Problem p03174 (C++)

Buggy submission (status: Time Limit Exceeded):

#pragma GCC optimize("-O3")
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <regex>
#include <set>
#include <stack>
#include <string>
#include <time.h>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <vector>
#ifdef _MSC_VER
#include <intrin.h>
#define popcnt __popcnt64
// #  define __builtin_popcount __popcnt
#else
#define popcnt __builtin_popcountll
#endif
// #include "boost/variant.hpp"

using namespace std;

typedef long long ll;
constexpr ll MOD = 1000000007;
constexpr ll INF = 1LL << 60;

#define rep(i, N, M) for (ll i = N, i##_len = (M); i < i##_len; ++i)
#define rep_skip(i, N, M, ...)                                                 \
  for (ll i = N, i##_len = (M); i < i##_len; i += (skip))
#define rrep(i, N, M) for (ll i = (M)-1, i##_len = (N - 1); i > i##_len; --i)
#define pb push_back

typedef pair<double, double> pd;
typedef pair<ll, ll> pll;

template <int n> struct tll_impl {
  using type = decltype(tuple_cat(tuple<ll>(),
                                  declval<typename tll_impl<n - 1>::type>()));
};
template <> struct tll_impl<1> {
  using type = tuple<ll>;
};
template <int n> using tll = typename tll_impl<n>::type;

template <class T> constexpr ll SZ(T &v) { return static_cast<ll>(v.size()); };

template <int n, typename T> struct vec_t_impl {
  using type = vector<typename vec_t_impl<n - 1, T>::type>;
};
template <typename T> struct vec_t_impl<1, T> {
  using type = vector<T>;
};
template <int n, typename T> using vec_t = typename vec_t_impl<n, T>::type;
// check
static_assert(is_same<vec_t<3, ll>, vector<vector<vector<ll>>>>::value, "");

// decompose vector into basetype and dimension.
template <typename T> struct vec_dec {
  static constexpr int dim = 0;
  using type = T;
};
template <typename T> struct vec_dec<vector<T>> {
  static constexpr int dim = vec_dec<T>::dim + 1;
  using type = typename vec_dec<T>::type;
};
static_assert(is_same<typename vec_dec<vec_t<3, ll>>::type, ll>::value, "");
static_assert(vec_dec<vec_t<3, ll>>::dim == 3, "");

template <typename T = ll> vector<T> make_v(size_t a) { return vector<T>(a); }

template <typename T = ll, typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}
// ex:  auto dp =  make_v<ll>(4,5) => vector<vector<ll>> dp(4,vector<ll>(5));

// check if T is vector
template <typename T> struct is_vector : std::false_type {};

template <typename T> struct is_vector<vector<T>> : std::true_type {};
static_assert(is_vector<vector<ll>>::value == true &&
                  is_vector<ll>::value == false,
              "");

template <typename T, typename V,
          typename enable_if<!is_vector<T>::value, nullptr_t>::type = nullptr>
void fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V,
          typename enable_if<is_vector<T>::value, nullptr_t>::type = nullptr>
void fill_v(T &t, const V &v) {
  for (auto &&x : t)
    fill_v(x, v);
}
// ex:  fill_v(dp, INF);

template <typename T,
          typename enable_if<!is_vector<T>::value, nullptr_t>::type = nullptr>
void read_v(T &x) {
  cin >> x;
}

template <typename T,
          typename enable_if<is_vector<T>::value, nullptr_t>::type = nullptr>
void read_v(T &x) {
  rep(i, 0, x.size()) read_v(x[i]);
}

template <typename T,
          typename enable_if<!is_vector<T>::value, nullptr_t>::type = nullptr>
void write_v(T &x) {
  cout << x << " ";
}

template <typename T,
          typename enable_if<is_vector<T>::value, nullptr_t>::type = nullptr>
void write_v(T &x) {
  rep(i, 0, x.size()) write_v(x[i]);
  cout << endl;
}

typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef vector<pll> vpll;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vector<string> vs;
template <typename T>
using pq_greater = priority_queue<T, vector<T>, greater<T>>;

