Problem: We have a board with an H \times W grid. Each square in the grid is painted in black or white. The square at the i-th row from the top and j-th column from the left is black if the j-th character in S_i is `#`, and white if that character is `.`.

Snuke can perform the following operation on the grid any number of times:

* Select a row or column in the grid, and invert the color of all the squares in that row or column (that is, black squares become white and vice versa).



Then, Snuke draws a rectangle along grid lines. Here, all the squares contained in the rectangle must be painted in black.

Find the maximum possible area of Snuke's rectangle when the operation is performed optimally.

Constraints

* 2 \leq H \leq 2000
* 2 \leq W \leq 2000
* |S_i| = W
* S_i consists of `#` and `.`.

Input

Input is given from Standard Input in the following format:


H W
S_1
S_2
:
S_H


Output

Print the maximum possible area of Snuke's rectangle.

Examples

Input

3 3
..#
##.
.#.


Output

6


Input

3 3
..#
.
.#.


Output

6


Input

4 4
....
....
....
....


Output

16


Input

10 8
...#.#
...#.#
..###.#.
.##.#.#
.#..#.#.
..##.#.#
.#.#..
...#.#..
.#.##
..###


Output

27

Solution (in JAVA):

Solution:
// package atcoder.arc.arc081;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int H = in.nextInt();
        int W = in.nextInt();

        int[][] table = new int[H][W];
        for (int i = 0; i < H ; i++) {
            char[] c = in.nextToken().toCharArray();
            for (int j = 0; j < W ; j++) {
                table[i][j] = c[j] == '.' ? 0 : 1;
            }
        }

        int[][] diff = new int[H][W-1];
        for (int i = 0 ; i < H ; i++) {
            for (int j = 0; j+1 < W; j++) {
                diff[i][j] = table[i][j] ^ table[i][j+1];
            }
        }

        W--;
        int[] bottom = new int[W];
        for (int j = 0; j < W ; j++) {
            int shouldSameTo = 0;
            while (bottom[j] < H && diff[bottom[j]][j] == diff[shouldSameTo][j]) {
                bottom[j]++;
            }
        }

        int answer = Math.max(H, W+1);
        int[] height = new int[W];
        for (int i = 0 ; i < H ; i++) {
            for (int j = 0; j < W ; j++) {
                height[j] = bottom[j] - i;
            }
            answer = Math.max(answer, solve(height));

            for (int j = 0; j < W ; j++) {
                if (bottom[j] == i+1) {
                    int shouldSameTo = bottom[j];
                    while (bottom[j] < H && diff[bottom[j]][j] == diff[shouldSameTo][j]) {
                        bottom[j]++;
                    }
                }
            }
        }
        out.println(answer);
        out.flush();
    }

    static int solve(int[] a) {
        int n = a.length;
        int[] stk = new int[n+1];
        int head = 0;

        int[] l = new int[n];
        for (int i = 0 ; i < n ; i++) {
            while (head > 0 && a[stk[head-1]] >= a[i]) {
                head--;
            }
            l[i] = head == 0 ? 0 : stk[head-1]+1;
            stk[head++] = i;
        }

        int[] r = new int[n];
        head = 0;
        for (int i = n-1 ; i >= 0 ; i--) {
            while (head > 0 && a[stk[head-1]] >= a[i]) {
                head--;
            }
            r[i] = head == 0 ? n : stk[head-1];
            stk[head++] = i;
        }

        int max = 0;
        for (int i = 0; i < n ; i++) {
            max = Math.max(max, a[i] * (r[i] - l[i] + 1));
        }
        return max;
    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int[] nextInts(int n) {
            int[] ret = new int[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextInt();
            }
            return ret;
        }

        private int[][] nextIntTable(int n, int m) {
            int[][] ret = new int[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    ret[i][j] = nextInt();
                }
            }
            return ret;
        }

        private long[] nextLongs(int n) {
            long[] ret = new long[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextLong();
            }
            return ret;
        }

        private long[][] nextLongTable(int n, int m) {
            long[][] ret = new long[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    ret[i][j] = nextLong();
                }
            }
            return ret;
        }

        private double[] nextDoubles(int n) {
            double[] ret = new double[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextDouble();
            }
            return ret;
        }

        private int next() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public char nextChar() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            if ('a' <= c && c <= 'z') {
                return (char) c;
            }
            if ('A' <= c && c <= 'Z') {
                return (char) c;
            }
            throw new InputMismatchException();
        }

        public String nextToken() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInt() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c-'0';
                c = next();
            } while (!isSpaceChar(c));
            return res*sgn;
        }

        public long nextLong() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            long sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c-'0';
                c = next();
            } while (!isSpaceChar(c));
            return res*sgn;
        }

        public double nextDouble() {
            return Double.valueOf(nextToken());
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }
}