Problem:
Score : 100 points

Problem Statement

There are N men and N women, both numbered 1, 2, \ldots, N.

For each i, j (1 \leq i, j \leq N), the compatibility of Man i and Woman j is given as an integer a_{i, j}.
If a_{i, j} = 1, Man i and Woman j are compatible; if a_{i, j} = 0, they are not.

Taro is trying to make N pairs, each consisting of a man and a woman who are compatible.
Here, each man and each woman must belong to exactly one pair.

Find the number of ways in which Taro can make N pairs, modulo 10^9 + 7.

Constraints

All values in input are integers.

1 \leq N \leq 21

a_{i, j} is 0 or 1.

Input

Input is given from Standard Input in the following format:

N
a_{1, 1} \ldots a_{1, N}
:
a_{N, 1} \ldots a_{N, N}

Output

Print the number of ways in which Taro can make N pairs, modulo 10^9 + 7.

Sample Input 1

3
0 1 1
1 0 1
1 1 1

Sample Output 1

3

There are three ways to make pairs, as follows ((i, j) denotes a pair of Man i and Woman j):

(1, 2), (2, 1), (3, 3)

(1, 2), (2, 3), (3, 1)

(1, 3), (2, 1), (3, 2)

Sample Input 2

4
0 1 0 0
0 0 0 1
1 0 0 0
0 0 1 0

Sample Output 2

1

There is one way to make pairs, as follows:

(1, 2), (2, 4), (3, 1), (4, 3)

Sample Input 3

1
0

Sample Output 3

0

Sample Input 4

21
0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 0 1
1 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0
0 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1
0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0
1 1 0 0 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0
0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1 1 0 0 1
0 1 0 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0
0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1
0 0 1 0 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1
0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1
0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0
0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1
0 1 1 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 1
1 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 1
0 0 0 1 1 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1
1 0 1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0
0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1
0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 0 1
0 0 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 0 1 1 0
1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0
1 0 0 1 1 0 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0

Sample Output 4

102515160

Be sure to print the number modulo 10^9 + 7.

Solution in C++14 (Clang 3.8.0) (judge verdict: Accepted)

//#define NDEBUG
#include <cstddef>
#include <cstdint>
#include <vector>

using i8 = ::std::int_least8_t;
using i32 = ::std::int_least32_t;
using i64 = ::std::int_least64_t;
using u8 = ::std::uint_least8_t;
using u32 = ::std::uint_least32_t;
using u64 = ::std::uint_least64_t;
using isize = ::std::ptrdiff_t;
using usize = ::std::size_t;

template <class T = usize> class rep {
	const T f, l;

public:
	class itr {
		friend rep;
		T i;
		constexpr itr(T x) noexcept : i(x) {}

	public:
		void operator++() noexcept { ++i; }
		constexpr T operator*() const noexcept { return i; }
		constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
	};
	constexpr rep(const T first, const T last) noexcept : f(first), l(last) {}
	constexpr itr begin() const noexcept { return itr(f); }
	constexpr itr end() const noexcept { return itr(l); }
};
template <class T = usize> class revrep {
	const T f, l;

public:
	class itr {
		friend revrep;
		T i;
		constexpr itr(T x) noexcept : i(x) {}

	public:
		void operator++() noexcept { --i; }
		constexpr T operator*() const noexcept { return i; }
		constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
	};
	constexpr revrep(const T first, const T last) noexcept : f(first), l(last) {}
	constexpr itr begin() const noexcept { return itr(l - 1); }
	constexpr itr end() const noexcept { return itr(f - 1); }
};
template <class T> bool amax(T &a, const T &b) {
	return a <= b ? (a = b, 1) : 0;
}
template <class T> bool amin(T &a, const T &b) {
	return b <= a ? (a = b, 1) : 0;
}
template <class T> bool asmax(T &a, const T &b) {
	return b <= a ? 0 : (a = b, 1);
}
template <class T> bool asmin(T &a, const T &b) {
	return a <= b ? 0 : (a = b, 1);
}
template <class T> using vec_alias = ::std::vector<T>;
template <class T> auto md_vec(usize n, const T &value) {
	return ::std::vector<T>(n, value);
}
template <class... Args> auto md_vec(usize n, Args... args) {
	return ::std::vector<decltype(md_vec(args...))>(n, md_vec(args...));
}
template <class T> const T &as_const(const T &v) noexcept { return v; }
template <class T> constexpr T difference(const T &a, const T &b) {
	return a <= b ? b - a : a - b;
}
#include <cassert>
#include <cstdint>

template <::std::uint_least32_t Modulus> class modint {
	using u32 = ::std::uint_least32_t;
	using u64 = ::std::uint_least64_t;
	using i64 = ::std::int_fast64_t;
	class optimize_tag_t {};
	static constexpr optimize_tag_t optimize_tag{};

public:
	using value_type = u32;
	value_type a;

private:
	static constexpr value_type cst(i64 x) noexcept {
		x %= static_cast<i64>(Modulus);
		if (x < static_cast<i64>(0)) {
			x += static_cast<i64>(Modulus);
		}
		return static_cast<value_type>(x);
	}