#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define perm(c)                                                                \
  sort(all(c));                                                                \
  for (bool c##perm = 1; c##perm; c##perm = next_permutation(all(c)))

template <typename T> void chmin(T &a, T b) {
  if (a > b)
    a = b;
}
template <typename T> void chmax(T &a, T b) {
  if (a < b)
    a = b;
}

vll seq(ll i, ll j) {
  vll res(j - i);
  rep(k, i, j) res[k] = i + k;
  return res;
}

constexpr ll POW_0(ll x, ll y) {
  if (y == 0)
    return 1;
  if (y == 1)
    return x;
  if (y == 2)
    return x * x;
  if (y % 2 == 0)
    return POW_0(POW_0(x, y / 2), 2LL);
  return ((POW_0(POW_0(x, y / 2), 2LL)) * (x));
}

constexpr ll POW(ll x, ll y, ll mod = MOD) {
  if (mod == 0)
    return POW_0(x, y);
  if (y == 0)
    return 1;
  if (y == 1)
    return x % mod;
  if (y == 2)
    return x * x % mod;
  if (y % 2 == 0)
    return POW(POW(x, y / 2, mod), 2LL, mod) % mod;
  return ((POW(POW(x, y / 2, mod), 2LL, mod)) * (x % mod)) % mod;
}

template <typename Inputs, typename Functor,
          typename T = typename Inputs::value_type>
void sort_by(Inputs &inputs, Functor f) {
  std::sort(std::begin(inputs), std::end(inputs),
            [&f](const T &lhs, const T &rhs) { return f(lhs) < f(rhs); });
}

template <typename Inputs, typename Functor,
          typename T = typename Inputs::value_type>
void stable_sort_by(Inputs &inputs, Functor f) {
  std::stable_sort(
      std::begin(inputs), std::end(inputs),
      [&f](const T &lhs, const T &rhs) { return f(lhs) < f(rhs); });
}

ll div_ferm(ll a, ll b, ll mod) { return (a * POW(b, mod - 2, mod)) % mod; }

// === Modint ===

template <std::uint_fast64_t Modulus = 1000000007> class modint {
  using u64 = std::uint_fast64_t;

public:
  u64 a;

  constexpr modint(const u64 x = 0) noexcept : a(x % Modulus) {}
  // constexpr modint(const modint& rhs) noexcept {
  //	this->a = rhs.value();
  // }
  // constexpr modint &operator=(const modint &rhs) noexcept {
  //	this->a = rhs.value();
  //	return *this;
  // }
  constexpr u64 value() const noexcept { return a; }
  constexpr modint operator+(const modint rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint operator-(const modint rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint operator*(const modint rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint operator/(const modint rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  modint &operator+=(const modint rhs) noexcept {
    a += rhs.a;
    if (a >= Modulus) {
      a -= Modulus;
    }
    return *this;
  }
  modint &operator-=(const modint rhs) noexcept {
    if (a < rhs.a) {
      a += Modulus;
    }
    a -= rhs.a;
    return *this;
  }
  modint &operator*=(const modint rhs) noexcept {
    a = a * rhs.a % Modulus;
    return *this;
  }
  modint &operator/=(modint rhs) noexcept {
    u64 exp = Modulus - 2;
    while (exp) {
      if (exp % 2) {
        *this *= rhs;
      }
      rhs *= rhs;
      exp /= 2;
    }
    return *this;
  }
  modint &operator++() noexcept { return *this += modint(1); }
  modint &operator++(int) noexcept {
    auto t = *this;
    *this += modint(1);
    return t;
  }
  modint &operator--() noexcept { return *this -= modint(1); }
  modint &operator--(int) noexcept {
    auto t = *this;
    *this -= modint(1);
    return t;
  }
  constexpr bool operator==(const modint rhs) const noexcept {
    return a == rhs.value();
  }
  constexpr bool operator!=(const modint rhs) const noexcept {
    return a != rhs.value();
  }
  constexpr bool operator<(const modint rhs) const noexcept {
    return a < rhs.value();
  }
  // should be moved to Google Test
  // constexpr void test(){
  //	constexpr auto x = modint<5>(3);
  //	constexpr auto y = modint<5>(4);
  //	constexpr auto z = modint<5>(2);
  //	static_assert(x + y == z, "");
  //	static_assert(x != y, "");
  //	static_assert(++x == y && x++ != y && x == --y && x != y--, "");
  //	static_assert(x + 6 == y, "");
  //	static_assert(x / 2 == y, "");
  //
  //}
};

template <uint_fast64_t Modulus>
ostream &operator<<(ostream &o, const modint<Modulus> &t) {
  o << t.value();
  return o;
}
template <uint_fast64_t Modulus>
istream &operator>>(istream &in, modint<Modulus> &t) {
  uint_fast64_t x;
  in >> x;
  t = modint<Modulus>(x);
  return in;
}
template <uint_fast64_t Modulus> modint<Modulus> POW(modint<Modulus> x, ll n) {
  return modint<Modulus>(POW(x.value(), n, Modulus));
}

