Problem p03174 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
using namespace std;

// Define
using ll = long long;
using ull = unsigned long long;
using ld = long double;
const ll dx[4] = {1, 0, -1, 0};
const ll dy[4] = {0, 1, 0, -1};
const ll MOD = 1e9 + 7;
const ll mod = 998244353;
const ll inf = 1 << 30;
const ll LINF = LONG_MAX;
const ll INF = 1LL << 60;
const ull MAX = ULONG_MAX;
#define mp make_pair
#define pb push_back
#define elif else if
#define endl '\n'
#define space ' '
#define def inline auto
#define func inline constexpr ll
#define run(a) __attribute__((constructor)) def _##a()
#define all(v) begin(v), end(v)
#define rall(v) rbegin(v), rend(v)
#define input(a) scanf("%lld", &(a))
#define print(a) printf("%lld\n", (a))
#define fi first
#define se second
#define ok(a, b) (0 <= (a) && (a) < (b))
template <class T> using vvector = vector<vector<T>>;
template <class T> using pvector = vector<pair<T, T>>;
template <class T>
using rpriority_queue = priority_queue<T, vector<T>, greater<T>>;

template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}

// Debug
#define debug(...)                                                             \
  {                                                                            \
    cerr << __LINE__ << ": " << #__VA_ARGS__ << " = ";                         \
    for (auto &&X : {__VA_ARGS__})                                             \
      cerr << "[" << X << "] ";                                                \
    cerr << endl;                                                              \
  }

#define dump(a, h, w)                                                          \
  {                                                                            \
    cerr << __LINE__ << ": " << #a << " = [" << endl;                          \
    rep(__i, h) {                                                              \
      rep(__j, w) { cerr << a[__i][__j] << space; }                            \
      cerr << endl;                                                            \
    }                                                                          \
    cerr << "]" << endl;                                                       \
  }

#define vdump(a, n)                                                            \
  {                                                                            \
    cerr << __LINE__ << ": " << #a << " = [";                                  \
    rep(__i, n) if (__i) cerr << space << a[__i];                              \
    else cerr << a[__i];                                                       \
    cerr << "]" << endl;                                                       \
  }

// Loop
#define inc(i, a, n) for (ll i = (a), _##i = (n); i <= _##i; ++i)
#define dec(i, a, n) for (ll i = (a), _##i = (n); i >= _##i; --i)
#define rep(i, n) for (ll i = 0, _##i = (n); i < _##i; ++i)
#define each(i, a) for (auto &&i : a)
#define loop() for (;;)

// Stream
#define fout(n) cout << fixed << setprecision(n)
#define fasten cin.tie(0), ios::sync_with_stdio(0)
run(0) { fasten, fout(10); }

// Speed
#pragma GCC optimize("O3")
#pragma GCC target("avx")

// Math
func gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
func lcm(ll a, ll b) { return a / gcd(a, b) * b; }
func sign(ll a) { return a ? abs(a) / a : 0; }

inline constexpr ll modulo(const ll n, const ll m = MOD) {
  ll k = n % m;
  return k + m * (k < 0);
}

inline constexpr ll chmod(ll &n, const ll m = MOD) {
  n %= m;
  return n += m * (n < 0);
}

inline constexpr ll mpow(ll a, ll n, const ll m = MOD) {
  ll r = 1;
  while (n) {
    if (n & 1)
      r *= a;
    chmod(r, m);
    a *= a;
    chmod(a, m);
    n >>= 1;
  }
  return r;
}

inline ll inv(const ll n, const ll m = MOD) {
  ll a = n, b = m, x = 1, y = 0;
  while (b) {
    ll t = a / b;
    a -= t * b;
    swap(a, b);
    x -= t * y;
    swap(x, y);
  }
  return modulo(x, m);
}

struct Factor {
  inline vector<ll> factors(ll N) {
    vector<ll> A;
    ll i = 2;
    while (i * i <= N) {
      if (N % i == 0) {
        A.push_back(i);
        N /= i;
      } else {
        i++;
      }
    }
    if (N != 1)
      A.push_back(N);
    sort(all(A));
    return A;
  }
  inline vector<ll> divisor(ll N) {
    vector<ll> A;
    inc(i, 1, sqrt(N)) {
      if (N % i == 0) {
        A.push_back(i);
        if (i * i != N)
          A.push_back(N / i);
      }
    }
    sort(all(A));
    return A;
  }
};

struct csum {
  ll N;
  vector<ll> A, S;
  csum(vector<ll> v) : A(v), S(1) { each(k, v) S.push_back(k + S.back()); }
  ll sum(ll l, ll r) { return S[r] - S[l]; }
  ll lsum(ll r) { return S[r]; }
  ll rsum(ll l) { return S.back() - S[l]; }
};

template <ull mod = MOD> struct mi {
  inline constexpr ll modulo(const ll n, const ll m) const noexcept {
    ll k = n % m;
    return k + m * (k < 0);
  }

  ll num;
  inline constexpr mi() noexcept : num() { num = 0; }
  inline constexpr mi(const int n) noexcept : num() { num = modulo(n, mod); }
  inline constexpr mi(const ll n) noexcept : num() { num = modulo(n, mod); }

