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:

public class Main {
  private static void solve() {
    int h = ni();
    int w = ni();
    
    int[][] map = new int[h][w];
    for (int i = 0; i < h; i ++) {
      char[] s = ns();
      for (int j = 0; j < w; j ++) {
        map[i][j] = s[j] == '.' ? 0 : 1;
      }
    }
    
    boolean[][] can = new boolean[h - 1][w - 1];
    for (int i = 0; i < h - 1; i ++) {
      for (int j = 0; j < w - 1; j ++) {
        int s = map[i][j] + map[i][j + 1] + map[i + 1][j] + map[i + 1][j + 1];
        can[i][j] = (s & 1) == 0;
      }
    }
    int[][] cnt = new int[h - 1][w - 1];
    for (int i = 0; i < h - 1; i ++) {
      for (int j = 0; j < w - 1; j ++) {
        cnt[i][j] = can[i][j] ? (i > 0 ? cnt[i - 1][j] : 0) + 1 : 0;
      }
    }
    long ret = Math.max(h, w);
    for (int i = 0; i < h  -1; i ++) {
      ret = Math.max(ret, maxRect(cnt[i]));
    }
    System.out.println(ret);
  }

  public static long maxRect(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--;
              max = Math.max(max, (long)(i-1-left[p]+2)*(stack[p] + 1));
          }
          if(o == p)left[p] = i;
          stack[p++] = a[i];
      }
      while(p > 0){
          p--;
          max = Math.max(max, (long)(n-1-left[p]+2)*(stack[p] + 1));
      }
      return max;
  }
  
  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

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

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}