// === Mll ===

template <typename T = ll, T MOD = 1000000007> struct Mint {
  T v;
  Mint() : v(0) {}
  Mint(signed v) : v(v) {}
  Mint(long long t) {
    v = t % MOD;
    if (v < 0)
      v += MOD;
  }

  Mint inv() { return pow(MOD - 2); }

  Mint &operator+=(Mint a) {
    v += a.v;
    if (v >= MOD)
      v -= MOD;
    return *this;
  }
  Mint &operator-=(Mint a) {
    v += MOD - a.v;
    if (v >= MOD)
      v -= MOD;
    return *this;
  }
  Mint &operator*=(Mint a) {
    v = 1LL * v * a.v % MOD;
    return *this;
  }
  Mint &operator/=(Mint a) { return (*this) *= a.inv(); }

  Mint operator+(Mint a) const { return Mint(v) += a; };
  Mint operator-(Mint a) const { return Mint(v) -= a; };
  Mint operator*(Mint a) const { return Mint(v) *= a; };
  Mint operator/(Mint a) const { return Mint(v) /= a; };

  Mint operator-() { return v ? MOD - v : v; }

  bool operator==(const Mint a) const { return v == a.v; }
  bool operator!=(const Mint a) const { return v != a.v; }
  bool operator<(const Mint a) const { return v < a.v; }

  static Mint pow(Mint v, long long k) {
    Mint res(1), tmp(v);
    while (k) {
      if (k & 1)
        res *= tmp;
      tmp *= tmp;
      k >>= 1;
    }
    return res;
  }

  // find x s.t. a^x = b
  static T log(Mint a, Mint b) {
    const T sq = 40000;
    unordered_map<T, T> dp;
    dp.reserve(sq);
    Mint res(1);
    for (ll r = 0; r < sq; r++) {
      if (!dp.count(res))
        dp[res] = r;
      res *= a;
    }
    Mint p = pow(a.inv(), sq);
    res = b;
    for (ll q = 0; q <= MOD / sq + 1; q++) {
      if (dp.count(res)) {
        T idx = q * sq + dp[res];
        if (idx > 0)
          return idx;
      }
      res *= p;
    }
    return T(-1);
  }

  static vector<Mint> fact, finv, invs;

  static void init(ll n) {
    if (n + 1 <= (signed)fact.size())
      return;
    fact.assign(n + 1, 1);
    finv.assign(n + 1, 1);
    invs.assign(n + 1, 1);

    for (ll i = 1; i <= n; i++)
      fact[i] = fact[i - 1] * Mint(i);
    finv[n] = Mint(1) / fact[n];
    for (ll i = n; i >= 1; i--)
      finv[i - 1] = finv[i] * Mint(i);
    for (ll i = 1; i <= n; i++)
      invs[i] = finv[i] * fact[i - 1];
  }

  static Mint comb(long long n, ll k) {
    Mint res(1);
    for (ll i = 0; i < k; i++) {
      res *= Mint(n - i);
      res /= Mint(i + 1);
    }
    return res;
  }

  static Mint C(ll n, ll k) {
    if (n < k || k < 0)
      return Mint(0);
    init(n);
    return fact[n] * finv[n - k] * finv[k];
  }

  static Mint P(ll n, ll k) {
    if (n < k || k < 0)
      return Mint(0);
    init(n);
    return fact[n] * finv[n - k];
  }

  static Mint H(ll n, ll k) {
    if (n < 0 || k < 0)
      return Mint(0);
    if (!n && !k)
      return Mint(1);
    init(n + k - 1);
    return C(n + k - 1, k);
  }

  static Mint S(ll n, ll k) {
    Mint res;
    init(k);
    for (ll i = 1; i <= k; i++) {
      Mint tmp = C(k, i) * Mint(i).pow(n);
      if ((k - i) & 1)
        res -= tmp;
      else
        res += tmp;
    }
    return res *= finv[k];
  }

  static vector<vector<Mint>> D(ll n, ll m) {
    vector<vector<Mint>> dp(n + 1, vector<Mint>(m + 1, 0));
    dp[0][0] = Mint(1);
    for (ll i = 0; i <= n; i++) {
      for (ll j = 1; j <= m; j++) {
        if (i - j >= 0)
          dp[i][j] = dp[i][j - 1] + dp[i - j][j];
        else
          dp[i][j] = dp[i][j - 1];
      }
    }
    return dp;
  }

