Problem p03174 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <climits>
#include <cmath>
#include <complex>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>

using namespace std;
#define rrep(i, m, n) for (int(i) = (int)(m); (i) >= (int)(n); (i)--)
#define rep(i, m, n) for (int(i) = (int)(m); i < (int)(n); i++)
#define REP(i, n) rep(i, 0, n)
#define FOR(i, c)                                                              \
  for (decltype((c).begin()) i = (c).begin(); i != (c).end(); ++i)
#define ll long long
#define ull unsigned long long
#define all(hoge) (hoge).begin(), (hoge).end()
#define M_PI 3.1415926535897932L;
typedef pair<ll, ll> P;
constexpr ll MOD = 1000000007;
constexpr ll INF = 1LL << 60;
constexpr long double EPS = 1e-10;
typedef vector<ll> Array;
typedef vector<Array> Matrix;
string operator*(const string &s, int k) {
  if (k == 0)
    return "";
  string p = (s + s) * (k / 2);
  if (k % 2 == 1)
    p += s;
  return p;
}

template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

struct Edge { // グラフ
  ll to, cap, rev;
  Edge(ll _to, ll _cap, ll _rev) {
    to = _to;
    cap = _cap;
    rev = _rev;
  }
};
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
void add_edge(Graph &G, ll from, ll to, ll cap, bool revFlag,
              ll revCap) { // 最大フロー求める Ford-fulkerson
  G[from].push_back(Edge(to, cap, (ll)G[to].size()));
  if (revFlag)
    G[to].push_back(Edge(
        from, revCap, (ll)G[from].size() - 1)); // 最小カットの場合逆辺は0にする
}

ll max_flow_dfs(Graph &G, ll v, ll t, ll f, vector<bool> &used) {
  if (v == t)
    return f;
  used[v] = true;
  for (int i = 0; i < G[v].size(); ++i) {
    Edge &e = G[v][i];
    if (!used[e.to] && e.cap > 0) {
      ll d = max_flow_dfs(G, e.to, t, min(f, e.cap), used);
      if (d > 0) {
        e.cap -= d;
        G[e.to][e.rev].cap += d;
        return d;
      }
    }
  }
  return 0;
}
// 二分グラフの最大マッチングを求めたりも出来る　また二部グラフの最大独立集合は頂点数-最大マッチングのサイズ
ll max_flow(Graph &G, ll s, ll t) // O(V(V+E))
{
  ll flow = 0;
  for (;;) {
    vector<bool> used(G.size());
    REP(i, used.size()) used[i] = false;
    ll f = max_flow_dfs(G, s, t, INF, used);
    if (f == 0) {
      return flow;
    }
    flow += f;
  }
}
void BellmanFord(Graph &G, ll s, Array &d, Array &negative) { // O(|E||V|)
  d.resize(G.size());
  negative.resize(G.size());
  REP(i, d.size()) d[i] = INF;
  REP(i, d.size()) negative[i] = false;
  d[s] = 0;
  REP(k, G.size() - 1) {
    REP(i, G.size()) {
      REP(j, G[i].size()) {
        if (d[i] != INF && d[G[i][j].to] > d[i] + G[i][j].cap) {
          d[G[i][j].to] = d[i] + G[i][j].cap;
        }
      }
    }
  }
  REP(k, G.size() - 1) {
    REP(i, G.size()) {
      REP(j, G[i].size()) {
        if (d[i] != INF && d[G[i][j].to] > d[i] + G[i][j].cap) {
          d[G[i][j].to] = d[i] + G[i][j].cap;
          negative[G[i][j].to] = true;
        }
        if (negative[i] == true)
          negative[G[i][j].to] = true;
      }
    }
  }
}

