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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.util.NoSuchElementException;

public class Main {
	private static void solve() {
		int h = nei();
		int w = nei();
		String[] ss = nss(h);
		int[][] d = new int[h][w]; // 0: wh, 1: bl
		for (int i = 0; i < h; i++) {
			for (int j = 0; j < w; j++) {
				d[i][j] = ss[i].charAt(j) == '.' ? 0 : 1;
			}
		}
		long ans = 0;
		int[][] stack = new int[400 * 400 + 10][2];
		for (int i = 0; i < h; i++) {
			for (int j = 0; j < w; j++) {
				if (d[i][j] == 0 || d[i][j] == 1) {
					long numB = 0;
					long numW = 0;

					int sc = 0;
					stack[sc][0] = i;
					stack[sc][1] = j;
					sc++;
					boolean ok = false;
					while (sc > 0) {
						sc--;
						int y = stack[sc][0];
						int x = stack[sc][1];
						if (d[y][x] == -1)
							continue;
						int other = d[y][x] ^ 1;

						if (y > 0 && d[y - 1][x] == other) {
							stack[sc][0] = y - 1;
							stack[sc][1] = x;
							sc++;
							ok = true;
						}
						if (x > 0 && d[y][x - 1] == other) {
							stack[sc][0] = y;
							stack[sc][1] = x - 1;
							sc++;
							ok = true;
						}
						if (y < h - 1 && d[y + 1][x] == other) {
							stack[sc][0] = y + 1;
							stack[sc][1] = x;
							sc++;
							ok = true;
						}
						if (x < w - 1 && d[y][x + 1] == other) {
							stack[sc][0] = y;
							stack[sc][1] = x + 1;
							sc++;
							ok = true;
						}
						if (ok) {
							if (d[y][x] == 0)
								numW++;
							else
								numB++;
						}

						d[y][x] = -1; // visited
					}

					ans += numB * numW;
				}
			}
		}
		out(ans);
	}

	// returns (x, y, d) s.t. ax + by = d
	static long[] exgcd(long a, long b) {
		int sa = a < 0 ? -1 : 1;
		int sb = b < 0 ? -1 : 1;
		a *= sa;
		b *= sb;
		long x = 1;
		long y = 0;
		long z = 0;
		long w = 1;
		while (b > 0) {
			long q = a / b;
			long t = z;
			z = x - q * z;
			x = t;
			t = w;
			w = y - q * w;
			y = t;
			t = b;
			b = a - q * b;
			a = t;
		}
		return new long[] { x * sa, y * sb, a };
	}

	static int[] lis(int[] s) {
		int n = s.length;
		int[] dp = new int[n];
		int[] ids = new int[n];
		int[] pids = new int[n];
		dp[0] = s[0];
		int len = 1;
		int lidx = 0;
		for (int i = 1; i < n; i++) {
			int idx = bs(s[i], dp, 0, len);
			dp[idx] = s[i];
			ids[idx] = i;
			if (idx == len) {
				lidx = i;
				len++;
			}
			if (idx > 0)
				pids[i] = ids[idx - 1];
		}
		int[] lis = new int[len];
		lis[len - 1] = s[lidx];
		for (int i = len - 1; i >= 0; i--) {
			lis[i] = s[lidx];
			lidx = pids[lidx];
		}
		return lis;
	}

	static int bs(int a, int[] as, int from, int num) {
		int min = from;
		int max = from + num - 1;
		while (min < max) {
			int mid = min + max >> 1;
			if (as[mid] < a)
				min = mid + 1;
			else if (as[mid] > a)
				max = mid;
			else
				return mid;
		}
		return as[min] < a ? min + 1 : min;
	}

	static int gcd(int x, int y) {
		x = (x ^ x >> 31) - (x >> 31);
		y = (y ^ y >> 31) - (y >> 31);
		if (x < y) {
			x ^= y;
			y ^= x;
			x ^= y;
		}
		int z = x % y;
		if (z == 0)
			return y;
		return gcd(y, z);
	}

	static long gcd(long x, long y) {
		x = (x ^ x >> 63) - (x >> 63);
		y = (y ^ y >> 63) - (y >> 63);
		if (x < y) {
			x ^= y;
			y ^= x;
			x ^= y;
		}
		long z = x % y;
		if (z == 0)
			return y;
		return gcd(y, z);
	}