  static Mint B(ll n, ll k) {
    Mint res;
    for (ll j = 1; j <= k; j++)
      res += S(n, j);
    return res;
  }

  static Mint montmort(ll n) {
    Mint res;
    init(n);
    for (ll k = 2; k <= n; k++) {
      if (k & 1)
        res -= finv[k];
      else
        res += finv[k];
    }
    return res *= fact[n];
  }

  static Mint LagrangePolynomial(vector<Mint> &y, Mint t) {
    ll n = y.size() - 1;
    if (t.v <= n)
      return y[t.v];
    init(n + 1);
    Mint num(1);
    for (ll i = 0; i <= n; i++)
      num *= t - Mint(i);
    Mint res;
    for (ll i = 0; i <= n; i++) {
      Mint tmp = y[i] * num / (t - Mint(i)) * finv[i] * finv[n - i];
      if ((n - i) & 1)
        res -= tmp;
      else
        res += tmp;
    }
    return res;
  }
};

class Combination {
  // this calculates combination (nCk).
  // Constructor runs in O(MAX).
  // get(n,k) returns nCk in O(1).

  ll MAX, MOD;
  vll fac;
  vll finv;
  vll inv;

public:
  Combination(ll MAX = 210000, ll MOD = 1000000007)
      : MOD(MOD), MAX(max(MAX, 2LL)), fac(vll(MAX + 1)), finv(vll(MAX + 1)),
        inv(vll(MAX + 1)) {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    pre_process(2LL, MAX + 1);
  }

  ll get(ll n, ll k) {
    if (MAX < n)
      pre_process(MAX + 1, n + 1);

    if (n < k)
      return 0;
    if (n < 0 || k < 0)
      return 0;
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
  }

private:
  void pre_process(ll m, ll n) {
    if (MAX < n) {
      fac.resize(n);
      inv.resize(n);
      finv.resize(n);
    }
    rep(i, m, n) {
      fac[i] = fac[i - 1] * i % MOD;
      inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
      finv[i] = finv[i - 1] * inv[i] % MOD;
    }
  }
};

ll choose(int n, int r) { // O(r) for small n
  ll acc = 1;
  rep(i, 0, r) acc = acc * (n - i) / (i + 1);
  return acc;
}

ll gcd(ll a, ll b) {
  if (a % b == 0)
    return b;
  else
    return gcd(b, a % b);
}

vll getDivisors(ll n) {
  vll res;
  ll i = 1;

  for (; i * i < n; i++) {
    if (n % i == 0) {
      res.push_back(i);
      res.push_back(n / i);
    }
  }
  if (i * i == n)
    res.push_back(i);
  sort(res.begin(), res.end());
  return res;
}

vll getDivisors(ll n, ll m) {
  // O(sqrt(min(n,m)))
  if (n > m)
    swap(n, m);
  vll res;
  ll i = 1;

  for (; i * i < n; i++) {
    if (n % i == 0) {
      if (m % i == 0)
        res.push_back(i);
      if (m % (n / i) == 0)
        res.push_back(n / i);
    }
  }
  if (i * i == n)
    if (m % i == 0)
      res.push_back(i);
  sort(res.begin(), res.end());
  return res;
}

vector<pll> prime_factorize(ll n) {
  vector<pll> res;
  for (ll p = 2; p * p <= n; ++p) {
    if (n % p != 0)
      continue;
    ll num = 0;
    while (n % p == 0) {
      ++num;
      n /= p;
    }
    res.push_back({p, num});
  }
  if (n != 1)
    res.push_back(make_pair(n, 1));
  return res;
}

// ============================ Header  =================================

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << setprecision(12);
  auto x = modint<MOD>(1);
  auto y = modint<>();
  auto z = y + x;

  ll n;
  cin >> n;
  vvll a(n, vll(n));
  read_v(a);

  vector<bitset<21>> as(n);
  rep(i, 0, n) rep(j, 0, n) { as[i][j] = a[i][j]; }
  vector<vector<int>> dp(n, vector<int>(1LL << 22));
  rep(i, 0, n) {

    rep(j, 0, 1 << n) {
      auto poss = as[i] & bitset<21>(j);
      if (i == 0) {
        dp[0][j] = poss.count();
        continue;
      }
      if (poss == 0)
        continue;
      rep(k, 0, n) {
        if (poss[k])
          dp[i][j] += dp[i - 1][j ^ (1LL << k)];
        if (dp[i][j] >= MOD)
          dp[i][j] -= MOD;
      }
    }
  }
  cout << dp[n - 1][(1LL << n) - 1] << endl;
  return 0;
}