void Dijkstra(Graph &G, ll s, Array &d) { // O(|E|log|V|)
  d.resize(G.size());
  REP(i, d.size()) d[i] = INF;
  d[s] = 0;
  priority_queue<P, vector<P>, greater<P>> q;
  q.push(make_pair(0, s));
  while (!q.empty()) {
    P a = q.top();
    q.pop();
    if (d[a.second] < a.first)
      continue;
    REP(i, G[a.second].size()) {
      Edge e = G[a.second][i];
      if (d[e.to] > d[a.second] + e.cap) {
        d[e.to] = d[a.second] + e.cap;
        q.push(make_pair(d[e.to], e.to));
      }
    }
  }
}
void WarshallFloyd(Graph &G, Matrix &d) { // O(V^3)
  d.resize(G.size());
  REP(i, d.size()) d[i].resize(G.size());
  REP(i, d.size()) {
    REP(j, d[i].size()) { d[i][j] = ((i != j) ? INF : 0); }
  }
  REP(i, G.size()) {
    REP(j, G[i].size()) { chmin(d[i][G[i][j].to], G[i][j].cap); }
  }
  REP(i, G.size()) {
    REP(j, G.size()) {
      REP(k, G.size()) { chmin(d[j][k], d[j][i] + d[i][k]); }
    }
  }
}
bool tsort(Graph &graph, vector<int> &order) { // トポロジカルソートO(E+V)
  int n = graph.size(), k = 0;
  Array in(n);
  for (auto &es : graph)
    for (auto &e : es)
      in[e.to]++;
  priority_queue<ll, Array, greater<ll>> que;
  REP(i, n)
  if (in[i] == 0)
    que.push(i);
  while (que.size()) {
    int v = que.top();
    que.pop();
    order.push_back(v);
    for (auto &e : graph[v])
      if (--in[e.to] == 0)
        que.push(e.to);
  }
  if (order.size() != n)
    return false;
  else
    return true;
}
class lca {
public:
  const int n = 0;
  const int log2_n = 0;
  std::vector<std::vector<int>> parent;
  std::vector<int> depth;

  lca() {}

  lca(const Graph &g, int root)
      : n(g.size()), log2_n(log2(n) + 1), parent(log2_n, std::vector<int>(n)),
        depth(n) {
    dfs(g, root, -1, 0);
    for (int k = 0; k + 1 < log2_n; k++) {
      for (int v = 0; v < (int)g.size(); v++) {
        if (parent[k][v] < 0)
          parent[k + 1][v] = -1;
        else
          parent[k + 1][v] = parent[k][parent[k][v]];
      }
    }
  }

  void dfs(const Graph &g, int v, int p, int d) {
    parent[0][v] = p;
    depth[v] = d;
    for (auto &e : g[v]) {
      if (e.to != p)
        dfs(g, e.to, v, d + 1);
    }
  }

  int get(int u, int v) {
    if (depth[u] > depth[v])
      std::swap(u, v);
    for (int k = 0; k < log2_n; k++) {
      if ((depth[v] - depth[u]) >> k & 1) {
        v = parent[k][v];
      }
    }
    if (u == v)
      return u;
    for (int k = log2_n - 1; k >= 0; k--) {
      if (parent[k][u] != parent[k][v]) {
        u = parent[k][u];
        v = parent[k][v];
      }
    }
    return parent[0][u];
  }
};
void visit(const Graph &g, int v, Matrix &scc, stack<ll> &S, Array &inS,
           Array &low, Array &num, int &time) {
  low[v] = num[v] = ++time;
  S.push(v);
  inS[v] = true;
  FOR(e, g[v]) {
    int w = e->to;
    if (num[w] == 0) {
      visit(g, w, scc, S, inS, low, num, time);
      low[v] = min(low[v], low[w]);
    } else if (inS[w])
      low[v] = min(low[v], num[w]);
  }
  if (low[v] == num[v]) {
    scc.push_back(Array());
    while (1) {
      int w = S.top();
      S.pop();
      inS[w] = false;
      scc.back().push_back(w);
      if (v == w)
        break;
    }
  }
}
void stronglyConnectedComponents(const Graph &g,
                                 Matrix &scc) { // 強連結成分分解 O(E+V)
  const int n = g.size();
  Array num(n), low(n);
  stack<ll> S;
  Array inS(n);
  int time = 0;
  REP(u, n) if (num[u] == 0) visit(g, u, scc, S, inS, low, num, time);
}

class UnionFind {
  vector<int> data;
  ll num;

