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 JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.text.*;
//Solution Credits: Taranpreet Singh
public class Main{
    //SOLUTION BEGIN
    void pre() throws Exception{}
    void solve(int TC) throws Exception{
        int r = ni(), c = ni();
        int[][] e = new int[4*r*c][];int cnt = 0;
        char[][] g = new char[r][];
        for(int i = 0; i< r; i++)g[i] = n().toCharArray();
        int[] gr = new int[r*c];
        for(int i = 0; i< r; i++){
            for(int j = 0; j< c; j++){
                if(i+1<r && g[i][j]!=g[i+1][j])e[cnt++] = new int[]{i*c+j, (i+1)*c+j};
                if(j+1<c && g[i][j]!=g[i][j+1])e[cnt++] = new int[]{i*c+j, i*c+j+1};
                gr[i*c+j] = g[i][j]=='#'?0:1;
            }
        }
        int[][] gg = makeU(r*c, e, cnt);
        boolean[] vis = new boolean[r*c];
        long ans = 0;
        for(int i = 0; i< gg.length; i++){
            if(vis[i])continue;
            cc[0] = 0;cc[1] = 0;
            dfs(gg,gr,vis, i);
            ans+=cc[0]*cc[1];
        }
        pn(ans);
    }
    long[] cc= new long[]{0,0};
    void dfs(int[][] gg, int[] gr,boolean[] vis, int u){
        cc[gr[u]]++;
        vis[u] = true;
        for(int v:gg[u])if(!vis[v])dfs(gg, gr, vis, v);
    }
    int[][] makeU(int n, int[][] edge, int cn){
        int[][] g = new int[n][];int[] cnt = new int[n];
        for(int i = 0; i< cn; i++){cnt[edge[i][0]]++;cnt[edge[i][1]]++;}
        for(int i = 0; i< n; i++)g[i] = new int[cnt[i]];
        for(int i = 0; i< cn; i++){
            g[edge[i][0]][--cnt[edge[i][0]]] = edge[i][1];
            g[edge[i][1]][--cnt[edge[i][1]]] = edge[i][0];
        }
        return g;
    }
    //SOLUTION END
    void hold()throws Exception{throw new Exception("Hold right there, Sparky!");}
    long mod = (long)1e9+7, IINF = (long)4e18;
    final int INF = (int)2e9, MX = (int)1e6+1;
    DecimalFormat df = new DecimalFormat("0.000000000000000");
    double PI = 3.1415926535897932384626433832792884197169399375105820974944, eps = 1e-8;
    static boolean multipleTC = false, memory = false;
    FastReader in;PrintWriter out;
    void run() throws Exception{
        in = new FastReader();
        out = new PrintWriter(System.out);
        int T = (multipleTC)?ni():1;
        //Solution Credits: Taranpreet Singh
        pre();for(int i = 1; i<= T; i++)solve(i);
        out.flush();
        out.close();
    }
    public static void main(String[] args) throws Exception{
        if(memory)new Thread(null, new Runnable() {public void run(){try{new Main().run();}catch(Exception e){e.printStackTrace();}}}, "1", 1 << 28).start();
        else new Main().run();
    }
    long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
    int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}
    int bit(long n){return (n==0)?0:(1+bit(n&(n-1)));}
    void p(Object o){out.print(o);}
    void pn(Object o){out.println(o);}
    void pni(Object o){out.println(o);out.flush();}
    String n(){return in.next();}
    String nln(){return in.nextLine();}
    int ni(){return Integer.parseInt(in.next());}
    long nl(){return Long.parseLong(in.next());}
    double nd(){return Double.parseDouble(in.next());}

    class FastReader{
        BufferedReader br;
        StringTokenizer st;
        public FastReader(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String s) throws Exception{
            br = new BufferedReader(new FileReader(s));
        }

        String next(){
            while (st == null || !st.hasMoreElements()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch (IOException  e){
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String nextLine(){
            String str = "";
            try{   
                str = br.readLine();
            }catch (IOException e){
                e.printStackTrace();
            }  
            return str;
        }
    }
}