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.BufferedReader;
import java.io.FileInputStream;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {
	private static final boolean local = false;
	private static BufferedReader br;
	private static StringTokenizer st;
	private static PrintWriter output;
	//char c = line.nextToken().charAt(0);

	private static void openFile() throws IOException {
		if (local) {
			String inp = "C:/Users/ztrong/Desktop/AndroidStudioProjects/Java/src/main/java/input.txt";
			String out = "C:/Users/ztrong/Desktop/AndroidStudioProjects/Java/src/main/java/output.txt";
			br = new BufferedReader(new InputStreamReader(new FileInputStream(inp)));
			output = new PrintWriter(new FileOutputStream(out));
		} else {
			br = new BufferedReader(new InputStreamReader(System.in));
			output = new PrintWriter(System.out);
		}
	}

	private static String _next() {
		while (st == null || !st.hasMoreElements()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				e.printStackTrace();
			}
		}
		return st.nextToken();
	}

	private static int nextInt() {
		return Integer.parseInt(_next());
	}

	private static long nextLong() {
		return Long.parseLong(_next());
	}

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

	private static String nextLine() {
		String str = "";
		try {
			str = br.readLine();
		} catch (IOException e) {
			e.printStackTrace();
		}
		return str;
	}

	private static final int maxN = (int) 2e3 + 5;
	private static final int maxM = (int) 1e6 + 5;
	private static final int inf = (int) 1e9 + 7;

	private static int N, M;
	private static String[] s = new String[maxN];
	private static int[] h = new int[maxN];
	private static int[] stack = new int[maxN];
	private static int top;
	private static int[] lef = new int[maxN];
	private static int[] rig = new int[maxN];

	private static void init() {

	}

	private static void enter() throws IOException {
		N = nextInt(); M = nextInt();
		for (int i = 1; i <= N; ++i) {
			s[i] = nextLine();
			s[i] = '!' + s[i];
		}
	}

	private static boolean ok(int i, int j) {
		if (j > M) return true;
		if (i == 1) return true;
		int num = ((s[i - 1].charAt(j - 1) - '#') + (s[i - 1].charAt(j) - '#')
		+ (s[i].charAt(j - 1) - '#') + (s[i].charAt(j) - '#'));
		return num % 2 == 0;
	}

	private static void solve() throws IOException {
		int res = 0;
		for (int i = 1; i <= N; ++i) {
			h[1] = h[1] + 1;
			for (int j = 2; j <= M + 1; ++j) {
				if (ok(i, j)) {
					h[j] += 1;
				}
				else {
					h[j] = 1;
				}
			}

			top = 0;

			for (int j = 1; j <= M + 1; ++j) {
				while (top > 0 && h[stack[top]] >= h[j]) --top;
				if (top == 0) lef[j] = 1;
				else lef[j] = stack[top];
				stack[++top] = j;
			}

			top = 0;

			for (int j = M + 1; j >= 1; --j) {
				while (top > 0 && h[stack[top]] >= h[j]) --top;
				if (top == 0) rig[j] = M + 1;
				else rig[j] = stack[top];
				stack[++top] = j;
			}

			for (int j = 1; j <= M + 1; ++j) {
				res = Math.max(res, h[j] * (rig[j] - lef[j]));
			}
		}

		output.println(res);
	}

	public static void main(String[] args) throws IOException {
		openFile();
		init();
		enter();
		solve();
		output.close();
	}
}