Fixed submission:

#pragma GCC optimize("-O3")
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <regex>
#include <set>
#include <stack>
#include <string>
#include <time.h>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <vector>
#ifdef _MSC_VER
#include <intrin.h>
#define popcnt __popcnt64
// #  define __builtin_popcount __popcnt
#else
#define popcnt __builtin_popcountll
#endif
// #include "boost/variant.hpp"

using namespace std;

typedef long long ll;
constexpr ll MOD = 1000000007;
constexpr ll INF = 1LL << 60;

#define rep(i, N, M) for (ll i = N, i##_len = (M); i < i##_len; ++i)
#define rep_skip(i, N, M, ...)                                                 \
  for (ll i = N, i##_len = (M); i < i##_len; i += (skip))
#define rrep(i, N, M) for (ll i = (M)-1, i##_len = (N - 1); i > i##_len; --i)
#define pb push_back

typedef pair<double, double> pd;
typedef pair<ll, ll> pll;

template <int n> struct tll_impl {
  using type = decltype(tuple_cat(tuple<ll>(),
                                  declval<typename tll_impl<n - 1>::type>()));
};
template <> struct tll_impl<1> {
  using type = tuple<ll>;
};
template <int n> using tll = typename tll_impl<n>::type;

template <class T> constexpr ll SZ(T &v) { return static_cast<ll>(v.size()); };

template <int n, typename T> struct vec_t_impl {
  using type = vector<typename vec_t_impl<n - 1, T>::type>;
};
template <typename T> struct vec_t_impl<1, T> {
  using type = vector<T>;
};
template <int n, typename T> using vec_t = typename vec_t_impl<n, T>::type;
// check
static_assert(is_same<vec_t<3, ll>, vector<vector<vector<ll>>>>::value, "");

// decompose vector into basetype and dimension.
template <typename T> struct vec_dec {
  static constexpr int dim = 0;
  using type = T;
};
template <typename T> struct vec_dec<vector<T>> {
  static constexpr int dim = vec_dec<T>::dim + 1;
  using type = typename vec_dec<T>::type;
};
static_assert(is_same<typename vec_dec<vec_t<3, ll>>::type, ll>::value, "");
static_assert(vec_dec<vec_t<3, ll>>::dim == 3, "");

template <typename T = ll> vector<T> make_v(size_t a) { return vector<T>(a); }

template <typename T = ll, typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}
// ex:  auto dp =  make_v<ll>(4,5) => vector<vector<ll>> dp(4,vector<ll>(5));

// check if T is vector
template <typename T> struct is_vector : std::false_type {};

template <typename T> struct is_vector<vector<T>> : std::true_type {};
static_assert(is_vector<vector<ll>>::value == true &&
                  is_vector<ll>::value == false,
              "");

template <typename T, typename V,
          typename enable_if<!is_vector<T>::value, nullptr_t>::type = nullptr>
void fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V,
          typename enable_if<is_vector<T>::value, nullptr_t>::type = nullptr>
void fill_v(T &t, const V &v) {
  for (auto &&x : t)
    fill_v(x, v);
}
// ex:  fill_v(dp, INF);

template <typename T,
          typename enable_if<!is_vector<T>::value, nullptr_t>::type = nullptr>
void read_v(T &x) {
  cin >> x;
}

template <typename T,
          typename enable_if<is_vector<T>::value, nullptr_t>::type = nullptr>
void read_v(T &x) {
  rep(i, 0, x.size()) read_v(x[i]);
}

template <typename T,
          typename enable_if<!is_vector<T>::value, nullptr_t>::type = nullptr>
void write_v(T &x) {
  cout << x << " ";
}

template <typename T,
          typename enable_if<is_vector<T>::value, nullptr_t>::type = nullptr>
void write_v(T &x) {
  rep(i, 0, x.size()) write_v(x[i]);
  cout << endl;
}

typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef vector<pll> vpll;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vector<string> vs;
template <typename T>
using pq_greater = priority_queue<T, vector<T>, greater<T>>;

