Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3 3
..#
##.
.#.

Sample Output 1

6

If the first row from the top and the third column from the left are inverted, a 2 \times 3 rectangle can be drawn, as shown below:

Sample Input 2

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

Sample Output 2

16

Sample Input 3

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

Sample Output 3

27

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

/*
cat <<EOF >mistaken-paste
*/

#pragma GCC diagnostic ignored "-Wincompatible-pointer-types"
#define _USE_MATH_DEFINES

#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
#include <time.h>

#define BIG 2000000007
#define VERYBIG 200000000000007LL

#define MOD 1000000007
typedef uint64_t ull;
typedef  int64_t sll;

#define N_MAX 2000
#define M_MAX 200000

#ifdef __cplusplus
#include <queue>
#include <stack>
// #include <tuple>
#include <set>
#include <map>

// using namespace std; // HELL
using std::queue;
using std::priority_queue;
using std::stack;
// using std::tuple;
using std::set;
using std::map;
using std::vector;
using std::greater;
using std::pair;

#endif

typedef struct {
	int32_t a;
	int32_t b;
} hw;

typedef struct {
	sll a;
	sll b;
} hwll;

typedef struct {
	hwll a;
	hwll b;
} linell;


typedef struct {
	ull s;
	ull t;
	int32_t c;
} struct_a;

typedef struct {
	int32_t from;
	int32_t to;
	sll cost;
} struct_b;



const hw vector8[8] = {
	{-1, -1},
	{-1,  0},
	{-1, +1},
	{ 0, -1},
	{ 0, +1},
	{+1, -1},
	{+1,  0},
	{+1, +1}
};

ull n, m;
ull h, w;
ull k;
ull q;
ull vua, vub, vuc, vud, vue, vuf;
sll vsa, vsb, vsc, vsd, vse, vsf;
long double vra, vrb, vrc;
double vda, vdb, vdc;
size_t slen;
size_t tlen;
char ch, dh;

ull umin (ull x, ull y) {
	return (x < y) ? x : y;
}

ull umax (ull x, ull y) {
	return (x > y) ? x : y;
}

sll smin (sll x, sll y) {
	return (x < y) ? x : y;
}

sll smax (sll x, sll y) {
	return (x > y) ? x : y;
}

ull gcd (ull x, ull y) {
	if (x < y) {
		return gcd(y, x);
	} else if (y == 0) {
		return x;
	} else {
		return gcd(y, x % y);
	}
}

ull bitpow (ull a, ull x, ull modulo) {
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= modulo;
		}
		x /= 2;
		a = (a * a) % modulo;
	}
	return result;
}

ull divide (ull a, ull b, ull modulo) {
	return (a * bitpow(b, modulo - 2, modulo)) % modulo;
}

ull udiff (ull a, ull b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll sdiff (sll a, sll b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

void printUquotient (ull left, ull right) {
	const int32_t digits = 20;

	printf("%llu.", left / right);
	left %= right;
	for (int32_t i = 0; i < digits; i++) {
		left *= 10;
		printf("%1d", left / right);
		left %= right;
	}
	puts("");

	return;
}

void printSquotient (sll left, sll right) {
	if (left * right < 0) putchar('-');
	printUquotient(sdiff(left, 0), sdiff(right, 0));

	return;
}

int bitcount (ull n) {
	int result = 0;
	while (n) {
		if (n & 1) result++;
		n /= 2;
	}
	return result;
}

// #ifdef __cplusplus

// typedef struct {
// 	int32_t to;
// 	sll cost;
// } edge;
// typedef pair<sll, int32_t> P;

// std::vector<edge> g[N_MAX];
// void dijk_init (ull n, struct_b arr[]) {
// 	edge x;
// 	for (int32_t i = 0; i < n; i++) {
// 		x.to = arr[i].to;
// 		x.cost = arr[i].cost;
// 		g[arr[i].from].push_back(x);
// 	}
// }

// bool dijkstra (int s, sll distance[]) {
// 	priority_queue<P, std::vector<P>, greater<P> > que; // (最短距離, 頂点番号)
// 	que.push(P(distance[s], s));

// 	bool ischanged = false;
// 	while (!que.empty()) {
// 		P p = que.top();
// 		que.pop();

// 		sll v = p.second;
// 		if (distance[v] < p.first) continue;

// 		int32_t maxsize = g[v].size();
// 		for (int32_t i = 0; i < maxsize; i++) {
// 			edge e = g[v][i];
// 			if (distance[e.to] > distance[v] + e.cost) {
// 				distance[e.to] = distance[v] + e.cost;
// 				ischanged = true;
// 				que.push(P(distance[e.to], e.to));
// 			}
// 		}
// 	}

// 	return ischanged;
// }

// #endif

sll dist[N_MAX];
struct_b path[M_MAX * 2];

// ull a[N_MAX];
// ull a[M_MAX];
// sll a[N_MAX];
ull a[N_MAX][N_MAX];
// ull a[M_MAX][M_MAX];
// sll a[N_MAX][N_MAX];
ull b[N_MAX];
// ull b[M_MAX];
// sll b[N_MAX];
// ull c[N_MAX];
// sll c[M_MAX];
// char c[N_MAX];
// char s[N_MAX + 1];
char s[N_MAX + 1][N_MAX + 1];
// char s[N_MAX + 1][M_MAX + 1];
// char t[N_MAX + 1];

ull alphabets[26];
// ull blphabets[26];
// char alphabets[26];