  inline constexpr mi<mod> inv() const noexcept {
    ll a = num, b = mod, x = 1, y = 0;
    while (b) {
      ll t = a / b;
      a -= t * b;
      swap(a, b);
      x -= t * y;
      swap(x, y);
    }
    return mi<mod>(x);
  }
  inline constexpr mi<mod> inv(ll n) const noexcept {
    ll a = n, b = mod, x = 1, y = 0;
    while (b) {
      ll t = a / b;
      a -= t * b;
      swap(a, b);
      x -= t * y;
      swap(x, y);
    }
    return mi<mod>(x);
  }
  inline constexpr mi<mod> inv(const mi<mod> m) const noexcept {
    return inv(m.num);
  }

  inline constexpr mi<mod> operator+() const noexcept { return mi(num); }
  inline constexpr mi<mod> operator+(const int n) const noexcept {
    return mi<mod>(num + n);
  }
  inline constexpr mi<mod> operator+(const ll n) const noexcept {
    return mi<mod>(num + n);
  }
  inline constexpr mi<mod> operator+(const mi<mod> m) const noexcept {
    return mi<mod>(num + m.num);
  }
  inline constexpr mi<mod> operator-() const noexcept { return -num; }
  inline constexpr mi<mod> operator-(const int n) const noexcept {
    return mi<mod>(num - n);
  }
  inline constexpr mi<mod> operator-(const ll n) const noexcept {
    return mi<mod>(num - n);
  }
  inline constexpr mi<mod> operator-(const mi<mod> m) const noexcept {
    return mi<mod>(num - m.num);
  }
  inline constexpr mi<mod> operator*(const int n) const noexcept {
    return mi<mod>(num * n);
  }
  inline constexpr mi<mod> operator*(const ll n) const noexcept {
    return mi<mod>(num * n);
  }
  inline constexpr mi<mod> operator*(const mi<mod> m) const noexcept {
    return mi<mod>(num * m);
  }
  inline constexpr mi<mod> operator/(const int n) const noexcept {
    return mi<mod>(num * (ll)inv(n));
  }
  inline constexpr mi<mod> operator/(const ll n) const noexcept {
    return mi<mod>(num * (ll)inv(n));
  }
  inline constexpr mi<mod> operator/(const mi<mod> m) const noexcept {
    return mi<mod>(num * (ll)inv(m));
  }
  inline constexpr mi<mod> &operator=(const int n) noexcept {
    num = modulo(n, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator=(const ll n) noexcept {
    num = modulo(n, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator=(const mi<mod> m) noexcept {
    num = m.num;
    return *this;
  }
  inline constexpr mi<mod> &operator+=(const int n) noexcept {
    num = modulo(num + n, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator+=(const ll n) noexcept {
    num = modulo(num + n, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator+=(const mi<mod> m) noexcept {
    num = modulo(num + m.num, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator++() noexcept {
    num = modulo(num + 1, mod);
    return *this;
  }
  inline constexpr mi<mod> operator++(int) noexcept {
    mi &pre = *this;
    num = modulo(num + 1, mod);
    return pre;
  }
  inline constexpr mi<mod> &operator-=(const int n) noexcept {
    num = modulo(num - n, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator-=(const ll n) noexcept {
    num = modulo(num - n, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator-=(const mi<mod> m) noexcept {
    num = modulo(num - m.num, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator--() noexcept {
    num = modulo(num - 1, mod);
    return *this;
  }
  inline constexpr mi<mod> operator--(int) noexcept {
    mi &pre = *this;
    num = modulo(num - 1, mod);
    return pre;
  }
  inline constexpr mi<mod> &operator*=(const int n) noexcept {
    num = modulo(num * n, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator*=(const ll n) noexcept {
    num = modulo(num * n, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator*=(const mi<mod> m) noexcept {
    num = modulo(num * m.num, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator/=(const int n) noexcept {
    num = modulo(num * (ll)inv(n), mod);
    return *this;
  }
  inline constexpr mi<mod> &operator/=(const ll n) noexcept {
    num = modulo(num * (ll)inv(n), mod);
    return *this;
  }
  inline constexpr mi<mod> &operator/=(const mi<mod> m) noexcept {
    num = modulo(num * (ll)inv(m), mod);
    return *this;
  }
  inline constexpr mi<mod> operator==(const int n) const noexcept {
    return num == modulo(n, mod);
  }
  inline constexpr mi<mod> operator==(const ll n) const noexcept {
    return num == modulo(n, mod);
  }
  inline constexpr mi<mod> operator==(const mi<mod> m) const noexcept {
    return num == m.num;
  }
  inline constexpr mi<mod> operator!=(const int n) const noexcept {
    return num != modulo(n, mod);
  }
  inline constexpr mi<mod> operator!=(const ll n) const noexcept {
    return num != modulo(n, mod);
  }
  inline constexpr mi<mod> operator!=(const mi<mod> m) const noexcept {
    return num != m.num;
  }
  constexpr operator int() const noexcept { return num; }
  constexpr operator ll() const noexcept { return num; }
  friend std::istream &operator>>(std::istream &, const mi<> &);
  friend std::ostream &operator<<(std::ostream &, const mi<> &);
};