#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define perm(c)                                                                \
  sort(all(c));                                                                \
  for (bool c##perm = 1; c##perm; c##perm = next_permutation(all(c)))

template <typename T> void chmin(T &a, T b) {
  if (a > b)
    a = b;
}
template <typename T> void chmax(T &a, T b) {
  if (a < b)
    a = b;
}

vll seq(ll i, ll j) {
  vll res(j - i);
  rep(k, i, j) res[k] = i + k;
  return res;
}

constexpr ll POW_0(ll x, ll y) {
  if (y == 0)
    return 1;
  if (y == 1)
    return x;
  if (y == 2)
    return x * x;
  if (y % 2 == 0)
    return POW_0(POW_0(x, y / 2), 2LL);
  return ((POW_0(POW_0(x, y / 2), 2LL)) * (x));
}

constexpr ll POW(ll x, ll y, ll mod = MOD) {
  if (mod == 0)
    return POW_0(x, y);
  if (y == 0)
    return 1;
  if (y == 1)
    return x % mod;
  if (y == 2)
    return x * x % mod;
  if (y % 2 == 0)
    return POW(POW(x, y / 2, mod), 2LL, mod) % mod;
  return ((POW(POW(x, y / 2, mod), 2LL, mod)) * (x % mod)) % mod;
}

template <typename Inputs, typename Functor,
          typename T = typename Inputs::value_type>
void sort_by(Inputs &inputs, Functor f) {
  std::sort(std::begin(inputs), std::end(inputs),
            [&f](const T &lhs, const T &rhs) { return f(lhs) < f(rhs); });
}

template <typename Inputs, typename Functor,
          typename T = typename Inputs::value_type>
void stable_sort_by(Inputs &inputs, Functor f) {
  std::stable_sort(
      std::begin(inputs), std::end(inputs),
      [&f](const T &lhs, const T &rhs) { return f(lhs) < f(rhs); });
}

ll div_ferm(ll a, ll b, ll mod) { return (a * POW(b, mod - 2, mod)) % mod; }

// === Modint ===

template <std::uint_fast64_t Modulus = 1000000007> class modint {
  using u64 = std::uint_fast64_t;

public:
  u64 a;

  constexpr modint(const u64 x = 0) noexcept : a(x % Modulus) {}
  // constexpr modint(const modint& rhs) noexcept {
  //	this->a = rhs.value();
  // }
  // constexpr modint &operator=(const modint &rhs) noexcept {
  //	this->a = rhs.value();
  //	return *this;
  // }
  constexpr u64 value() const noexcept { return a; }
  constexpr modint operator+(const modint rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint operator-(const modint rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint operator*(const modint rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint operator/(const modint rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  modint &operator+=(const modint rhs) noexcept {
    a += rhs.a;
    if (a >= Modulus) {
      a -= Modulus;
    }
    return *this;
  }
  modint &operator-=(const modint rhs) noexcept {
    if (a < rhs.a) {
      a += Modulus;
    }
    a -= rhs.a;
    return *this;
  }
  modint &operator*=(const modint rhs) noexcept {
    a = a * rhs.a % Modulus;
    return *this;
  }
  modint &operator/=(modint rhs) noexcept {
    u64 exp = Modulus - 2;
    while (exp) {
      if (exp % 2) {
        *this *= rhs;
      }
      rhs *= rhs;
      exp /= 2;
    }
    return *this;
  }
  modint &operator++() noexcept { return *this += modint(1); }
  modint &operator++(int) noexcept {
    auto t = *this;
    *this += modint(1);
    return t;
  }
  modint &operator--() noexcept { return *this -= modint(1); }
  modint &operator--(int) noexcept {
    auto t = *this;
    *this -= modint(1);
    return t;
  }
  constexpr bool operator==(const modint rhs) const noexcept {
    return a == rhs.value();
  }
  constexpr bool operator!=(const modint rhs) const noexcept {
    return a != rhs.value();
  }
  constexpr bool operator<(const modint rhs) const noexcept {
    return a < rhs.value();
  }
  // should be moved to Google Test
  // constexpr void test(){
  //	constexpr auto x = modint<5>(3);
  //	constexpr auto y = modint<5>(4);
  //	constexpr auto z = modint<5>(2);
  //	static_assert(x + y == z, "");
  //	static_assert(x != y, "");
  //	static_assert(++x == y && x++ != y && x == --y && x != y--, "");
  //	static_assert(x + 6 == y, "");
  //	static_assert(x / 2 == y, "");
  //
  //}
};

template <uint_fast64_t Modulus>
ostream &operator<<(ostream &o, const modint<Modulus> &t) {
  o << t.value();
  return o;
}
template <uint_fast64_t Modulus>
istream &operator>>(istream &in, modint<Modulus> &t) {
  uint_fast64_t x;
  in >> x;
  t = modint<Modulus>(x);
  return in;
}
template <uint_fast64_t Modulus> modint<Modulus> POW(modint<Modulus> x, ll n) {
  return modint<Modulus>(POW(x.value(), n, Modulus));
}

