J - Bugs Couples

#include <bits/stdc++.h>

using namespace std;

#define cin_2d(vec, n, m) for(int i = 0; i < n; i++) for(int j = 0; j < m && cin >> vec[i][j]; j++);
#define cout_2d(vec, n, m) for(int i = 0; i < n; i++, cout << "\n") for(int j = 0; j < m && cout << vec[i][j] << " "; j++);
#define cout_map(mp) for(auto& [f, s] : mp) cout << f << "  " << s << "\n";
#define Time cerr << "Time Taken: " << (float)clock() / CLOCKS_PER_SEC << " Secs" << "\n";
#define fixed(n) fixed << setprecision(n)
#define ceil(n, m) (((n) / (m)) + ((n) % (m) ? 1 : 0))
#define fill(vec, value) memset(vec, value, sizeof(vec));
#define Num_of_Digits(n) ((int)log10(n) + 1)
#define mod_combine(a, b, m) (((a % m) * (b % m)) % m)
#define all(vec) vec.begin(), vec.end()
#define rall(vec) vec.rbegin(), vec.rend()
#define sz(x) int(x.size())
#define debug(x) cout << #x << ": " << (x) << "\n";
#define fi first
#define se second
#define ll long long
#define ull unsigned long long
#define Mod  1'000'000'007
#define OO 2'000'000'000
#define EPS 1e-9
#define PI acos(-1)
template < typename T = int > using Pair = pair < T, T >;

template < typename T = int > istream& operator >> (istream &in, vector < T > &v) {
    for (auto &x: v) in >> x;
    return in;
}

template < typename T = int > ostream& operator << (ostream &out, const vector < T > &v) {
    for (const T &x: v) out << x << ' ';
    return out;
}

template < int MOD = 1000000007 > struct ModInt {

    int val;

    ModInt(int V = 0) : val(V) { val %= MOD; }

    ModInt& operator += (const ModInt& rhs) {
        if ((val += rhs.val) >= MOD) val -= MOD;
        return *this;
    }
    ModInt& operator += (const int rhs) {
        if ((val += rhs) >= MOD) val -= MOD;
        return *this;
    }

    ModInt& operator -= (const ModInt& rhs) {
        if ((val += MOD - rhs.val) >= MOD) val -= MOD;
        return *this;
    }
    ModInt& operator -= (const int rhs) {
        if ((val += MOD - rhs) >= MOD) val -= MOD;
        return *this;
    }

    ModInt& operator *= (const ModInt& rhs) { val = (1ll * val * rhs.val) % MOD; return *this; }
    ModInt& operator *= (const int rhs) { val = (1ll * val * rhs) % MOD; return *this; }

    ModInt& operator /= (const ModInt& rhs) { return *this *= rhs.inverse(); }
    ModInt& operator /= (const int rhs) { return *this *= ModInt(rhs).inverse(); }

    ModInt& operator %= (const ModInt& rhs) { val %= rhs.val; return *this; }
    ModInt& operator %= (const int rhs) { val %= rhs; return *this; }

    ModInt& operator ++() { return *this += 1; }
    ModInt& operator --() { return *this -= 1; }

    ModInt operator ++(int unused) { ModInt res(*this); ++*this; return res; }
    ModInt operator --(int unused) { ModInt res(*this); --*this; return res; }

    ModInt operator + (const ModInt& rhs) const { ModInt res(*this); return res += rhs; }
    ModInt operator + (const int rhs) const { ModInt res(*this); return res += rhs; }

    ModInt operator % (const ModInt& rhs) const { ModInt res(*this); return res %= rhs; }
    ModInt operator % (const int rhs) const { ModInt res(*this); return res %= rhs; }

    ModInt operator - (const ModInt& rhs) const { ModInt res(*this); return res -= rhs; }
    ModInt operator - (const int rhs) const { ModInt res(*this); return res -= rhs; }

    ModInt operator * (const ModInt& rhs) const { ModInt res(*this); return res *= rhs; }
    ModInt operator * (const int rhs) const { ModInt res(*this); return res *= rhs; }

    ModInt operator / (const ModInt& rhs) const { ModInt res(*this); return res /= rhs; }
    ModInt operator / (const int rhs) const { ModInt res(*this); return res /= rhs; }

    ModInt& operator = (const ModInt& rhs) { val = rhs.val; return *this; }
    ModInt& operator = (const int rhs) { val = rhs; return *this; }

    bool operator == (const ModInt& rhs) const { return val == rhs.val; }
    bool operator == (const int rhs) const { return val == rhs; }

    bool operator != (const ModInt& rhs) const { return val != rhs.val; }
    bool operator != (const int rhs) const { return val != rhs; }

    bool operator < (const ModInt& rhs) const { return val < rhs.val; }
    bool operator < (const int rhs) const { return val < rhs; }

    bool operator <= (const ModInt& rhs) const { return val <= rhs.val; }
    bool operator <= (const int rhs) const { return val <= rhs; }

    bool operator > (const ModInt& rhs) const { return val > rhs.val; }
    bool operator > (const int rhs) const { return val > rhs; }

    bool operator >= (const ModInt& rhs) const { return val >= rhs.val; }
    bool operator >= (const int rhs) const { return val >= rhs; }

    int operator () () const { return val; }

    ModInt inverse() const { return power(MOD - 2); }

    ModInt power(ll n) const {
        ModInt a = *this, res = 1;
        while (n > 0) {
            if (n & 1) res *= a;
            a *= a, n >>= 1;
        }
        return res;
    }

    ModInt power(ModInt n) const {
        ModInt a = *this, res = 1;
        int e = n();
        while (e > 0) {
            if (e & 1) res *= a;
            a *= a, e >>= 1;
        }
        return res;
    }

    friend ModInt operator ^ (ModInt rhs, ll n) { return rhs.power(n); }
    friend ModInt operator ^ (ModInt rhs, ModInt n) { return rhs.power(n); }

    friend std::istream& operator>>(std::istream& is, ModInt& x) noexcept { return is >> x.val; }
    friend std::ostream& operator<<(std::ostream& os, const ModInt& x) noexcept { return os << x.val; }

};
using Mint = ModInt < >;

constexpr int N = 20;
vector < vector < int > > adj(N + 5);
vector < Mint > dp(1 << N, -1);
int n;

Mint cnt_ways(int u, int mask){
    if(u == n) return 1;
    Mint& ret = dp[mask];
    if(ret != -1) return ret;
    ret = 0;
    for(auto& v : adj[u])
        if(!(mask & (1 << v)))
            ret += cnt_ways(u + 1, mask | (1 << v));
    return ret;
}

void Solve(){
    cin >> n;
    for(int i = 0; i < n; i++)
        for(int j = 0, val; j < n && cin >> val; j++)
            if(val == 1)
                adj[i].push_back(j);
    cout << cnt_ways(0, 0) << "\n";
}

int main(){
    ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
    int t = 1;
    //cin >> t;
    while(t--)
        Solve();
    return 0;
}