	constexpr modint(optimize_tag_t, const value_type &x) noexcept : a(x) {}

public:
	constexpr modint() noexcept : a(static_cast<value_type>(0)) {}
	constexpr modint(const i64 &x) noexcept : a(cst(x)) {}
	constexpr value_type value() const noexcept { return a; }
	constexpr modint operator+(const modint &o) const noexcept {
		return modint(optimize_tag,
			a + o.a < Modulus ? a + o.a : a + o.a - Modulus);
	}
	constexpr modint operator-(const modint &o) const noexcept {
		return modint(optimize_tag, a < o.a ? a + Modulus - o.a : a - o.a);
	}
	constexpr modint operator*(const modint &o) const noexcept {
		return modint(
			optimize_tag,
			static_cast<value_type>(static_cast<u64>(a) * static_cast<u64>(o.a) %
				static_cast<u64>(Modulus)));
	}
	constexpr modint operator/(const modint &o) const {
		return modint(
			optimize_tag,
			static_cast<value_type>(static_cast<u64>(a) * static_cast<u64>((~o).a) %
				static_cast<u64>(Modulus)));
	}
	modint &operator+=(const modint &o) noexcept {
		if ((a += o.a) >= Modulus)
			a -= Modulus;
		return *this;
	}
	modint &operator-=(const modint &o) noexcept {
		if (a < o.a)
			a += Modulus;
		a -= o.a;
		return *this;
	}
	modint &operator*=(const modint &o) noexcept {
		a = static_cast<value_type>(static_cast<u64>(a) * static_cast<u64>(o.a) %
			static_cast<u64>(Modulus));
		return *this;
	}
	modint &operator/=(const modint &o) {
		a = static_cast<u64>(a) * (~o).a % Modulus;
		return *this;
	}
	constexpr modint inverse() const noexcept {
		assert(a != static_cast<value_type>(0) && "0 does not have inverse");
		return pow(static_cast<u64>(Modulus - static_cast<value_type>(2)));
	}
	constexpr modint operator~() const noexcept { return inverse(); }
	constexpr modint operator-() const noexcept {
		if (a == static_cast<value_type>(0)) {
			return modint(optimize_tag, static_cast<value_type>(0));
		}
		else {
			return modint(optimize_tag, Modulus - a);
		}
	}
	modint &operator++() noexcept {
		if (++a == Modulus) {
			a = static_cast<value_type>(0);
		}
		return *this;
	}
	modint &operator--() noexcept {
		if (a == static_cast<value_type>(0)) {
			a = Modulus;
		}
		--a;
		return *this;
	}
	constexpr bool operator==(const modint &o) const noexcept { return a == o.a; }
	constexpr bool operator!=(const modint &o) const noexcept { return a != o.a; }
	constexpr bool operator<(const modint &o) const noexcept { return a < o.a; }
	constexpr bool operator<=(const modint &o) const noexcept { return a <= o.a; }
	constexpr bool operator>(const modint &o) const noexcept { return a > o.a; }
	constexpr bool operator>=(const modint &o) const noexcept { return a >= o.a; }
	constexpr explicit operator bool() const noexcept { return a; }
	constexpr explicit operator value_type() const noexcept { return a; }
	modint pow(u64 x) const noexcept {
		u64 t = a, u = 1;
		while (x) {
			if (x & 1)
				u = u * t % Modulus;
			t = (t * t) % Modulus;
			x >>= 1;
		}
		return modint(optimize_tag, static_cast<value_type>(u));
	}
};
#include <array>
#include <cstddef>
#include <cstdint>

::std::size_t ctz64(const ::std::uint_fast64_t c) {
#ifdef __has_builtin
	return __builtin_ctzll(c);
#else
	static const ::std::array<::std::size_t, 64> table = {
		0,  1,  2,  7,  3,  13, 8,  27, 4,  33, 14, 36, 9,  49, 28, 19,
		5,  25, 34, 17, 15, 53, 37, 55, 10, 46, 50, 39, 29, 42, 20, 57,
		63, 6,  12, 26, 32, 35, 48, 18, 24, 16, 52, 54, 45, 38, 41, 56,
		62, 11, 31, 47, 23, 51, 44, 40, 61, 30, 22, 43, 60, 21, 59, 58 };
	return table[(c & ~c + 1) * 0x218A7A392DD9ABFULL >> 58 & 0x3F];
#endif
}
#include <cstddef>
#include <cstdint>

::std::size_t popcount64(::std::uint_fast64_t c) {
#ifdef __has_builtin
	return __builtin_popcountll(c);
#else
	c = (c & 0x5555555555555555ULL) + (c >> 1 & 0x5555555555555555ULL);
	c = (c & 0x3333333333333333ULL) + (c >> 2 & 0x3333333333333333ULL);
	c = (c + (c >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
	return static_cast<::std::size_t>(c * 0x0101010101010101ULL >> 56 & 0x7f);
#endif
}



#include <algorithm>
#include <iostream>
#include <utility>

int main() {
	using mint = modint<1000000007>;
	usize n;
	::std::cin >> n;
	auto a = md_vec(n, n, mint());
	for (auto &v : a) {
		for (auto &e : v) {
			::std::cin >> e.a;
		}
	}
	const usize s = static_cast<usize>(1) << n;
	::std::vector<mint> res(s, mint(1));
	for(const auto r:rep<>(0,n)){
		::std::vector<mint> temp(s, mint(0));
		for (const auto i : rep<>(1, s)) {
			const auto p = ctz64(i);
			temp[i] = temp[i^usize(1) << p] + a[r][p];
			res[i] *= temp[i];
		}
	}
	mint ans;
	for (const auto i : rep<>(1, s)) {
		if ((n - popcount64(i)) % 2 == 0) {
			ans += res[i];
		}
		else {
			ans -= res[i];
		}
	}
	::std::cout << ans.value() << ::std::endl;
	return 0;
}