template <ull mod = MOD>
inline constexpr mi<mod> operator+(const int n, const mi<mod> m) noexcept {
  return mi<mod>(n + m.num);
}
template <ull mod = MOD>
inline constexpr mi<mod> operator+(const ll n, const mi<mod> m) noexcept {
  return mi<mod>(n + m.num);
}
template <ull mod = MOD>
inline constexpr mi<mod> operator-(const int n, const mi<mod> m) noexcept {
  return mi<mod>(n - m.num);
}
template <ull mod = MOD>
inline constexpr mi<mod> operator-(const ll n, const mi<mod> m) noexcept {
  return mi<mod>(n - m.num);
}
template <ull mod = MOD>
inline constexpr mi<mod> operator*(const int n, const mi<mod> m) noexcept {
  return mi<mod>(n * m.num);
}
template <ull mod = MOD>
inline constexpr mi<mod> operator*(const ll n, const mi<mod> m) noexcept {
  return mi<mod>(n * m.num);
}
template <ull mod = MOD>
inline constexpr mi<mod> operator/(const int n, const mi<mod> m) noexcept {
  return mi<mod>(n * (ll)m.inv());
}
template <ull mod = MOD>
inline constexpr mi<mod> operator/(const ll n, const mi<mod> m) noexcept {
  return mi<mod>(n * (ll)m.inv());
}
inline constexpr mi<MOD> operator""_m(ull n) { return mi<MOD>((ll)n); }

template <ull mod = MOD>
inline constexpr mi<mod> pow(mi<mod> m, ll n) noexcept {
  mi<mod> r = mi<mod>(1);
  while (n) {
    if (n & 1)
      r *= m;
    m *= m;
    n >>= 1;
  }
  return r;
}
template <ull mod> istream &operator>>(istream &is, mi<mod> &m) {
  is >> m.num;
  return is;
}
template <ull mod> ostream &operator<<(ostream &is, mi<mod> &m) {
  is << (ll)m;
  return is;
}

template <ull mod = MOD> struct modmath {
  ll max;
  vector<mi<mod>> fac, inv;
  modmath() : max(1 << 20), fac(max + 1), inv(max + 1) {
    fac[0] = mi<mod>(1);
    rep(i, max) fac[i + 1] = fac[i] * (i + 1);
    inv[max] = fac[max].inv();
    dec(i, max - 1, 0) inv[i] = inv[i + 1] * (i + 1);
  }
  modmath(ll n) : max(n), fac(n + 1), inv(n + 1) {
    fac[0] = 1;
    rep(i, n) fac[i + 1] = fac[i] * (i + 1);
    inv[n] = 1 / fac[n];
    dec(i, n - 1, 0) inv[i] = inv[i + 1] * (i + 1);
  }

  inline mi<mod> fact(ll n) {
    if (n < 0)
      return mi<mod>(0);
    return fac[n];
  }
  inline mi<mod> perm(ll n, ll r) {
    if (r < 0 || n < r)
      return mi<mod>(0);
    return fac[n] * inv[n - r];
  }
  inline mi<mod> comb(ll n, ll r) {
    if (r < 0 || n < r)
      return mi<mod>(0);
    return fac[n] * inv[r] * inv[n - r];
  }
  inline mi<mod> nHr(ll n, ll r) { return comb(n + r - 1, n - 1); }
};

struct UFR {
  vector<ll> data;
  UFR(ll N) : data(N) { rep(i, N) data[i] = -1; }
  def root(ll x) {
    if (data[x] < 0)
      return x;
    else
      return data[x] = root(data[x]);
  }
  def unite(ll x, ll y) {
    ll root_x = root(x), root_y = root(y);
    if (root_x != root_y) {
      if (data[root_x] > data[root_y])
        swap(root_x, root_y);
      data[root_x] -= data[root_x] == data[root_y];
      data[root_y] = root_x;
      return true;
    }
    return false;
  }
  def same(ll x, ll y) { return root(x) == root(y); }
};

struct position {
  ll x, y;
  position() {}
  position(ll a, ll b) : x(a), y(b) {}
  position next(ll i) { return {x + dx[i], y + dy[i]}; }
  ll mdist() { return abs(x) + abs(y); }
  double dist() { return sqrt(x * x + y * y); }
  double norm(ll d) {
    if (d == inf)
      return max(x, y);
    if (d == 1)
      return mdist();
    if (d == 2)
      return dist();
    return 0;
  }
  ll num(ll width) { return abs(x) * width + abs(y); }