	static long modinv(long a, long mod) {
		return modpow(a, mod - 2, mod);
	}

	static long modpow(long a, long b, long mod) {
		if (b == 0)
			return 1;
		if ((b & 1) == 0) {
			long sqrt = modpow(a, b >> 1, mod);
			return sqrt * sqrt % mod;
		}
		return a * modpow(a, b - 1, mod) % mod;
	}

	static long fact(long n) {
		if (n <= 1)
			return 1;
		long res = 2;
		for (long i = 3; i <= n; i++) {
			res *= i;
		}
		return res;
	}

	static long modfact(long n, long mod) {
		if (n <= 1)
			return 1 % mod;
		long res = 2;
		for (long i = 3; i <= n; i++) {
			res *= i;
			res %= mod;
		}
		return res % mod;
	}

	// returns facts([0]) and invfacts([1])
	static long[][] enumfacts(int n, long mod) {
		int num = n + 10;
		long[][] res = new long[2][num];
		long[] facts = res[0];
		long[] invfacts = res[1];
		for (int i = 0; i < num; i++) {
			if (i <= 1) {
				facts[i] = 1;
				invfacts[i] = 1;
			} else {
				facts[i] = facts[i - 1] * i % mod;
				invfacts[i] = modinv(facts[i], mod);
			}
		}
		return res;
	}

	static long modcomb(long n, long m, long mod) {
		if (m > n)
			return 0;
		if (m > n - m) {
			m = n - m;
		}
		long numer = 1;
		for (int i = 0; i < m; i++) {
			numer = numer * (n - i) % mod;
		}
		long denom = modfact(m, mod);
		return numer * modinv(denom, mod) % mod;
	}

	static long modcomb(int n, int m, long[] facts, long[] invfacts, long mod) {
		if (m > n)
			return 0;
		long numer = facts[n];
		long denom = invfacts[m] * invfacts[n - m] % mod;
		return numer * denom % mod;
	}

	// res[i][0]: prime factor, res[i][1]: exponent
	static int[][] factorize(int n) {
		int[][] pfs = new int[32][2];
		int num = 0;
		for (int i = 2; i * i <= n; i++) {
			int count = 0;
			while (n % i == 0) {
				n /= i;
				count++;
			}
			if (count > 0) {
				pfs[num][0] = i;
				pfs[num][1] = count;
				num++;
			}
		}
		if (n > 1) {
			pfs[num][0] = n;
			pfs[num][1] = 1;
			num++;
		}
		int[][] res = new int[num][2];
		for (int i = 0; i < num; i++) {
			res[i][0] = pfs[i][0];
			res[i][1] = pfs[i][1];
		}
		return res;
	}

	static long lcm(long x, long y) {
		x = (x ^ x >> 63) - (x >> 63);
		y = (y ^ y >> 63) - (y >> 63);
		return x / gcd(x, y) * y;
	}

	static int abs(int x) {
		return x < 0 ? -x : x;
	}

	static long abs(long x) {
		return x < 0 ? -x : x;
	}

	static int min(int a, int b) {
		return a < b ? a : b;
	}

	static long min(long a, long b) {
		return a < b ? a : b;
	}

	static int max(int a, int b) {
		return a > b ? a : b;
	}

	static long max(long a, long b) {
		return a > b ? a : b;
	}

	static int clamp(int a, int min, int max) {
		return a < min ? min : a > max ? max : a;
	}

	static long clamp(long a, long min, long max) {
		return a < min ? min : a > max ? max : a;
	}

	static double clamp(double a, double min, double max) {
		return a < min ? min : a > max ? max : a;
	}

	static void out(String val) {
		IO.out(val);
	}

	static void out(Object val) {
		IO.out(String.valueOf(val));
	}

	static void out(int val) {
		IO.out(String.valueOf(val));
	}

	static void out(long val) {
		IO.out(String.valueOf(val));
	}

	static void out(char val) {
		IO.out(String.valueOf(val));
	}

	static void out(double val) {
		IO.out(Double.isFinite(val) ? BigDecimal.valueOf(val).toPlainString() : String.valueOf(val));
	}

