        }
        else{
            white++;
        }
        used[sh+1][sw] = 1;
        dfs(S, used, sh+1, sw, H, W);
    }
    if(sh > 0 && used[sh-1][sw] == 0 && S[sh-1][sw] == S[sh][sw]){
        if((sh + sw) % 2 == 1){
            black++;
        }
        else{
            white++;
        }
        used[sh-1][sw] = 1;
        dfs(S, used, sh-1, sw, H, W);
    }   
    if(sw < W-1 && used[sh][sw+1] == 0 && S[sh][sw+1] == S[sh][sw]){
        if((sh + sw) % 2 == 1){
            black++;
        }
        else{
            white++;
        }
        used[sh][sw+1] = 1;
        dfs(S, used, sh, sw+1, H, W);
    }
    if(sw > 0 && used[sh][sw-1] == 0 && S[sh][sw-1] == S[sh][sw]){
        if((sh + sw) % 2 == 1){
            black++;
        }
        else{
            white++;
        }
        used[sh][sw-1] = 1;
        dfs(S, used, sh, sw-1, H, W);
    }
}

int main(){
    int H, W;
    cin >> H >> W;
    vector<vector<char>> S(H, vector<char> (W));
    for (int i = 0; i < H; i++) {
        for (int j = 0; j < W; j++) {
            cin >> S[i][j];
        }
    }
    for (int i = 0; i < H; i++) {
        for (int j = 0; j < W; j++) {
            if((i+j) % 2 == 0){
                if(S[i][j] == '.'){
                    S[i][j] = '#';
                }
                else{
                    S[i][j] = '.';
                }
            }
        }
    }

    vector<vector<int>> used(H, vector<int> (W, 0));
    int sh, sw;
    sh = 0; sw = 0;
    bool check = true;
    ll ans = 0;

    for (int i = 0; i < H; i++) {
        for (int j = 0; j < W; j++) {
            used[i][j] = 1;
            black = 0;
            white = 0;
            if((i + j) % 2 == 1){
                white++;
            }
            else{
                black++;
            }  
            dfs(S, used, i, j, H, W);
            ans += black * white;
        }
    }

    printf("%lld\n", ans);
}