public:
  UnionFind(int size) : data(size, -1), num(size) {}
  bool unite(int x, int y) { // xとyの集合を統合する
    x = root(x);
    y = root(y);
    if (x != y) {
      if (data[y] < data[x])
        swap(x, y);
      data[x] += data[y];
      data[y] = x;
    }
    num -= (x != y);
    return x != y;
  }
  bool findSet(int x, int y) { // xとyが同じ集合か返す
    return root(x) == root(y);
  }
  int root(int x) { // xのルートを返す
    return data[x] < 0 ? x : data[x] = root(data[x]);
  }
  ll size(int x) { // xの集合のサイズを返す
    return -data[root(x)];
  }
  ll numSet() { // 集合の数を返す
    return num;
  }
};
class SumSegTree {
private:
  ll _sum(ll a, ll b, ll k, ll l, ll r) {
    if (r <= a || b <= l)
      return 0; // 交差しない
    if (a <= l && r <= b)
      return dat[k]; // a,l,r,bの順で完全に含まれる
    else {
      ll s1 = _sum(a, b, 2 * k + 1, l, (l + r) / 2); // 左の子
      ll s2 = _sum(a, b, 2 * k + 2, (l + r) / 2, r); // 右の子
      return s1 + s2;
    }
  }

public:
  ll n, height;
  vector<ll> dat;

  // 初期化（_nは最大要素数）
  SumSegTree(ll _n) {
    n = 1;
    height = 1;
    while (n < _n) {
      n *= 2;
      height++;
    }
    dat = vector<ll>(2 * n - 1, 0);
  }

  // 場所i(0-indexed)にxを足す
  void add(ll i, ll x) {
    i += n - 1; // i番目の葉ノードへ
    dat[i] += x;
    while (i > 0) { // 下から上がっていく
      i = (i - 1) / 2;
      dat[i] += x;
    }
  }

  // 区間[a,b)の総和。ノードk=[l,r)に着目している。
  ll sum(ll a, ll b) { return _sum(a, b, 0, 0, n); }
};
class RmqTree {
private:
  ll _find(ll a, ll b, ll k, ll l, ll r) {
    if (r <= a || b <= l)
      return INF; // 交差しない
    if (a <= l && r <= b)
      return dat[k]; // a,l,r,bの順で完全に含まれる
    else {
      ll s1 = _find(a, b, 2 * k + 1, l, (l + r) / 2); // 左の子
      ll s2 = _find(a, b, 2 * k + 2, (l + r) / 2, r); // 右の子
      return min(s1, s2);
    }
  }

public:
  ll n, height;
  vector<ll> dat;

  // 初期化（_nは最大要素数）
  RmqTree(ll _n) {
    n = 1;
    height = 1;
    while (n < _n) {
      n *= 2;
      height++;
    }
    dat = vector<ll>(2 * n - 1, INF);
  }

  // 場所i(0-indexed)をxにする
  void update(ll i, ll x) {
    i += n - 1; // i番目の葉ノードへ
    dat[i] = x;
    while (i > 0) { // 下から上がっていく
      i = (i - 1) / 2;
      dat[i] = min(dat[i * 2 + 1], dat[i * 2 + 2]);
    }
  }

  // 区間[a,b)の最小値。ノードk=[l,r)に着目している。
  ll find(ll a, ll b) { return _find(a, b, 0, 0, n); }
};

// 約数求める //約数
void divisor(ll n, vector<ll> &ret) {
  for (ll i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      ret.push_back(i);
      if (i * i != n)
        ret.push_back(n / i);
    }
  }
  sort(ret.begin(), ret.end());
}

void divisor_prime(ll n, vector<P> &ret) {
  for (ll i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      ret.push_back({i, 0});
      while (n % i == 0) {
        n /= i;
        ret[ret.size() - 1].second++;
      }
    }
  }
  if (n != 1)
    ret.push_back({n, 1});
}

ll mod_pow(ll x, ll n, ll mod) {
  ll res = 1;
  while (n > 0) {
    if (n & 1)
      res = res * x % mod;
    x = x * x % mod;
    n >>= 1;
  }
  return res;
}

ll mod_inv(ll x, ll mod) { return mod_pow(x, mod - 2, mod); }
// nCrとか
class Combination {
public:
  Array fact;
  Array inv;
  ll mod;
  ll mod_inv(ll x) {
    ll n = mod - 2LL;
    ll res = 1LL;
    while (n > 0) {
      if (n & 1)
        res = res * x % mod;
      x = x * x % mod;
      n >>= 1;
    }
    return res;
  }
  // if n >= mod use lucas
  ll nCr(ll n, ll r) {
    if (n < r)
      return 0;
    if (n < mod)
      return ((fact[n] * inv[r] % mod) * inv[n - r]) % mod;

