Problem:
Score : 700 points

Problem Statement

There are N bags, each containing two white balls. The i-th box contains two balls with integers x_i and y_i written on them, respectively.

For each of these bags, you will paint one of the balls red, and paint the other blue.

Afterwards, the 2N balls will be classified according to color.

Then, we will define the following:

R_{max}: the maximum integer written on a ball painted in red

R_{min}: the minimum integer written on a ball painted in red

B_{max}: the maximum integer written on a ball painted in blue

B_{min}: the minimum integer written on a ball painted in blue

Find the minimum possible value of (R_{max} - R_{min}) \times (B_{max} - B_{min}).

Constraints

1 ≤ N ≤ 200,000

1 ≤ x_i, y_i ≤ 10^9

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_N y_N

Output

Print the minimum possible value.

Sample Input 1

3
1 2
3 4
5 6

Sample Output 1

15

The optimal solution is to paint the balls with x_1, x_2, y_3 red, and paint the balls with y_1, y_2, x_3 blue.

Sample Input 2

3
1010 10
1000 1
20 1020

Sample Output 2

380

Sample Input 3

2
1 1
1000000000 1000000000

Sample Output 3

999999998000000001

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
#define FOD  998244353
typedef uint64_t ull;
typedef  int64_t sll;

#define N_MAX 1000000
#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 {
	sll a;
	sll b;
	sll c;
} hwllc;

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

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

bool setfind (set<ull> s, ull x) {
	return (s.find(x) != s.end());
}

#endif

// 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 psllcomp (const void *left, const void *right) {
	sll l = *(sll*)left;
	sll r = *(sll*)right;
	if (l < r) {
		return -1;
	}
	if (l > r) {
		return +1;
	}
	return 0;
}

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

int32_t pstrcomp (const void *left, const void *right) {
	char* l = *(char**)left;
	char* r = *(char**)right;

	return strcmp(l, r);
}

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;
}

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

int32_t ptriplecomp (const void *left, const void *right) {
	hwllc l = *(hwllc*)left;
	hwllc r = *(hwllc*)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;
	}
	if (l.c < r.c) {
		return -1;
	}
	if (l.c > r.c) {
		return +1;
	}
	return 0;
}

bool isinrange (sll left, sll x, sll right) {
	return (left <= x && x <= right);
}

bool isinrange_soft (sll left, sll x, sll right) {
	return (left <= x && x <= right) || (left >= x && x >= right);
}

ull parent[N_MAX];
ull rank[N_MAX];
void uf_init (ull n) {
	for (sll i = 0; i < n; i++) {
		parent[i] = i;
		rank[i] = 0;
	}
}
ull uf_find (ull x) {
	if (parent[x] == x) return x;
	return parent[x] = uf_find(parent[x]);
}
bool uf_union (ull a, ull b) {
	a = uf_find(a);
	b = uf_find(b);
	if (a == b) return false;

	if (rank[a] > rank[b]) {
		parent[b] = a;
	} else {
		parent[a] = b;
		if (rank[a] == rank[b]) {
			rank[b]++;
		}
	}
	return true;
}


sll a[N_MAX];
// sll a[3001][3001];
sll b[N_MAX];
sll c[N_MAX];
char s[N_MAX + 1];
// char s[3010][3010];
char t[N_MAX + 1];
// hwll xy[N_MAX];

hwll sorted[N_MAX * 2];
hwll srev[N_MAX];
bool isconsted[N_MAX];
bool isred[N_MAX * 2];

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

	ull mina = BIG, maxa = 0, minb = BIG, maxb = 0;
	for (i = 0; i < n; i++) {
		if (a[i] > b[i]) {
			a[i] ^= (b[i] ^= (a[i] ^= b[i]));
		}

		mina = umin(mina, a[i]);
		maxa = umax(maxa, a[i]);
		minb = umin(minb, b[i]);
		maxb = umax(maxb, b[i]);
	}
	result = (maxa - mina) * (maxb - minb);

	for (i = 0; i < n; i++) {
		sorted[i].a = a[i];
		sorted[n + i].a = b[i];

		sorted[i].b = sorted[n + i].b = i;
	}
	qsort(sorted, n * 2, sizeof(hwll), phwllABcomp);
	ull slastb = sorted[n * 2 - 1].b;

	if (sorted[0].b != slastb) {
		ull bluer = BIG;

		for (i = 0; i < n; i++) {
			srev[i].a = -1;
		}
		for (i = 0; i < n * 2; i++) {
			ull v = sorted[i].b;
			if (srev[v].a < 0) {
				srev[v].a = i;
				isred[i] = true;
			} else {
				srev[v].b = i;
				isred[i] = false;
			}
		}

		isconsted[sorted[0].b] = isconsted[slastb] = true;
		isred[srev[slastb].a] = false;
		isred[srev[slastb].b] = true;

		ull bl = n * 2 - 1;
		while (isred[bl]) bl--;

		ull bs = 1;
		while (bs < n * 2) {
			// for (i = 0; i < n * 2; i++) {
			// 	printf("%d", isred[i] ? 1 : 0);
			// }
			// puts("");

			bluer = umin(bluer, sorted[bl].a - sorted[bs].a);
			// printf("%lld(%lld) - %lld(%lld)?\n", sorted[bl].a, bl, sorted[bs].a, bs);

			ull v = sorted[bs].b;
			if (!isconsted[v]) {
				isred[srev[v].a] = true;
				isred[srev[v].b] = false;
				isconsted[v] = true;

				bl = umax(bl, srev[v].b);
			}

			bs++;
		}

		result = umin(result, (sorted[n * 2 - 1].a - sorted[0].a) * bluer);
	}

	printf("%llu\n", result);
	// printf("%.15lf\n", dresult);
	// 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%lf", &vda, &vdb, &vdc);
	// scanf("%lld%lld", &vsa, &vsb, &vsc, &vsd);
	// scanf("%llu%llu", &vua, &vub, &vuc, &vud);
	// scanf("%*llu%*llu");
	// scanf("%llu%llu", &h, &w);
	scanf("%llu", &n, &m);
	// scanf("%llu", &k, &n);
	// scanf("%llu%llu", &vua, &vub, &vuc, &vud, &vue, &vuf);
	// vua--;
	// vub--;
	// vuc--;
	// vud--;
	// scanf("%lld%lld", &vsa, &vsb, &vsc);
	// scanf("%s", s);
	// scanf("%s", t);
	// scanf("%llu", &k);
	// scanf("%llu", &q);
	for (i = 0; i < n; i++) {
		scanf("%lld", &a[i]);
		scanf("%lld", &b[i]);
		// scanf("%lld%lld", &xy[i].a, &xy[i].b);
		// scanf("%lld", &c[i]);
		// a[i]--;
		// b[i]--;
		// c[i]--;
	}
	// scanf("%llu%llu", &m, &k);
	// for (i = 0; i < m; i++) {
	// 	scanf("%llu", &b[i]);
	// 	b[i]--;
	// }
	// scanf("%llu", &q);

	// for (i = 0; i < n; i++) {
	// 	for (j = 0; j < n; 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;
}