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.io.*;
import java.util.*;
import java.util.Map.Entry;

public class Main {
		
	public static void main(String[] args) throws IOException {
		FastScanner sc = new FastScanner(System.in);
		
		int H = sc.nextInt();
		int W = sc.nextInt();
		char[][] board = new char[H][W];
		
		UnionFind uf = new UnionFind(H*W);
		for(int i = 0; i < H; i++){
			board[i] = sc.next().toCharArray();
		}
		
		for(int i = 0; i < H; i++){
			for(int j = 0; j < W; j++){
				int now = W * i + j;
				if(i + 1 < H && board[i][j] != board[i+1][j]){
					int next = W * (i + 1) + j;
					uf.unite(now, next);
				}
				if(j + 1 < W && board[i][j] != board[i][j+1]){
					int next = W * i + (j + 1);
					uf.unite(now, next);
				}
			}
		}
		
		int[] numB = new int[H*W];
		int[] numW = new int[H*W];
		for(int i = 0; i < H; i++){
			for(int j = 0; j < W; j++){
				int index = uf.find(W * i + j);
				//System.out.print(index + " ");
				if(board[i][j] == '#')
					numB[index]++;
				else
					numW[index]++;
			}
			//System.out.println();
		}
		
		long ans = 0;
		for(int i = 0; i < H*W; i++){
			ans += (long)numB[i] * numW[i];
			//System.out.println(numB[i] + " " + numW[i]);
		}
		
		System.out.println(ans);
		
	}//end main
	
}//end Main

class UnionFind{
	int[] par;
	int[] rank;
	int group;
	
	UnionFind(int n){
		par = new int[n];
		rank = new int[n];
		group = n;
		for(int i = 0; i < n; i++){
			par[i] = i;
			rank[i] = 0;
		}
	}
	//経路圧縮しながらrootを求める
	int find(int x){
		if(par[x] == x) return x;
		return par[x] = find(par[x]);
	}
	void unite(int x, int y){
		x = find(x);
		y = find(y);
		if(x == y) return;
		group--;
		if(rank[x] > rank[y]) par[x] = y;
		else{
			par[y] = x;
			if(rank[x] == rank[y]) rank[x]++;
		}
	}
	boolean same(int x, int y){
		return find(x) == find(y);
	}
}

class Pair{
	int y; int x;
	public Pair(int y, int x){
		this.x = x;
		this.y = y;
	}
}

class FastScanner {
    private InputStream in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    public FastScanner(InputStream in) {
		this.in = in;
	}
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() {
    	if (hasNextByte()) return buffer[ptr++];
    	else return -1;
    }
    private static boolean isPrintableChar(int c){
    	return 33 <= c && c <= 126;
    }
    public boolean hasNext() {
    	while(hasNextByte() && !isPrintableChar(buffer[ptr]))
    		ptr++; return hasNextByte();
    }
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() {
    	return Double.parseDouble(next());
    }
}