    ll ret = 1;
    while (n || r) {
      ll _n = n % mod, _r = r % mod;
      n /= mod;
      r /= mod;
      (ret *= nCr(_n, _r)) %= mod;
    }
    return ret;
  }
  ll nPr(ll n, ll r) { return (fact[n] * inv[n - r]) % mod; }
  ll nHr(ll n, ll r) { return nCr(r + n - 1, r); }
  Combination(ll _n, ll _mod) {
    mod = _mod;
    ll n = min(_n + 1, mod);
    fact.resize(n);
    fact[0] = 1;
    REP(i, n - 1) { fact[i + 1] = (fact[i] * (i + 1LL)) % mod; }
    inv.resize(n);
    inv[n - 1] = mod_inv(fact[n - 1]);
    for (int i = n - 1; i > 0; i--) {
      inv[i - 1] = inv[i] * i % mod;
    }
  }
};

ll gcd(ll m, ll n) {
  if (n == 0)
    return m;
  return gcd(n, m % n);
} // gcd

ll lcm(ll m, ll n) { return m / gcd(m, n) * n; }

ll popcount(ll x) {
  x = (x & 0x5555555555555555) + (x >> 1 & 0x5555555555555555);
  x = (x & 0x3333333333333333) + (x >> 2 & 0x3333333333333333);
  x = (x & 0x0F0F0F0F0F0F0F0F) + (x >> 4 & 0x0F0F0F0F0F0F0F0F);
  x = (x & 0x00FF00FF00FF00FF) + (x >> 8 & 0x00FF00FF00FF00FF);
  x = (x & 0x0000FFFF0000FFFF) + (x >> 16 & 0x0000FFFF0000FFFF);
  x = (x & 0x00000000FFFFFFFF) + (x >> 32 & 0x00000000FFFFFFFF);

  return x;
}

ll dp[22][1 << 21];

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);

  ll n;
  cin >> n;
  Matrix a(n, Array(n));
  REP(i, n) REP(j, n) cin >> a[i][j];
  dp[0][0] = 1;
  REP(i, n) {
    REP(j, 1 << n) {
      if (dp[i][j] == 0)
        continue;
      REP(k, n) {
        if (a[i][k] == 1)
          (dp[i + 1][j | (1 << k)] += dp[i][j]) %= MOD;
      }
    }
  }
  cout << dp[n][(1 << n) - 1] << "\n";

  return 0;
}


Fixed submission:
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <climits>
#include <cmath>
#include <complex>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>

using namespace std;
#define rrep(i, m, n) for (int(i) = (int)(m); (i) >= (int)(n); (i)--)
#define rep(i, m, n) for (int(i) = (int)(m); i < (int)(n); i++)
#define REP(i, n) rep(i, 0, n)
#define FOR(i, c)                                                              \
  for (decltype((c).begin()) i = (c).begin(); i != (c).end(); ++i)
#define ll long long
#define ull unsigned long long
#define all(hoge) (hoge).begin(), (hoge).end()
#define M_PI 3.1415926535897932L;
typedef pair<ll, ll> P;
constexpr ll MOD = 1000000007;
constexpr ll INF = 1LL << 60;
constexpr long double EPS = 1e-10;
typedef vector<ll> Array;
typedef vector<Array> Matrix;
string operator*(const string &s, int k) {
  if (k == 0)
    return "";
  string p = (s + s) * (k / 2);
  if (k % 2 == 1)
    p += s;
  return p;
}

template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

struct Edge { // グラフ
  ll to, cap, rev;
  Edge(ll _to, ll _cap, ll _rev) {
    to = _to;
    cap = _cap;
    rev = _rev;
  }
};
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
void add_edge(Graph &G, ll from, ll to, ll cap, bool revFlag,
              ll revCap) { // 最大フロー求める Ford-fulkerson
  G[from].push_back(Edge(to, cap, (ll)G[to].size()));
  if (revFlag)
    G[to].push_back(Edge(
        from, revCap, (ll)G[from].size() - 1)); // 最小カットの場合逆辺は0にする
}