  bool operator==(position a) { return x == a.x && y == a.y; }
  bool operator!=(position a) { return x != a.x || y != a.y; }
  bool operator<(position a) { return x < a.x && y < a.y; }
  bool operator>(position a) { return x > a.x && y > a.y; }
  bool operator<=(position a) { return x <= a.x && y <= a.y; }
  bool operator>=(position a) { return x >= a.x && y >= a.y; }
  position operator+(position a) { return position(x + a.x, y + a.y); }
  position operator-(position a) { return position(x - a.x, y - a.y); }
  position operator*(position a) { return position(x * a.x, y * a.y); }
  position operator/(position a) { return position(x / a.x, y / a.y); }
  position operator%(position a) { return position(x % a.x, y % a.y); }
  position complex(position a) {
    return position(x * a.x - y * a.y, x * a.y + y * a.x);
  }
  /*
      // for sort:
      bool operator<(position a) { return x ^ a.x ? x < a.x : y < a.y; }
      bool operator>(position a) { return x ^ a.x ? x > a.x : y > a.y; }
      bool operator<=(position a) { return x ^ a.x ? x < a.x : y <= a.y; }
      bool operator>=(position a) { return x ^ a.x ? x > a.x : y >= a.y; }
  */
};
position Origin = position(0, 0);
using pos = position;
using vec = position;

template <class T> struct Array {
  struct node {
    ll childl, childr;
    T data;
    node(ll l, ll r, T t) : childl(l), childr(r), data(t) {}
  };
  ll n, depth;
  vector<ll> versions;
  vector<ll> prev_versions;
  vector<node> nodes;
  Array(ll n = 1 << 20, T val = T()) : n(n), depth(0) {
    while (n /= 2)
      depth++;
    init(val);
  }
  void init(T val) {
    versions.push_back(0);
    prev_versions.push_back(0);
    rep(i, 2 * n - 1) {
      if (i < n - 1) {
        nodes.push_back(node(2 * i + 1, 2 * i + 2, T()));
      } else {
        nodes.push_back(node(0, 0, val));
      }
    }
  }
  void set(ll index, ll val, ll version = -1) {
    ll id, par = nodes.size(), left = 0, right = n;
    if (version == -1) {
      id = versions.back();
      version = versions.size() - 1;
    } else {
      id = versions[version];
    }
    versions.push_back(par);
    prev_versions.push_back(version);
    if (right == -1)
      right = n;
    rep(i, depth) {
      ll mid = (left + right) / 2;
      if (index < mid) {
        nodes.push_back(node(par + i + 1, nodes[id].childr, T()));
        id = nodes[id].childl;
        right = mid;
      } else {
        nodes.push_back(node(nodes[id].childl, par + i + 1, T()));
        id = nodes[id].childr;
        left = mid;
      }
    }
    nodes.push_back(node(0, 0, val));
  }
  T get(ll index, ll version = -1) {
    ll id, left = 0, right = n;
    if (version == -1) {
      id = versions.back();
    } else {
      id = versions[version];
    }
    rep(i, depth) {
      ll mid = (left + right) / 2;
      if (index < mid) {
        id = nodes[id].childl;
        right = mid;
      } else {
        id = nodes[id].childr;
        left = mid;
      }
    }
    return nodes[id].data;
  }
  ll latest() { return versions.size() - 1; }
};

struct BipartiteGraph {
  ll V;
  vector<vector<ll>> G;
  vector<ll> match;
  vector<bool> used;
  BipartiteGraph(ll N) : V(N), G(N), match(N), used(N) {}
  void addEdge(ll i, ll j) {
    G[i].push_back(j);
    G[j].push_back(i);
  }
  bool dfs(ll now) {
    used[now] = true;
    rep(i, G[now].size()) {
      ll next = G[now][i], w = match[next];
      if (w == -1 || (!used[w] && dfs(w))) {
        match[now] = next, match[next] = now;
        return true;
      }
    }
    return false;
  }
  ll matching() {
    ll res = 0;
    fill(all(match), -1);
    rep(i, V) {
      if (match[i] == -1) {
        fill(all(used), false);
        if (dfs(i))
          res++;
      }
    }
    return res;
  }
};

template <typename T = ll> struct Dijkstra {
  ll V;
  using P = pair<ll, ll>;
  vector<vector<P>> G;
  vector<T> dist;
  vector<bool> used;
  Dijkstra(ll v) : V(v), G(v), dist(v), used(v) {}
  void setDist(ll a, ll b, ll d) { G[a].push_back(P(d, b)); }
  void culc(ll s = 0) {
    priority_queue<P, vector<P>, greater<P>> Q;
    Q.push(P(0, s));
    fill_n(dist.begin(), V, INF);
    fill_n(used.begin(), V, false);
    while (!Q.empty()) {
      T d;
      ll t;
      tie(d, t) = Q.top(), Q.pop();
      if (used[t])
        continue;
      used[t] = true, dist[t] = d;
      for (P e : G[t]) {
        if (dist[e.second] <= d + e.first)
          continue;
        Q.push(P(d + e.first, e.second));
      }
    }
  }
};

ll N, A[21][21], DP[22][1 << 21];
signed main() {
  cin >> N;
  rep(i, N) rep(j, N) cin >> A[i][j];
  rep(i, N + 1) rep(j, 1 << N) DP[i][j] = 0;
  DP[0][0] = 1;
  rep(i, N) {
    rep(j, 1 << N) {
      rep(k, N) {
        if (!(j & (1 << k)) && A[i][k]) {
          DP[i + 1][j | (1 << k)] += DP[i][j];
          DP[i + 1][j | (1 << k)] %= MOD;
        }
      }
    }
  }
  cout << DP[N][(1 << N) - 1] << endl;
}


Fixed submission:
#include <bits/stdc++.h>
using namespace std;