// === Mll ===

template <typename T = ll, T MOD = 1000000007> struct Mint {
  T v;
  Mint() : v(0) {}
  Mint(signed v) : v(v) {}
  Mint(long long t) {
    v = t % MOD;
    if (v < 0)
      v += MOD;
  }

  Mint inv() { return pow(MOD - 2); }

  Mint &operator+=(Mint a) {
    v += a.v;
    if (v >= MOD)
      v -= MOD;
    return *this;
  }
  Mint &operator-=(Mint a) {
    v += MOD - a.v;
    if (v >= MOD)
      v -= MOD;
    return *this;
  }
  Mint &operator*=(Mint a) {
    v = 1LL * v * a.v % MOD;
    return *this;
  }
  Mint &operator/=(Mint a) { return (*this) *= a.inv(); }

  Mint operator+(Mint a) const { return Mint(v) += a; };
  Mint operator-(Mint a) const { return Mint(v) -= a; };
  Mint operator*(Mint a) const { return Mint(v) *= a; };
  Mint operator/(Mint a) const { return Mint(v) /= a; };

  Mint operator-() { return v ? MOD - v : v; }

  bool operator==(const Mint a) const { return v == a.v; }
  bool operator!=(const Mint a) const { return v != a.v; }
  bool operator<(const Mint a) const { return v < a.v; }

  static Mint pow(Mint v, long long k) {
    Mint res(1), tmp(v);
    while (k) {
      if (k & 1)
        res *= tmp;
      tmp *= tmp;
      k >>= 1;
    }
    return res;
  }

  // find x s.t. a^x = b
  static T log(Mint a, Mint b) {
    const T sq = 40000;
    unordered_map<T, T> dp;
    dp.reserve(sq);
    Mint res(1);
    for (ll r = 0; r < sq; r++) {
      if (!dp.count(res))
        dp[res] = r;
      res *= a;
    }
    Mint p = pow(a.inv(), sq);
    res = b;
    for (ll q = 0; q <= MOD / sq + 1; q++) {
      if (dp.count(res)) {
        T idx = q * sq + dp[res];
        if (idx > 0)
          return idx;
      }
      res *= p;
    }
    return T(-1);
  }

  static vector<Mint> fact, finv, invs;

  static void init(ll n) {
    if (n + 1 <= (signed)fact.size())
      return;
    fact.assign(n + 1, 1);
    finv.assign(n + 1, 1);
    invs.assign(n + 1, 1);

    for (ll i = 1; i <= n; i++)
      fact[i] = fact[i - 1] * Mint(i);
    finv[n] = Mint(1) / fact[n];
    for (ll i = n; i >= 1; i--)
      finv[i - 1] = finv[i] * Mint(i);
    for (ll i = 1; i <= n; i++)
      invs[i] = finv[i] * fact[i - 1];
  }

  static Mint comb(long long n, ll k) {
    Mint res(1);
    for (ll i = 0; i < k; i++) {
      res *= Mint(n - i);
      res /= Mint(i + 1);
    }
    return res;
  }

  static Mint C(ll n, ll k) {
    if (n < k || k < 0)
      return Mint(0);
    init(n);
    return fact[n] * finv[n - k] * finv[k];
  }

  static Mint P(ll n, ll k) {
    if (n < k || k < 0)
      return Mint(0);
    init(n);
    return fact[n] * finv[n - k];
  }

  static Mint H(ll n, ll k) {
    if (n < 0 || k < 0)
      return Mint(0);
    if (!n && !k)
      return Mint(1);
    init(n + k - 1);
    return C(n + k - 1, k);
  }

  static Mint S(ll n, ll k) {
    Mint res;
    init(k);
    for (ll i = 1; i <= k; i++) {
      Mint tmp = C(k, i) * Mint(i).pow(n);
      if ((k - i) & 1)
        res -= tmp;
      else
        res += tmp;
    }
    return res *= finv[k];
  }

  static vector<vector<Mint>> D(ll n, ll m) {
    vector<vector<Mint>> dp(n + 1, vector<Mint>(m + 1, 0));
    dp[0][0] = Mint(1);
    for (ll i = 0; i <= n; i++) {
      for (ll j = 1; j <= m; j++) {
        if (i - j >= 0)
          dp[i][j] = dp[i][j - 1] + dp[i - j][j];
        else
          dp[i][j] = dp[i][j - 1];
      }
    }
    return dp;
  }

  static Mint B(ll n, ll k) {
    Mint res;
    for (ll j = 1; j <= k; j++)
      res += S(n, j);
    return res;
  }

