Problem:
Score : 1500 points

Problem Statement

#nck {
width: 30px;
height: auto;
}

Snuke received two matrices A and B as birthday presents.
Each of the matrices is an N by N matrix that consists of only 0 and 1.

Then he computed the product of the two matrices, C = AB.
Since he performed all computations in modulo two, C was also an N by N matrix that consists of only 0 and 1.
For each 1 ≤ i, j ≤ N, you are given c_{i, j}, the (i, j)-element of the matrix C.

However, Snuke accidentally ate the two matrices A and B, and now he only knows C.
Compute the number of possible (ordered) pairs of the two matrices A and B, modulo 10^9+7.

Constraints

1 ≤ N ≤ 300

c_{i, j} is either 0 or 1.

Input

The input is given from Standard Input in the following format:

N
c_{1, 1} ... c_{1, N}
:
c_{N, 1} ... c_{N, N}

Output

Print the number of possible (ordered) pairs of two matrices A and B (modulo 10^9+7).

Sample Input 1

2
0 1
1 0

Sample Output 1

6

Sample Input 2

10
1 0 0 1 1 1 0 0 1 0
0 0 0 1 1 0 0 0 1 0
0 0 1 1 1 1 1 1 1 1
0 1 0 1 0 0 0 1 1 0
0 0 1 0 1 1 1 1 1 1
1 0 0 0 0 1 0 0 0 0
1 1 1 0 1 0 0 0 0 1
0 0 0 1 0 0 1 0 1 0
0 0 0 1 1 1 0 0 0 0
1 0 1 0 0 1 1 1 1 1

Sample Output 2

741992411

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

#if 0
cat <<EOF >mistaken-paste
#endif
// thanks for @rsk0315_h4x

#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 2000000000000007LL

#define MOD 1000000007
#define FOD  998244353
typedef uint64_t ull;
typedef  int64_t sll;

#define N_MAX 1000000

#ifdef __cplusplus
#include <queue>
#include <stack>
#include <tuple>
#include <set>
#include <map>
#include <string>
#include <algorithm>
#include <functional>
#include <array>

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;
using std::string;
using std::get;

template <typename T, typename U>
pair<T, U> operator+(pair<T, U> l, pair<T, U> r) {
	return pair<T, U>(l.first + r.first, l.second + r.second);
}

#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;
sll va, vb, vc, vd, ve, vf;
ull ua, ub, uc, ud, ue, uf;
long double vra, vrb, vrc;
double vda, vdb, vdc;
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;
	}
}

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

#define BEGCMP(NAME) int32_t NAME (const void *left, const void *right)
#define DEFLR(TYPE) TYPE l=*(TYPE*)left,r=*(TYPE*)right
#define CMPRET(L, R) if((L)<(R))return-1;if((L)>(R))return+1

// 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;
// }
BEGCMP(pullcomp){
	DEFLR(ull);
	CMPRET(l, r);
	return 0;
}
BEGCMP(prevcomp){
	DEFLR(ull);
	CMPRET(r, l);
	return 0;
}
BEGCMP(psllcomp){
	DEFLR(sll);
	CMPRET(l, r);
	return 0;
}
BEGCMP(pcharcomp){
	DEFLR(char);
	CMPRET(l, r);
	return 0;
}
BEGCMP(pdoublecomp){
	DEFLR(double);
	CMPRET(l, r);
	return 0;
}

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

	return strcmp(l, r);
}

BEGCMP(phwllABcomp){
	DEFLR(hwll);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	return 0;
}
BEGCMP(phwllREVcomp){
	DEFLR(hwll);
	CMPRET(l.b, r.b);
	CMPRET(l.a, r.a);
	return 0;
}
BEGCMP(ptriplecomp){
	DEFLR(hwllc);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	CMPRET(l.c, r.c);
	return 0;
}
BEGCMP(ptripleREVcomp){
	DEFLR(hwllc);
	CMPRET(l.b, r.b);
	CMPRET(l.a, r.a);
	CMPRET(l.c, r.c);
	return 0;
}

int32_t pquadcomp (const void *left, const void *right) {
	linell l = *(linell*)left;
	linell r = *(linell*)right;

	sll ac = phwllABcomp(&(l.a), &(r.a));
	if (ac) return ac;
	sll bc = phwllABcomp(&(l.b), &(r.b));
	if (bc) return bc;

	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);
}

sll a[N_MAX + 5];
// ull a[N_MAX + 5];
// sll a[3001][3001];
sll b[N_MAX + 5];
// ull b[N_MAX + 5];
// sll b[3001][3001];
sll c[N_MAX + 5];
ull d[N_MAX + 5];
sll e[N_MAX];
char s[N_MAX + 1];
// char s[3010][3010];
char t[N_MAX + 1];
// char t[3010][3010];
char u[N_MAX + 1];
hwll xy[N_MAX + 5];
hwllc tup[N_MAX + 5];
sll table[3005][3005];
// here we go

ull frac[N_MAX], invf[N_MAX];
ull dp[900][900], dq[900][900];
ull ncr (ull n, ull r) {
	if (n < r) return 0;
	return frac[n] * (invf[r] * invf[n - r] % MOD) % MOD;
}