// Define
using ll = long long;
using ull = unsigned long long;
using ld = long double;
const ll dx[4] = {1, 0, -1, 0};
const ll dy[4] = {0, 1, 0, -1};
const ll MOD = 1e9 + 7;
const ll mod = 998244353;
const ll inf = 1 << 30;
const ll LINF = LONG_MAX;
const ll INF = 1LL << 60;
const ull MAX = ULONG_MAX;
#define mp make_pair
#define pb push_back
#define elif else if
#define endl '\n'
#define space ' '
#define def inline auto
#define func inline constexpr ll
#define run(a) __attribute__((constructor)) def _##a()
#define all(v) begin(v), end(v)
#define rall(v) rbegin(v), rend(v)
#define input(a) scanf("%lld", &(a))
#define print(a) printf("%lld\n", (a))
#define fi first
#define se second
#define ok(a, b) (0 <= (a) && (a) < (b))
template <class T> using vvector = vector<vector<T>>;
template <class T> using pvector = vector<pair<T, T>>;
template <class T>
using rpriority_queue = priority_queue<T, vector<T>, greater<T>>;

template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}

// Debug
#define debug(...)                                                             \
  {                                                                            \
    cerr << __LINE__ << ": " << #__VA_ARGS__ << " = ";                         \
    for (auto &&X : {__VA_ARGS__})                                             \
      cerr << "[" << X << "] ";                                                \
    cerr << endl;                                                              \
  }

#define dump(a, h, w)                                                          \
  {                                                                            \
    cerr << __LINE__ << ": " << #a << " = [" << endl;                          \
    rep(__i, h) {                                                              \
      rep(__j, w) { cerr << a[__i][__j] << space; }                            \
      cerr << endl;                                                            \
    }                                                                          \
    cerr << "]" << endl;                                                       \
  }

#define vdump(a, n)                                                            \
  {                                                                            \
    cerr << __LINE__ << ": " << #a << " = [";                                  \
    rep(__i, n) if (__i) cerr << space << a[__i];                              \
    else cerr << a[__i];                                                       \
    cerr << "]" << endl;                                                       \
  }

// Loop
#define inc(i, a, n) for (ll i = (a), _##i = (n); i <= _##i; ++i)
#define dec(i, a, n) for (ll i = (a), _##i = (n); i >= _##i; --i)
#define rep(i, n) for (ll i = 0, _##i = (n); i < _##i; ++i)
#define each(i, a) for (auto &&i : a)
#define loop() for (;;)

// Stream
#define fout(n) cout << fixed << setprecision(n)
#define fasten cin.tie(0), ios::sync_with_stdio(0)
run(0) { fasten, fout(10); }

// Speed
#pragma GCC optimize("O3")
#pragma GCC target("avx")

// Math
func gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
func lcm(ll a, ll b) { return a / gcd(a, b) * b; }
func sign(ll a) { return a ? abs(a) / a : 0; }

inline constexpr ll modulo(const ll n, const ll m = MOD) {
  ll k = n % m;
  return k + m * (k < 0);
}

inline constexpr ll chmod(ll &n, const ll m = MOD) {
  n %= m;
  return n += m * (n < 0);
}

inline constexpr ll mpow(ll a, ll n, const ll m = MOD) {
  ll r = 1;
  while (n) {
    if (n & 1)
      r *= a;
    chmod(r, m);
    a *= a;
    chmod(a, m);
    n >>= 1;
  }
  return r;
}

inline ll inv(const ll n, const ll m = MOD) {
  ll a = n, b = m, x = 1, y = 0;
  while (b) {
    ll t = a / b;
    a -= t * b;
    swap(a, b);
    x -= t * y;
    swap(x, y);
  }
  return modulo(x, m);
}

struct Factor {
  inline vector<ll> factors(ll N) {
    vector<ll> A;
    ll i = 2;
    while (i * i <= N) {
      if (N % i == 0) {
        A.push_back(i);
        N /= i;
      } else {
        i++;
      }
    }
    if (N != 1)
      A.push_back(N);
    sort(all(A));
    return A;
  }
  inline vector<ll> divisor(ll N) {
    vector<ll> A;
    inc(i, 1, sqrt(N)) {
      if (N % i == 0) {
        A.push_back(i);
        if (i * i != N)
          A.push_back(N / i);
      }
    }
    sort(all(A));
    return A;
  }
};

struct csum {
  ll N;
  vector<ll> A, S;
  csum(vector<ll> v) : A(v), S(1) { each(k, v) S.push_back(k + S.back()); }
  ll sum(ll l, ll r) { return S[r] - S[l]; }
  ll lsum(ll r) { return S[r]; }
  ll rsum(ll l) { return S.back() - S[l]; }
};

template <ull mod = MOD> struct mi {
  inline constexpr ll modulo(const ll n, const ll m) const noexcept {
    ll k = n % m;
    return k + m * (k < 0);
  }

  ll num;
  inline constexpr mi() noexcept : num() { num = 0; }
  inline constexpr mi(const int n) noexcept : num() { num = modulo(n, mod); }
  inline constexpr mi(const ll n) noexcept : num() { num = modulo(n, mod); }

