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:
import java.io.*;
import java.util.Arrays;
import java.util.StringJoiner;
import java.util.StringTokenizer;
import java.util.function.Function;

public class Main {

    static int H, W;
    static char[][] C;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        H = sc.nextInt();
        W = sc.nextInt();
        C = new char[H][];
        for (int i = 0; i < H; i++) {
            C[i] = sc.next().toCharArray();
        }

        System.out.println(solve());
    }

    static long solve() {
        int[][] D = new int[H-1][W-1];

        for (int h = 0; h < H-1; h++) {
            for (int w = 0; w < W-1; w++) {
                D[h][w] = isOk(h, w) ? 1 : 0;
            }
        }

        // 1 1 0 1 1 -> 1 2 0 1 2
        // 縦に
        for (int w = 0; w < W-1; w++) {
            for (int h = 0; h < H-1; h++) {
                if( D[h][w] == 1 ) {
                    D[h][w] += h == 0 ? 0 : D[h-1][w];
                }
            }
        }

        long ans = Math.max(H, W); // 最悪でも一列(行)は確保できる
        for (int h = 0; h < H-1; h++) {
            ans = Math.max(maxRectPlus(D[h]), ans);
        }
        return ans;
    }

    static int[] DH = {0, 1, 0, 1};
    static int[] DW = {0, 0, 1, 1};

    static boolean isOk(int h, int w) {
        // h, wは左上
        int cnt = 0;
        for (int i = 0; i < 4; i++) {
            if( C[h + DH[i]][w + DW[i]] == '#' ) cnt++;
        }
        return cnt % 2 == 0;
    }

    static long maxRectPlus(int[] a) {
        int n = a.length;
        int[] stack = new int[n];
        int[] left = new int[n];
        int p = 0;
        long max = 0;
        for(int i = 0; i < n; i++){
            int o = p;
            while(p > 0 && stack[p-1] >= a[i]) {
                p--;
                int w = i-1-left[p]+1;
                int h = stack[p];
                max = Math.max(max, (long)(w+1)*(h+1));
            }
            if(o == p) left[p] = i;
            stack[p++] = a[i];
        }
        while(p > 0) {
            p--;
            int w = n-1-left[p]+1;
            int h = stack[p];
            max = Math.max(max, (long)(w+1)*(h+1));
        }
        return max;
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        int[] nextIntArray(int n, int delta) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt() + delta;
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
    }

    static <A> void writeLines(A[] as, Function<A, String> f) {
        PrintWriter pw = new PrintWriter(System.out);
        for (A a : as) {
            pw.println(f.apply(a));
        }
        pw.flush();
    }

    static void writeLines(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int a : as) pw.println(a);
        pw.flush();
    }

    static void writeLines(long[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (long a : as) pw.println(a);
        pw.flush();
    }

    static int max(int... as) {
        int max = Integer.MIN_VALUE;
        for (int a : as) max = Math.max(a, max);
        return max;
    }

    static int min(int... as) {
        int min = Integer.MAX_VALUE;
        for (int a : as) min = Math.min(a, min);
        return min;
    }

    static void debug(Object... args) {
        StringJoiner j = new StringJoiner(" ");
        for (Object arg : args) {
            if (arg instanceof int[]) j.add(Arrays.toString((int[]) arg));
            else if (arg instanceof long[]) j.add(Arrays.toString((long[]) arg));
            else if (arg instanceof double[]) j.add(Arrays.toString((double[]) arg));
            else if (arg instanceof Object[]) j.add(Arrays.toString((Object[]) arg));
            else j.add(arg.toString());
        }
        System.err.println(j.toString());
    }
}