ll max_flow_dfs(Graph &G, ll v, ll t, ll f, vector<bool> &used) {
  if (v == t)
    return f;
  used[v] = true;
  for (int i = 0; i < G[v].size(); ++i) {
    Edge &e = G[v][i];
    if (!used[e.to] && e.cap > 0) {
      ll d = max_flow_dfs(G, e.to, t, min(f, e.cap), used);
      if (d > 0) {
        e.cap -= d;
        G[e.to][e.rev].cap += d;
        return d;
      }
    }
  }
  return 0;
}
// 二分グラフの最大マッチングを求めたりも出来る　また二部グラフの最大独立集合は頂点数-最大マッチングのサイズ
ll max_flow(Graph &G, ll s, ll t) // O(V(V+E))
{
  ll flow = 0;
  for (;;) {
    vector<bool> used(G.size());
    REP(i, used.size()) used[i] = false;
    ll f = max_flow_dfs(G, s, t, INF, used);
    if (f == 0) {
      return flow;
    }
    flow += f;
  }
}
void BellmanFord(Graph &G, ll s, Array &d, Array &negative) { // O(|E||V|)
  d.resize(G.size());
  negative.resize(G.size());
  REP(i, d.size()) d[i] = INF;
  REP(i, d.size()) negative[i] = false;
  d[s] = 0;
  REP(k, G.size() - 1) {
    REP(i, G.size()) {
      REP(j, G[i].size()) {
        if (d[i] != INF && d[G[i][j].to] > d[i] + G[i][j].cap) {
          d[G[i][j].to] = d[i] + G[i][j].cap;
        }
      }
    }
  }
  REP(k, G.size() - 1) {
    REP(i, G.size()) {
      REP(j, G[i].size()) {
        if (d[i] != INF && d[G[i][j].to] > d[i] + G[i][j].cap) {
          d[G[i][j].to] = d[i] + G[i][j].cap;
          negative[G[i][j].to] = true;
        }
        if (negative[i] == true)
          negative[G[i][j].to] = true;
      }
    }
  }
}

void Dijkstra(Graph &G, ll s, Array &d) { // O(|E|log|V|)
  d.resize(G.size());
  REP(i, d.size()) d[i] = INF;
  d[s] = 0;
  priority_queue<P, vector<P>, greater<P>> q;
  q.push(make_pair(0, s));
  while (!q.empty()) {
    P a = q.top();
    q.pop();
    if (d[a.second] < a.first)
      continue;
    REP(i, G[a.second].size()) {
      Edge e = G[a.second][i];
      if (d[e.to] > d[a.second] + e.cap) {
        d[e.to] = d[a.second] + e.cap;
        q.push(make_pair(d[e.to], e.to));
      }
    }
  }
}
void WarshallFloyd(Graph &G, Matrix &d) { // O(V^3)
  d.resize(G.size());
  REP(i, d.size()) d[i].resize(G.size());
  REP(i, d.size()) {
    REP(j, d[i].size()) { d[i][j] = ((i != j) ? INF : 0); }
  }
  REP(i, G.size()) {
    REP(j, G[i].size()) { chmin(d[i][G[i][j].to], G[i][j].cap); }
  }
  REP(i, G.size()) {
    REP(j, G.size()) {
      REP(k, G.size()) { chmin(d[j][k], d[j][i] + d[i][k]); }
    }
  }
}
bool tsort(Graph &graph, vector<int> &order) { // トポロジカルソートO(E+V)
  int n = graph.size(), k = 0;
  Array in(n);
  for (auto &es : graph)
    for (auto &e : es)
      in[e.to]++;
  priority_queue<ll, Array, greater<ll>> que;
  REP(i, n)
  if (in[i] == 0)
    que.push(i);
  while (que.size()) {
    int v = que.top();
    que.pop();
    order.push_back(v);
    for (auto &e : graph[v])
      if (--in[e.to] == 0)
        que.push(e.to);
  }
  if (order.size() != n)
    return false;
  else
    return true;
}
class lca {
public:
  const int n = 0;
  const int log2_n = 0;
  std::vector<std::vector<int>> parent;
  std::vector<int> depth;

  lca() {}

  lca(const Graph &g, int root)
      : n(g.size()), log2_n(log2(n) + 1), parent(log2_n, std::vector<int>(n)),
        depth(n) {
    dfs(g, root, -1, 0);
    for (int k = 0; k + 1 < log2_n; k++) {
      for (int v = 0; v < (int)g.size(); v++) {
        if (parent[k][v] < 0)
          parent[k + 1][v] = -1;
        else
          parent[k + 1][v] = parent[k][parent[k][v]];
      }
    }
  }

  void dfs(const Graph &g, int v, int p, int d) {
    parent[0][v] = p;
    depth[v] = d;
    for (auto &e : g[v]) {
      if (e.to != p)
        dfs(g, e.to, v, d + 1);
    }
  }