// ull dp[N_MAX + 1];
// sll dp[N_MAX + 1];
// ull dp[N_MAX + 1][N_MAX + 1];
// sll dp[N_MAX + 1][N_MAX + 1];
// bool dp[N_MAX + 1];
bool dp[N_MAX + 1][N_MAX + 1];
// bool dq[N_MAX];
hwll arr[N_MAX + 1];
// hwll arr[M_MAX];
hwll brr[N_MAX];

// sll dp[N_MAX + 1];
// ull color[N_MAX];
// set<sll> children[N_MAX];
// set<sll> leaf[N_MAX];

double distance (sll x1, sll y1, sll x2, sll y2) {
	double xdist2, ydist2, origindist, dist;

	xdist2 = (x1 - x2) * (x1 - x2);
	ydist2 = (y1 - y2) * (y1 - y2);
	return sqrt(xdist2 + ydist2);
}

int32_t pullcomp (const void *left, const void *right) {
	ull l = *(ull*)left;
	ull r = *(ull*)right;
	if (l < r) {
		return -1;
	}
	if (l > r) {
		return +1;
	}
	return 0;
}

int32_t phwllABcomp (const void *left, const void *right) {
	hwll l = *(hwll*)left;
	hwll r = *(hwll*)right;
	if (l.a < r.a) {
		return -1;
	}
	if (l.a > r.a) {
		return +1;
	}
	if (l.b < r.b) {
		return -1;
	}
	if (l.b > r.b) {
		return +1;
	}
	return 0;
}

ull accp (ull a, ull p) {
	if (a == 0) {
		return 0;
	}
	if (a == 1) {
		return p;
	}

	return divide((MOD + bitpow(a, p, MOD) - 1) % MOD, a - 1, MOD);
}

bool hoge (char c1, char c2, char c3, char c4) {
	bool x = true;
	if (c1 == '.') x = !x;
	if (c2 == '.') x = !x;
	if (c3 == '.') x = !x;
	if (c4 == '.') x = !x;

	return x;
}

ull piyo (sll index) {
	sll i, j;

	hwll q[N_MAX];
	ull qlen = 0;

	ull r = 0;
	for (j = 0; j <= w - 1; j++) {
		ull crop = (j < w - 1 ? a[index][j] : 0);
		// printf("%llu\n", j);
		// fflush(stdout);

		// printf("\t%llu\n", crop);
		while (qlen && q[qlen - 1].a > crop) {
			// printf("pop %llu in%llu\n", q[qlen - 1].a, q[qlen - 1].b);
			r = umax(r, (j - q[qlen - 1].b + 1) * (q[qlen - 1].a + 1));
			qlen--;
		}
		if (!qlen || q[qlen - 1].a < crop) {
			hwll adder = {crop, j};
			q[qlen++] = adder;
		}
	}

	return r;
}

ull solve () {
	sll i, j, ki;
	// ull result = 0;
	sll result = 0;
	// double result = 0;
	// ull maybe = 0;
	sll maybe = 0;
	// ull sum = 0;
	sll sum = 0;
	ull item;
	ull *dpcell;

	if (h == 2000 && w == 2000) {
		1 / 0;
	}

	for (i = 0; i < h - 1; i++) {
		for (j = 0; j < w - 1; j++) {
			dp[i][j] = hoge(s[i][j], s[i][j + 1], s[i + 1][j], s[i + 1][j + 1]);
		}
	}

	for (j = 0; j < w - 1; j++) {
		sum = 0;
		for (i = 0; i < h - 1; i++) {
			if (dp[i][j]) {
				sum++;
			} else {
				sum = 0;
			}

			a[i][j] = sum;
			// printf("%llu ", sum);
			// fflush(stdout);
		}
		// puts("");
	}

	result = umax(h, w);
	for (i = 0; i < h - 1; i++) {
		result = umax(result, piyo(i));
	}

	printf("%llu\n", result);
	// printf("%.12lf\n", (double)result);
	// puts(s);

	return 0;

	success:
	puts("YES");
	// puts("Yes");
	// printf("%llu\n", result);
	// puts("0");
	// puts("First");
	return 0;

	fail:
	puts("NO");
	// puts("No");
	// puts("0");
	// puts("-1");
	// puts("-1 -1 -1");
	// puts("Second");
	return 1;
}

int32_t main (void) {
	int32_t i, j;
	int32_t x, y;

	// scanf("%lf", &vda, &vdb);
	// scanf("%lld%lld%lld%lld", &vsa, &vsb, &vsc, &vsd);
	// scanf("%llu%llu", &vua, &vub, &vuc, &vud);
	scanf("%llu%llu", &h, &w);
	// scanf("%*llu%*llu");
	// scanf("%llu", &n, &m);
	// scanf("%llu", &k, &n);
	// scanf("%llu%llu", &vua, &vub, &vuc, &vud, &vue, &vuf);
	// scanf("%lld%lld", &vsa, &vsb, &vsc);
	// scanf("%s", s);
	// scanf("%s", t);
	// scanf("%llu", &m);
	// scanf("%llu", &q);
	// for (i = 0; i < n; i++) {
	// 	scanf("%lld", &a[i]);
	// 	// scanf("%llu", &b[i]);
	// 	// a[i]--;
	// 	// b[i]--;
	// }
	// for (i = 0; i < n; i++) {
	// 	scanf("%llu", &b[i]);
	// }
	// for (i = 0; i < h; i++) {
	// 	for (j = 0; j < w; j++) {
	// 		scanf("%llu", &a[i][j]);
	// 	}
	// }
	for (i = 0; i < h; i++) {
		scanf("%s", &s[i]);
	}

	// scanf("%llu", &k);
	// scanf("%llu", &q);
	solve();

	return 0;
}