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;

	frac[0] = invf[0] = 1;
	for (i = 1; i <= n; i++) {
		frac[i] = (frac[i - 1] * i) % MOD;
		invf[i] = divide(invf[i - 1], i, MOD);
	}

	ull rank;
	for (rank = 0; rank < n; rank++) {
		for (i = rank; i < n; i++) {
			for (j = rank; j < n; j++) {
				if (table[i][j]) break;
			}
			if (j < n) break;
		}
		if (i == n) break;

		if (j > rank) {
			for (ki = rank; ki < n; ki++) {
				table[ki][rank] ^= table[ki][j];
			}
		}
		if (i > rank) {
			for (ki = rank; ki < n; ki++) {
				table[rank][ki] ^= table[i][ki];
			}
		}
		for (ki = rank + 1; ki < n; ki++) {
			if (!table[rank][ki]) continue;
			for (li = rank; li < n; li++) {
				table[li][ki] ^= table[li][rank];
			}
		}
		for (li = rank + 1; li < n; li++) {
			table[li][rank] ^= table[rank][rank];
		}
	}
	// printf("%llu\n", rank);

	dp[0][n - rank] = 1;
	for (i = 1; i <= n - rank; i++) {
		for (j = 0; j < n - rank; j++) {
			dp[i][j] = 0;
			for (ki = j + 1; ki <= n - rank; ki++) {
				dp[i][j] += dp[i - 1][ki] * ncr(ki, ki - j) % MOD;
			}
			dp[i][j] %= MOD;
			// printf("%llu %llu: %llu\n", i, j, dp[i][j]);
		}
	}
	dq[0][0] = 1;
	for (i = 1; i <= n; i++) {
		for (j = 0; j <= i; j++) {
			dq[i][j] = ((j ? dq[i - 1][j - 1] : 0) + bitpow(2, j, MOD) * dq[i - 1][j] % MOD) % MOD;
			// printf("%llu %llu; %llu\n", i, j, dq[i][j]);
		}
	}

	result = 0;
	for (i = rank; i <= n; i++) {
		ull item1 = dq[n][i] * invf[i - rank] % MOD;
		ull item2 = 0;
		ull item3 = 1;
		for (j = 0; j <= n - rank; j++) {
			item2 += dp[i - rank][j];
		}
		item2 %= MOD;
		for (j = 0; j < i; j++) {
			item3 *= (MOD + bitpow(2, i, MOD) - bitpow(2, j, MOD));
			item3 %= MOD;
		}
		result += ((item1 * item2 % MOD) * item3 % MOD) * bitpow(2, (n - i) * n, MOD) % MOD;
	}
	result %= MOD;

	printf("%lld\n", result);
	// printf("%.15lf\n", dresult);
	// puts(s);

	return 0;

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

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

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

	n = 3;

	// scanf("%llu%llu", &h, &w);
	scanf("%llu", &n, &m);
	// scanf("%llu", &k, &n, &m);
	// scanf("%llu%llu", &h, &w);
	// scanf("%s", s);
	// scanf("%llu", &q);
	// scanf("%lld%lld", &va, &vb, &vc, &vd);
	// scanf("%llu%llu%llu", &ua, &ub, &uc, &ud, &ue);
	// scanf("%s", t);
	// scanf("%s", u);
	// scanf("%llu", &k);
	// scanf("%lld", &m);
	// for (i = 0; i < n; i++) {
	// 	scanf("%llu", &d[i]);
	// }
	// for (i = 0; i < n; i++) {
	// 	// scanf("%lld%lld", &xy[i].a, &xy[i].b);
	// 	// scanf("%lld%lld%lld", &tup[i].a, &tup[i].b, &tup[i].c);
	// 	scanf("%lld", &a[i]);
	// 	scanf("%lld", &b[i]);
	// 	// scanf("%lld", &c[i]);
	// 	// scanf("%lld", &d[i]);
	// 	a[i]--;
	// 	b[i]--;
	// 	// c[i]--;
	// 	// d[i]--;
	// 	// xy[i].a--;
	// 	// xy[i].b--;
	// 	// tup[i].a--;
	// 	// tup[i].b--;
	// }
	// for (i = 0; i < m; i++) {
	// 	scanf("%lld%lld", &a[i], &b[i]);
	// 	a[i]--;
	// 	b[i]--;
	// }
	// for (i = 1; i <= n; i++) {
	// 	scanf("%llu", &d[i]);
	// }
	// for (i = 0; i < n; i++) {
	// 	scanf("%lld%lld%lld", &c[i], &a[i], &b[i]);
	// }

	// for (i = 0; i < q; i++) {
	// 	// scanf("%lld%lld", &xy[i].a, &xy[i].b);
	// 	scanf("%lld", &c[i]);
	// 	// xy[i].a--;
	// 	// xy[i].b--;
	// }

	for (i = 0; i < n; i++) {
		for (j = 0; j < n; j++) {
			scanf("%lld", &table[i][j]);
			// table[i][j]--;
		}
	}
	// for (i = 0; i < h; i++) {
	// 	scanf("%s", s[i]);
	// }
	// scanf("%llu", &q);

	solve();

	return 0;
}