	static void out(boolean val) {
		IO.out(val ? "true" : "false");
	}

	static void kil(String val) {
		IO.out(val);
		IO.flush();
		System.exit(0);
	}

	static void kil(Object val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(int val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(long val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(char val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(double val) {
		IO.out(Double.isFinite(val) ? BigDecimal.valueOf(val).toPlainString() : String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(boolean val) {
		IO.out(val ? "true" : "false");
		IO.flush();
		System.exit(0);
	}

	static String nes() {
		return IO.next();
	}

	static int nei() {
		return IO.nextInt();
	}

	static long nel() {
		return IO.nextLong();
	}

	static double ned() {
		return IO.nextDouble();
	}

	static char nec() {
		return IO.nextChar();
	}

	static String[] nss(int n) {
		String[] as = new String[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.next();
		}
		return as;
	}

	static int[] nis(int n) {
		int[] as = new int[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextInt();
		}
		return as;
	}

	static long[] nls(int n) {
		long[] as = new long[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextLong();
		}
		return as;
	}

	static double[] nds(int n) {
		double[] as = new double[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextDouble();
		}
		return as;
	}

	static char[] ncs(int n) {
		char[] as = new char[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextChar();
		}
		return as;
	}

	static String[][] nss2(int n, int m) {
		String[][] as = new String[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.next();
			}
		}
		return as;
	}

	static int[][] nis2(int n, int m) {
		int[][] as = new int[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextInt();
			}
		}
		return as;
	}

	static long[][] nls2(int n, int m) {
		long[][] as = new long[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextLong();
			}
		}
		return as;
	}

	static double[][] nds2(int n, int m) {
		double[][] as = new double[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextDouble();
			}
		}
		return as;
	}

	static char[][] ncs2(int n, int m) {
		char[][] as = new char[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextChar();
			}
		}
		return as;
	}

	static int parseInt(String val) {
		return Integer.parseInt(val);
	}

	static int parseInt(char val) {
		return Integer.parseInt(String.valueOf(val));
	}

	static long parseLong(String val) {
		return Long.parseLong(val);
	}

	public static void main(String[] args) {
		try {
			solve();
			IO.flush();
		} catch (NumberFormatException e) {
			e.printStackTrace();
		}
	}
}

final class IO {
	private static final InputStream in = System.in;
	private static final PrintWriter out = new PrintWriter(System.out, false);
	private static final byte[] buffer = new byte[1024];
	private static int ptr = 0;
	private static int len = 0;

	private static boolean hasNextByte() {
		if (ptr < len)
			return true;
		ptr = 0;
		try {
			len = in.read(buffer);
		} catch (IOException e) {
			e.printStackTrace();
		}
		return len > 0;
	}

	private static int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	static boolean hasNext() {
		byte c;
		while (hasNextByte() && ((c = buffer[ptr]) < '!' || c > '~'))
			ptr++;
		return hasNextByte();
	}

	static String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (b >= '!' && b <= '~') {
			sb.append((char) b);
			b = readByte();
		}
		return sb.toString();
	}

	static char nextChar() {
		if (!hasNext())
			throw new NoSuchElementException();
		return (char) readByte();
	}

	static long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		int sign = 1;
		int b = readByte();
		if (b == '-') {
			sign = -1;
			b = readByte();
		}
		if (b < '0' || '9' < b)
			throw new NumberFormatException();
		while (true) {
			if ('0' <= b && b <= '9')
				n = n * 10 + b - '0';
			else if (b == -1 || b < '!' || b > '~')
				return n * sign;
			else
				throw new NumberFormatException();
			b = readByte();
		}
	}

	static int nextInt() {
		if (!hasNext())
			throw new NoSuchElementException();
		int n = 0;
		int sign = 1;
		int b = readByte();
		if (b == '-') {
			sign = -1;
			b = readByte();
		}
		if (b < '0' || '9' < b)
			throw new NumberFormatException();
		while (true) {
			if ('0' <= b && b <= '9')
				n = n * 10 + b - '0';
			else if (b == -1 || b < '!' || b > '~')
				return n * sign;
			else
				throw new NumberFormatException();
			b = readByte();
		}
	}

	static double nextDouble() {
		return Double.parseDouble(next());
	}

	static void out(String val) {
		out.println(val);
	}

	static void flush() {
		out.flush();
	}
}