  inline constexpr mi<mod> inv() const noexcept {
    ll a = num, b = mod, x = 1, y = 0;
    while (b) {
      ll t = a / b;
      a -= t * b;
      swap(a, b);
      x -= t * y;
      swap(x, y);
    }
    return mi<mod>(x);
  }
  inline constexpr mi<mod> inv(ll n) const noexcept {
    ll a = n, b = mod, x = 1, y = 0;
    while (b) {
      ll t = a / b;
      a -= t * b;
      swap(a, b);
      x -= t * y;
      swap(x, y);
    }
    return mi<mod>(x);
  }
  inline constexpr mi<mod> inv(const mi<mod> m) const noexcept {
    return inv(m.num);
  }

  inline constexpr mi<mod> operator+() const noexcept { return mi(num); }
  inline constexpr mi<mod> operator+(const int n) const noexcept {
    return mi<mod>(num + n);
  }
  inline constexpr mi<mod> operator+(const ll n) const noexcept {
    return mi<mod>(num + n);
  }
  inline constexpr mi<mod> operator+(const mi<mod> m) const noexcept {
    return mi<mod>(num + m.num);
  }
  inline constexpr mi<mod> operator-() const noexcept { return -num; }
  inline constexpr mi<mod> operator-(const int n) const noexcept {
    return mi<mod>(num - n);
  }
  inline constexpr mi<mod> operator-(const ll n) const noexcept {
    return mi<mod>(num - n);
  }
  inline constexpr mi<mod> operator-(const mi<mod> m) const noexcept {
    return mi<mod>(num - m.num);
  }
  inline constexpr mi<mod> operator*(const int n) const noexcept {
    return mi<mod>(num * n);
  }
  inline constexpr mi<mod> operator*(const ll n) const noexcept {
    return mi<mod>(num * n);
  }
  inline constexpr mi<mod> operator*(const mi<mod> m) const noexcept {
    return mi<mod>(num * m);
  }
  inline constexpr mi<mod> operator/(const int n) const noexcept {
    return mi<mod>(num * (ll)inv(n));
  }
  inline constexpr mi<mod> operator/(const ll n) const noexcept {
    return mi<mod>(num * (ll)inv(n));
  }
  inline constexpr mi<mod> operator/(const mi<mod> m) const noexcept {
    return mi<mod>(num * (ll)inv(m));
  }
  inline constexpr mi<mod> &operator=(const int n) noexcept {
    num = modulo(n, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator=(const ll n) noexcept {
    num = modulo(n, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator=(const mi<mod> m) noexcept {
    num = m.num;
    return *this;
  }
  inline constexpr mi<mod> &operator+=(const int n) noexcept {
    num = modulo(num + n, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator+=(const ll n) noexcept {
    num = modulo(num + n, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator+=(const mi<mod> m) noexcept {
    num = modulo(num + m.num, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator++() noexcept {
    num = modulo(num + 1, mod);
    return *this;
  }
  inline constexpr mi<mod> operator++(int) noexcept {
    mi &pre = *this;
    num = modulo(num + 1, mod);
    return pre;
  }
  inline constexpr mi<mod> &operator-=(const int n) noexcept {
    num = modulo(num - n, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator-=(const ll n) noexcept {
    num = modulo(num - n, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator-=(const mi<mod> m) noexcept {
    num = modulo(num - m.num, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator--() noexcept {
    num = modulo(num - 1, mod);
    return *this;
  }
  inline constexpr mi<mod> operator--(int) noexcept {
    mi &pre = *this;
    num = modulo(num - 1, mod);
    return pre;
  }
  inline constexpr mi<mod> &operator*=(const int n) noexcept {
    num = modulo(num * n, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator*=(const ll n) noexcept {
    num = modulo(num * n, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator*=(const mi<mod> m) noexcept {
    num = modulo(num * m.num, mod);
    return *this;
  }
  inline constexpr mi<mod> &operator/=(const int n) noexcept {
    num = modulo(num * (ll)inv(n), mod);
    return *this;
  }
  inline constexpr mi<mod> &operator/=(const ll n) noexcept {
    num = modulo(num * (ll)inv(n), mod);
    return *this;
  }
  inline constexpr mi<mod> &operator/=(const mi<mod> m) noexcept {
    num = modulo(num * (ll)inv(m), mod);
    return *this;
  }
  inline constexpr mi<mod> operator==(const int n) const noexcept {
    return num == modulo(n, mod);
  }
  inline constexpr mi<mod> operator==(const ll n) const noexcept {
    return num == modulo(n, mod);
  }
  inline constexpr mi<mod> operator==(const mi<mod> m) const noexcept {
    return num == m.num;
  }
  inline constexpr mi<mod> operator!=(const int n) const noexcept {
    return num != modulo(n, mod);
  }
  inline constexpr mi<mod> operator!=(const ll n) const noexcept {
    return num != modulo(n, mod);
  }
  inline constexpr mi<mod> operator!=(const mi<mod> m) const noexcept {
    return num != m.num;
  }
  constexpr operator int() const noexcept { return num; }
  constexpr operator ll() const noexcept { return num; }
  friend std::istream &operator>>(std::istream &, const mi<> &);
  friend std::ostream &operator<<(std::ostream &, const mi<> &);
};