  int get(int u, int v) {
    if (depth[u] > depth[v])
      std::swap(u, v);
    for (int k = 0; k < log2_n; k++) {
      if ((depth[v] - depth[u]) >> k & 1) {
        v = parent[k][v];
      }
    }
    if (u == v)
      return u;
    for (int k = log2_n - 1; k >= 0; k--) {
      if (parent[k][u] != parent[k][v]) {
        u = parent[k][u];
        v = parent[k][v];
      }
    }
    return parent[0][u];
  }
};
void visit(const Graph &g, int v, Matrix &scc, stack<ll> &S, Array &inS,
           Array &low, Array &num, int &time) {
  low[v] = num[v] = ++time;
  S.push(v);
  inS[v] = true;
  FOR(e, g[v]) {
    int w = e->to;
    if (num[w] == 0) {
      visit(g, w, scc, S, inS, low, num, time);
      low[v] = min(low[v], low[w]);
    } else if (inS[w])
      low[v] = min(low[v], num[w]);
  }
  if (low[v] == num[v]) {
    scc.push_back(Array());
    while (1) {
      int w = S.top();
      S.pop();
      inS[w] = false;
      scc.back().push_back(w);
      if (v == w)
        break;
    }
  }
}
void stronglyConnectedComponents(const Graph &g,
                                 Matrix &scc) { // 強連結成分分解 O(E+V)
  const int n = g.size();
  Array num(n), low(n);
  stack<ll> S;
  Array inS(n);
  int time = 0;
  REP(u, n) if (num[u] == 0) visit(g, u, scc, S, inS, low, num, time);
}

class UnionFind {
  vector<int> data;
  ll num;

public:
  UnionFind(int size) : data(size, -1), num(size) {}
  bool unite(int x, int y) { // xとyの集合を統合する
    x = root(x);
    y = root(y);
    if (x != y) {
      if (data[y] < data[x])
        swap(x, y);
      data[x] += data[y];
      data[y] = x;
    }
    num -= (x != y);
    return x != y;
  }
  bool findSet(int x, int y) { // xとyが同じ集合か返す
    return root(x) == root(y);
  }
  int root(int x) { // xのルートを返す
    return data[x] < 0 ? x : data[x] = root(data[x]);
  }
  ll size(int x) { // xの集合のサイズを返す
    return -data[root(x)];
  }
  ll numSet() { // 集合の数を返す
    return num;
  }
};
class SumSegTree {
private:
  ll _sum(ll a, ll b, ll k, ll l, ll r) {
    if (r <= a || b <= l)
      return 0; // 交差しない
    if (a <= l && r <= b)
      return dat[k]; // a,l,r,bの順で完全に含まれる
    else {
      ll s1 = _sum(a, b, 2 * k + 1, l, (l + r) / 2); // 左の子
      ll s2 = _sum(a, b, 2 * k + 2, (l + r) / 2, r); // 右の子
      return s1 + s2;
    }
  }

public:
  ll n, height;
  vector<ll> dat;

  // 初期化（_nは最大要素数）
  SumSegTree(ll _n) {
    n = 1;
    height = 1;
    while (n < _n) {
      n *= 2;
      height++;
    }
    dat = vector<ll>(2 * n - 1, 0);
  }

  // 場所i(0-indexed)にxを足す
  void add(ll i, ll x) {
    i += n - 1; // i番目の葉ノードへ
    dat[i] += x;
    while (i > 0) { // 下から上がっていく
      i = (i - 1) / 2;
      dat[i] += x;
    }
  }

  // 区間[a,b)の総和。ノードk=[l,r)に着目している。
  ll sum(ll a, ll b) { return _sum(a, b, 0, 0, n); }
};
class RmqTree {
private:
  ll _find(ll a, ll b, ll k, ll l, ll r) {
    if (r <= a || b <= l)
      return INF; // 交差しない
    if (a <= l && r <= b)
      return dat[k]; // a,l,r,bの順で完全に含まれる
    else {
      ll s1 = _find(a, b, 2 * k + 1, l, (l + r) / 2); // 左の子
      ll s2 = _find(a, b, 2 * k + 2, (l + r) / 2, r); // 右の子
      return min(s1, s2);
    }
  }

public:
  ll n, height;
  vector<ll> dat;

  // 初期化（_nは最大要素数）
  RmqTree(ll _n) {
    n = 1;
    height = 1;
    while (n < _n) {
      n *= 2;
      height++;
    }
    dat = vector<ll>(2 * n - 1, INF);
  }