  static Mint montmort(ll n) {
    Mint res;
    init(n);
    for (ll k = 2; k <= n; k++) {
      if (k & 1)
        res -= finv[k];
      else
        res += finv[k];
    }
    return res *= fact[n];
  }

  static Mint LagrangePolynomial(vector<Mint> &y, Mint t) {
    ll n = y.size() - 1;
    if (t.v <= n)
      return y[t.v];
    init(n + 1);
    Mint num(1);
    for (ll i = 0; i <= n; i++)
      num *= t - Mint(i);
    Mint res;
    for (ll i = 0; i <= n; i++) {
      Mint tmp = y[i] * num / (t - Mint(i)) * finv[i] * finv[n - i];
      if ((n - i) & 1)
        res -= tmp;
      else
        res += tmp;
    }
    return res;
  }
};

class Combination {
  // this calculates combination (nCk).
  // Constructor runs in O(MAX).
  // get(n,k) returns nCk in O(1).

  ll MAX, MOD;
  vll fac;
  vll finv;
  vll inv;

public:
  Combination(ll MAX = 210000, ll MOD = 1000000007)
      : MOD(MOD), MAX(max(MAX, 2LL)), fac(vll(MAX + 1)), finv(vll(MAX + 1)),
        inv(vll(MAX + 1)) {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    pre_process(2LL, MAX + 1);
  }

  ll get(ll n, ll k) {
    if (MAX < n)
      pre_process(MAX + 1, n + 1);

    if (n < k)
      return 0;
    if (n < 0 || k < 0)
      return 0;
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
  }

private:
  void pre_process(ll m, ll n) {
    if (MAX < n) {
      fac.resize(n);
      inv.resize(n);
      finv.resize(n);
    }
    rep(i, m, n) {
      fac[i] = fac[i - 1] * i % MOD;
      inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
      finv[i] = finv[i - 1] * inv[i] % MOD;
    }
  }
};

ll choose(int n, int r) { // O(r) for small n
  ll acc = 1;
  rep(i, 0, r) acc = acc * (n - i) / (i + 1);
  return acc;
}

ll gcd(ll a, ll b) {
  if (a % b == 0)
    return b;
  else
    return gcd(b, a % b);
}

vll getDivisors(ll n) {
  vll res;
  ll i = 1;

  for (; i * i < n; i++) {
    if (n % i == 0) {
      res.push_back(i);
      res.push_back(n / i);
    }
  }
  if (i * i == n)
    res.push_back(i);
  sort(res.begin(), res.end());
  return res;
}

vll getDivisors(ll n, ll m) {
  // O(sqrt(min(n,m)))
  if (n > m)
    swap(n, m);
  vll res;
  ll i = 1;

  for (; i * i < n; i++) {
    if (n % i == 0) {
      if (m % i == 0)
        res.push_back(i);
      if (m % (n / i) == 0)
        res.push_back(n / i);
    }
  }
  if (i * i == n)
    if (m % i == 0)
      res.push_back(i);
  sort(res.begin(), res.end());
  return res;
}

vector<pll> prime_factorize(ll n) {
  vector<pll> res;
  for (ll p = 2; p * p <= n; ++p) {
    if (n % p != 0)
      continue;
    ll num = 0;
    while (n % p == 0) {
      ++num;
      n /= p;
    }
    res.push_back({p, num});
  }
  if (n != 1)
    res.push_back(make_pair(n, 1));
  return res;
}

// ============================ Header  =================================

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << setprecision(12);
  auto x = modint<MOD>(1);
  auto y = modint<>();
  auto z = y + x;

  ll n;
  cin >> n;
  vvll a(n, vll(n));
  read_v(a);

  vector<bitset<21>> as(n);
  rep(i, 0, n) rep(j, 0, n) { as[i][j] = a[i][j]; }
  vector<vector<int>> dp(n, vector<int>(1LL << 22));
  rep(i, 0, n) {

    rep(j, 0, 1 << n) {
      if (i + 1 != popcnt(j))
        continue;
      auto poss = as[i] & bitset<21>(j);
      if (i == 0) {
        dp[0][j] = poss.count();
        continue;
      }
      if (poss == 0)
        continue;
      rep(k, 0, n) {
        if (poss[k])
          dp[i][j] += dp[i - 1][j ^ (1LL << k)];
        if (dp[i][j] >= MOD)
          dp[i][j] -= MOD;
      }
    }
  }
  cout << dp[n - 1][(1LL << n) - 1] << endl;
  return 0;
}