template <ull mod = MOD>
inline constexpr mi<mod> operator+(const int n, const mi<mod> m) noexcept {
  return mi<mod>(n + m.num);
}
template <ull mod = MOD>
inline constexpr mi<mod> operator+(const ll n, const mi<mod> m) noexcept {
  return mi<mod>(n + m.num);
}
template <ull mod = MOD>
inline constexpr mi<mod> operator-(const int n, const mi<mod> m) noexcept {
  return mi<mod>(n - m.num);
}
template <ull mod = MOD>
inline constexpr mi<mod> operator-(const ll n, const mi<mod> m) noexcept {
  return mi<mod>(n - m.num);
}
template <ull mod = MOD>
inline constexpr mi<mod> operator*(const int n, const mi<mod> m) noexcept {
  return mi<mod>(n * m.num);
}
template <ull mod = MOD>
inline constexpr mi<mod> operator*(const ll n, const mi<mod> m) noexcept {
  return mi<mod>(n * m.num);
}
template <ull mod = MOD>
inline constexpr mi<mod> operator/(const int n, const mi<mod> m) noexcept {
  return mi<mod>(n * (ll)m.inv());
}
template <ull mod = MOD>
inline constexpr mi<mod> operator/(const ll n, const mi<mod> m) noexcept {
  return mi<mod>(n * (ll)m.inv());
}
inline constexpr mi<MOD> operator""_m(ull n) { return mi<MOD>((ll)n); }

template <ull mod = MOD>
inline constexpr mi<mod> pow(mi<mod> m, ll n) noexcept {
  mi<mod> r = mi<mod>(1);
  while (n) {
    if (n & 1)
      r *= m;
    m *= m;
    n >>= 1;
  }
  return r;
}
template <ull mod> istream &operator>>(istream &is, mi<mod> &m) {
  is >> m.num;
  return is;
}
template <ull mod> ostream &operator<<(ostream &is, mi<mod> &m) {
  is << (ll)m;
  return is;
}

template <ull mod = MOD> struct modmath {
  ll max;
  vector<mi<mod>> fac, inv;
  modmath() : max(1 << 20), fac(max + 1), inv(max + 1) {
    fac[0] = mi<mod>(1);
    rep(i, max) fac[i + 1] = fac[i] * (i + 1);
    inv[max] = fac[max].inv();
    dec(i, max - 1, 0) inv[i] = inv[i + 1] * (i + 1);
  }
  modmath(ll n) : max(n), fac(n + 1), inv(n + 1) {
    fac[0] = 1;
    rep(i, n) fac[i + 1] = fac[i] * (i + 1);
    inv[n] = 1 / fac[n];
    dec(i, n - 1, 0) inv[i] = inv[i + 1] * (i + 1);
  }

  inline mi<mod> fact(ll n) {
    if (n < 0)
      return mi<mod>(0);
    return fac[n];
  }
  inline mi<mod> perm(ll n, ll r) {
    if (r < 0 || n < r)
      return mi<mod>(0);
    return fac[n] * inv[n - r];
  }
  inline mi<mod> comb(ll n, ll r) {
    if (r < 0 || n < r)
      return mi<mod>(0);
    return fac[n] * inv[r] * inv[n - r];
  }
  inline mi<mod> nHr(ll n, ll r) { return comb(n + r - 1, n - 1); }
};

struct UFR {
  vector<ll> data;
  UFR(ll N) : data(N) { rep(i, N) data[i] = -1; }
  def root(ll x) {
    if (data[x] < 0)
      return x;
    else
      return data[x] = root(data[x]);
  }
  def unite(ll x, ll y) {
    ll root_x = root(x), root_y = root(y);
    if (root_x != root_y) {
      if (data[root_x] > data[root_y])
        swap(root_x, root_y);
      data[root_x] -= data[root_x] == data[root_y];
      data[root_y] = root_x;
      return true;
    }
    return false;
  }
  def same(ll x, ll y) { return root(x) == root(y); }
};

struct position {
  ll x, y;
  position() {}
  position(ll a, ll b) : x(a), y(b) {}
  position next(ll i) { return {x + dx[i], y + dy[i]}; }
  ll mdist() { return abs(x) + abs(y); }
  double dist() { return sqrt(x * x + y * y); }
  double norm(ll d) {
    if (d == inf)
      return max(x, y);
    if (d == 1)
      return mdist();
    if (d == 2)
      return dist();
    return 0;
  }
  ll num(ll width) { return abs(x) * width + abs(y); }