  // 場所i(0-indexed)をxにする
  void update(ll i, ll x) {
    i += n - 1; // i番目の葉ノードへ
    dat[i] = x;
    while (i > 0) { // 下から上がっていく
      i = (i - 1) / 2;
      dat[i] = min(dat[i * 2 + 1], dat[i * 2 + 2]);
    }
  }

  // 区間[a,b)の最小値。ノードk=[l,r)に着目している。
  ll find(ll a, ll b) { return _find(a, b, 0, 0, n); }
};

// 約数求める //約数
void divisor(ll n, vector<ll> &ret) {
  for (ll i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      ret.push_back(i);
      if (i * i != n)
        ret.push_back(n / i);
    }
  }
  sort(ret.begin(), ret.end());
}

void divisor_prime(ll n, vector<P> &ret) {
  for (ll i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      ret.push_back({i, 0});
      while (n % i == 0) {
        n /= i;
        ret[ret.size() - 1].second++;
      }
    }
  }
  if (n != 1)
    ret.push_back({n, 1});
}

ll mod_pow(ll x, ll n, ll mod) {
  ll res = 1;
  while (n > 0) {
    if (n & 1)
      res = res * x % mod;
    x = x * x % mod;
    n >>= 1;
  }
  return res;
}

ll mod_inv(ll x, ll mod) { return mod_pow(x, mod - 2, mod); }
// nCrとか
class Combination {
public:
  Array fact;
  Array inv;
  ll mod;
  ll mod_inv(ll x) {
    ll n = mod - 2LL;
    ll res = 1LL;
    while (n > 0) {
      if (n & 1)
        res = res * x % mod;
      x = x * x % mod;
      n >>= 1;
    }
    return res;
  }
  // if n >= mod use lucas
  ll nCr(ll n, ll r) {
    if (n < r)
      return 0;
    if (n < mod)
      return ((fact[n] * inv[r] % mod) * inv[n - r]) % mod;

    ll ret = 1;
    while (n || r) {
      ll _n = n % mod, _r = r % mod;
      n /= mod;
      r /= mod;
      (ret *= nCr(_n, _r)) %= mod;
    }
    return ret;
  }
  ll nPr(ll n, ll r) { return (fact[n] * inv[n - r]) % mod; }
  ll nHr(ll n, ll r) { return nCr(r + n - 1, r); }
  Combination(ll _n, ll _mod) {
    mod = _mod;
    ll n = min(_n + 1, mod);
    fact.resize(n);
    fact[0] = 1;
    REP(i, n - 1) { fact[i + 1] = (fact[i] * (i + 1LL)) % mod; }
    inv.resize(n);
    inv[n - 1] = mod_inv(fact[n - 1]);
    for (int i = n - 1; i > 0; i--) {
      inv[i - 1] = inv[i] * i % mod;
    }
  }
};

ll gcd(ll m, ll n) {
  if (n == 0)
    return m;
  return gcd(n, m % n);
} // gcd

ll lcm(ll m, ll n) { return m / gcd(m, n) * n; }

ll popcount(ll x) {
  x = (x & 0x5555555555555555) + (x >> 1 & 0x5555555555555555);
  x = (x & 0x3333333333333333) + (x >> 2 & 0x3333333333333333);
  x = (x & 0x0F0F0F0F0F0F0F0F) + (x >> 4 & 0x0F0F0F0F0F0F0F0F);
  x = (x & 0x00FF00FF00FF00FF) + (x >> 8 & 0x00FF00FF00FF00FF);
  x = (x & 0x0000FFFF0000FFFF) + (x >> 16 & 0x0000FFFF0000FFFF);
  x = (x & 0x00000000FFFFFFFF) + (x >> 32 & 0x00000000FFFFFFFF);

  return x;
}

ll dp[22][1 << 21];

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);

  ll n;
  cin >> n;
  Matrix a(n, Array(n));
  REP(i, n) REP(j, n) cin >> a[i][j];
  dp[0][0] = 1;
  REP(i, n) {
    REP(j, 1 << n) {
      if (dp[i][j] == 0 || popcount(j) != i)
        continue;
      REP(k, n) {
        if (a[i][k] == 1)
          (dp[i + 1][j | (1 << k)] += dp[i][j]) %= MOD;
      }
    }
  }
  cout << dp[n][(1 << n) - 1] << "\n";

  return 0;
}