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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.util.InputMismatchException;
import java.util.HashMap;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.AbstractCollection;
import java.util.TreeMap;
import java.util.StringTokenizer;
import java.util.Map;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int h = in.nextInt();
            int w = in.nextInt();

            String[] s = in.nextStringArray(h);

            boolean[][] a = new boolean[h][w];
            for (int i = 0; i < h; i++) {
                for (int j = 0; j < w; j++) {
                    a[i][j] = s[i].charAt(j) == '#';
                }
            }

            UnionFind uf = new UnionFind(h * w);
            for (int i = 0; i < h; i++) {
                for (int j = 0; j < w; j++) {
                    if (j < w - 1 && (a[i][j] ^ a[i][j + 1])) {
                        uf.union(i * w + j, i * w + j + 1);
                    }
                    if (i < h - 1 && (a[i][j] ^ a[i + 1][j])) {
                        uf.union(i * w + j, (i + 1) * w + j);
                    }
                }
            }

            Map<Integer, Integer> count = new TreeMap<>();
            for (int i = 0; i < h; i++) {
                for (int j = 0; j < w; j++) {
                    if (a[i][j]) {
                        count.merge(uf.root(i * w + j), 1, Integer::sum);
                    }
                }
            }

            long ans = 0;
            for (int i = 0; i < h; i++) {
                for (int j = 0; j < w; j++) {
                    if (!a[i][j] && count.containsKey(uf.root(i * w + j))) ans += count.get(uf.root(i * w + j));
                }
            }

            out.println(ans);
        }

    }

    static class InputReader {
        private BufferedReader br;
        private StringTokenizer st;

        public InputReader(InputStream inputStream) {
            br = new BufferedReader(new InputStreamReader(inputStream));
            st = new StringTokenizer("");
        }

        public String nextString() {
            while (!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine(), " ");
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextString());
        }

        public String[] nextStringArray(int n) {
            String[] res = new String[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextString();
            }
            return res;
        }

    }

    static class UnionFind {
        int[] parent;

        public UnionFind(int size) {
            parent = new int[size];
            Arrays.fill(parent, -1);
        }

        public boolean union(int x, int y) {
            x = root(x);
            y = root(y);
            if (x != y) {
                if (parent[y] < parent[x]) {
                    int tmp = y;
                    y = x;
                    x = tmp;
                }
                parent[x] += parent[y];
                parent[y] = x;
                return true;
            }
            return false;
        }

        public int root(int x) {
            return parent[x] < 0 ? x : (parent[x] = root(parent[x]));
        }

        public ArrayList<ArrayList<Integer>> getGroups() {
            int n = parent.length;
            ArrayList<ArrayList<Integer>> groups = new ArrayList<>();
            HashMap<Integer, Integer> map = new HashMap<>();
            for (int i = 0; i < n; i++) {
                int r = root(i);
                if (!map.containsKey(r)) {
                    map.put(r, groups.size());
                    groups.add(new ArrayList<>());
                }
                groups.get(map.get(r)).add(i);
            }
            return groups;
        }

        public String toString() {
            return getGroups().toString();
        }

    }
}