  bool operator==(position a) { return x == a.x && y == a.y; }
  bool operator!=(position a) { return x != a.x || y != a.y; }
  bool operator<(position a) { return x < a.x && y < a.y; }
  bool operator>(position a) { return x > a.x && y > a.y; }
  bool operator<=(position a) { return x <= a.x && y <= a.y; }
  bool operator>=(position a) { return x >= a.x && y >= a.y; }
  position operator+(position a) { return position(x + a.x, y + a.y); }
  position operator-(position a) { return position(x - a.x, y - a.y); }
  position operator*(position a) { return position(x * a.x, y * a.y); }
  position operator/(position a) { return position(x / a.x, y / a.y); }
  position operator%(position a) { return position(x % a.x, y % a.y); }
  position complex(position a) {
    return position(x * a.x - y * a.y, x * a.y + y * a.x);
  }
  /*
      // for sort:
      bool operator<(position a) { return x ^ a.x ? x < a.x : y < a.y; }
      bool operator>(position a) { return x ^ a.x ? x > a.x : y > a.y; }
      bool operator<=(position a) { return x ^ a.x ? x < a.x : y <= a.y; }
      bool operator>=(position a) { return x ^ a.x ? x > a.x : y >= a.y; }
  */
};
position Origin = position(0, 0);
using pos = position;
using vec = position;

template <class T> struct Array {
  struct node {
    ll childl, childr;
    T data;
    node(ll l, ll r, T t) : childl(l), childr(r), data(t) {}
  };
  ll n, depth;
  vector<ll> versions;
  vector<ll> prev_versions;
  vector<node> nodes;
  Array(ll n = 1 << 20, T val = T()) : n(n), depth(0) {
    while (n /= 2)
      depth++;
    init(val);
  }
  void init(T val) {
    versions.push_back(0);
    prev_versions.push_back(0);
    rep(i, 2 * n - 1) {
      if (i < n - 1) {
        nodes.push_back(node(2 * i + 1, 2 * i + 2, T()));
      } else {
        nodes.push_back(node(0, 0, val));
      }
    }
  }
  void set(ll index, ll val, ll version = -1) {
    ll id, par = nodes.size(), left = 0, right = n;
    if (version == -1) {
      id = versions.back();
      version = versions.size() - 1;
    } else {
      id = versions[version];
    }
    versions.push_back(par);
    prev_versions.push_back(version);
    if (right == -1)
      right = n;
    rep(i, depth) {
      ll mid = (left + right) / 2;
      if (index < mid) {
        nodes.push_back(node(par + i + 1, nodes[id].childr, T()));
        id = nodes[id].childl;
        right = mid;
      } else {
        nodes.push_back(node(nodes[id].childl, par + i + 1, T()));
        id = nodes[id].childr;
        left = mid;
      }
    }
    nodes.push_back(node(0, 0, val));
  }
  T get(ll index, ll version = -1) {
    ll id, left = 0, right = n;
    if (version == -1) {
      id = versions.back();
    } else {
      id = versions[version];
    }
    rep(i, depth) {
      ll mid = (left + right) / 2;
      if (index < mid) {
        id = nodes[id].childl;
        right = mid;
      } else {
        id = nodes[id].childr;
        left = mid;
      }
    }
    return nodes[id].data;
  }
  ll latest() { return versions.size() - 1; }
};

struct BipartiteGraph {
  ll V;
  vector<vector<ll>> G;
  vector<ll> match;
  vector<bool> used;
  BipartiteGraph(ll N) : V(N), G(N), match(N), used(N) {}
  void addEdge(ll i, ll j) {
    G[i].push_back(j);
    G[j].push_back(i);
  }
  bool dfs(ll now) {
    used[now] = true;
    rep(i, G[now].size()) {
      ll next = G[now][i], w = match[next];
      if (w == -1 || (!used[w] && dfs(w))) {
        match[now] = next, match[next] = now;
        return true;
      }
    }
    return false;
  }
  ll matching() {
    ll res = 0;
    fill(all(match), -1);
    rep(i, V) {
      if (match[i] == -1) {
        fill(all(used), false);
        if (dfs(i))
          res++;
      }
    }
    return res;
  }
};

template <typename T = ll> struct Dijkstra {
  ll V;
  using P = pair<ll, ll>;
  vector<vector<P>> G;
  vector<T> dist;
  vector<bool> used;
  Dijkstra(ll v) : V(v), G(v), dist(v), used(v) {}
  void setDist(ll a, ll b, ll d) { G[a].push_back(P(d, b)); }
  void culc(ll s = 0) {
    priority_queue<P, vector<P>, greater<P>> Q;
    Q.push(P(0, s));
    fill_n(dist.begin(), V, INF);
    fill_n(used.begin(), V, false);
    while (!Q.empty()) {
      T d;
      ll t;
      tie(d, t) = Q.top(), Q.pop();
      if (used[t])
        continue;
      used[t] = true, dist[t] = d;
      for (P e : G[t]) {
        if (dist[e.second] <= d + e.first)
          continue;
        Q.push(P(d + e.first, e.second));
      }
    }
  }
};

ll N, A[21][21], DP[22][1 << 21];
signed main() {
  cin >> N;
  rep(i, N) rep(j, N) cin >> A[i][j];
  rep(i, N + 1) rep(j, 1 << N) DP[i][j] = 0;
  DP[0][0] = 1;
  rep(i, N) {
    rep(j, 1 << N) {
      if (__builtin_popcount(unsigned(j)) != i)
        continue;
      rep(k, N) {
        if (!(j & (1 << k)) && A[i][k]) {
          DP[i + 1][j | (1 << k)] += DP[i][j];
          DP[i + 1][j | (1 << k)] %= MOD;
        }
      }
    }
  }
  cout << DP[N][(1 << N) - 1] << endl;
}