Problem p02704 (C++) — buggy submission, verdict: Time Limit Exceeded

/* #region Head */

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

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;

#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d)                                                       \\
  for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d)                                                      \\
  for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define PERM(c)                                                                \\
  sort(ALL(c));                                                                \\
  for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());

#define endl '\\n'
#define sqrt sqrtl
#define floor floorl
#define log2 log2l

constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;

template <typename T>
istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
  for (T &x : vec)
    is >> x;
  return is;
}
template <typename T>
ostream &operator<<(ostream &os, vc<T> &vec) { // vector 出力 (for dump)
  os << "{";
  REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
  os << "}";
  return os;
}
template <typename T>
ostream &operator>>(ostream &os, vc<T> &vec) { // vector 出力 (inline)
  REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\\n" : " ");
  return os;
}

template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
  is >> pair_var.first >> pair_var.second;
  return is;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, pair<T, U> &pair_var) { // pair 出力
  os << "(" << pair_var.first << ", " << pair_var.second << ")";
  return os;
}

// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, T &map_var) {
  os << "{";
  REPI(itr, map_var) {
    os << *itr;
    auto itrcp = itr;
    if (++itrcp != map_var.end())
      os << ", ";
  }
  return os << "}";
}
template <typename T, typename U>
ostream &operator<<(ostream &os, map<T, U> &map_var) {
  return out_iter(os, map_var);
}
template <typename T, typename U>
ostream &operator<<(ostream &os, um<T, U> &map_var) {
  return out_iter(os, map_var);
}
template <typename T> ostream &operator<<(ostream &os, set<T> &set_var) {
  return out_iter(os, set_var);
}
template <typename T> ostream &operator<<(ostream &os, us<T> &set_var) {
  return out_iter(os, set_var);
}
template <typename T> ostream &operator<<(ostream &os, pq<T> &pq_var) {
  pq<T> pq_cp(pq_var);
  os << "{";
  if (!pq_cp.empty()) {
    os << pq_cp.top(), pq_cp.pop();
    while (!pq_cp.empty())
      os << ", " << pq_cp.top(), pq_cp.pop();
  }
  return os << "}";
}

// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail>
void dump_func(Head &&head, Tail &&...tail) {
  DUMPOUT << head;
  if (sizeof...(Tail) > 0)
    DUMPOUT << ", ";
  dump_func(move(tail)...);
}

// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>>
bool chmax(T &xmax, const U &x, Comp comp = {}) {
  if (comp(xmax, x)) {
    xmax = x;
    return true;
  }
  return false;
}

// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>>
bool chmin(T &xmin, const U &x, Comp comp = {}) {
  if (comp(x, xmin)) {
    xmin = x;
    return true;
  }
  return false;
}

// ローカル用
#define DEBUG_

#ifdef DEBUG_
#define DEB
#define dump(...)                                                              \\
  DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                              \\
          << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl  \\
          << "    ",                                                           \\
      dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif

struct AtCoderInitialize {
  static constexpr int IOS_PREC = 15;
  static constexpr bool AUTOFLUSH = false;
  AtCoderInitialize() {
    ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
    cout << fixed << setprecision(IOS_PREC);
    if (AUTOFLUSH)
      cout << unitbuf;
  }
} ATCODER_INITIALIZE;

string yes = "Yes", no = "No";
// string yes = "YES", no = "NO";
void yn(bool p) { cout << (p ? yes : no) << endl; }

/* #endregion */

/* #region Graph */

// グラフ用テンプレ
using Weight = ll;
using Flow = ll;

// エッジ（本来エッジは双方向だが，ここでは単方向で管理）
struct Edge {
  ll src;        // エッジ始点となる頂点
  ll dst;        // エッジ終点となる頂点
  Weight weight; // 重み
  Flow cap;
  Edge() : src(0), dst(0), weight(0) {}
  Edge(ll src, ll dst, Weight weight) : src(src), dst(dst), weight(weight) {}
  Edge(ll src, ll dst, Weight weight, Flow cap)
      : src(src), dst(dst), weight(weight), cap(cap) {}
};
using Node = vc<Edge>;  // 同じ頂点を始点とするエッジ集合
using Graph = vc<Node>; // graph[i] := 頂点 i を始点とするエッジ集合
using Array = vc<Weight>;
using Matrix = vc<Array>;

// デフォルト引数を使うと Language Server が壊れる，たぶん　Weight=pll
// にしたことがあるせい 双方向のエッジを追加する
void add_edge(Graph &g, ll a, ll b, Weight w) {
  g[a].emplace_back(a, b, w);
  g[b].emplace_back(b, a, w);
}
// 双方向のエッジを追加する
void add_edge(Graph &g, ll a, ll b) { add_edge(g, a, b, 1LL); }
// 単方向のアークを追加する
void add_arc(Graph &g, ll a, ll b, Weight w) { g[a].emplace_back(a, b, w); }
// 単方向のアークを追加する
void add_arc(Graph &g, ll a, ll b, Weight w, Flow cap) {
  g[a].emplace_back(a, b, w, cap);
}
// 単方向のアークを追加する
void add_arc(Graph &g, ll a, ll b) { g[a].emplace_back(a, b, 1LL); }

// Edge 標準出力
ostream &operator<<(ostream &os, Edge &edge) {
  os << "(" << edge.src << " -> " << edge.dst << ", " << edge.weight << ")";
  return os;
}

/* #endregion */

/* #region Dinic */

// 最大流 (Dinic) | libalgo https://tubo28.me/compprog/algorithm/dinic/
struct dinic {
  int n, s, t;
  vc<int> level, prog, que;
  vc<vc<Flow>> cap, flow;
  vc<vc<int>> g;
  Flow inf;
  dinic(const Graph &graph)
      : n(graph.size()), cap(n, vc<Flow>(n)), flow(n, vc<Flow>(n)),
        g(n, vc<int>()), inf(std::numeric_limits<Flow>::max() / 8) {
    for (int i = 0; i < n; i++) {
      for (auto &e : graph[i]) {
        int u = e.src, v = e.dst;
        Flow c = e.cap;
        cap[u][v] += c;
        cap[v][u] += c;
        flow[v][u] += c;
        g[u].push_back(v);
        g[v].push_back(u);
      }
    }
  }
  inline Flow residue(int u, int v) { return cap[u][v] - flow[u][v]; }
  Flow solve(int s_, int t_) {
    this->t = t_, this->s = s_;
    que.resize(n + 1);
    Flow res = 0;
    while (levelize()) {
      prog.assign(n, 0);
      res += augment(s, inf);
    }
    return res;
  }
  bool levelize() {
    int l = 0, r = 0;
    level.assign(n, -1);
    level[s] = 0;
    que[r++] = s;
    while (l != r) {
      int v = que[l++];
      if (v == t)
        break;
      for (const int &d : g[v])
        if (level[d] == -1 && residue(v, d) != 0) {
          level[d] = level[v] + 1;
          que[r++] = d;
        }
    }
    return level[t] != -1;
  }
  Flow augment(int v, Flow lim) {
    Flow res = 0;
    if (v == t)
      return lim;
    for (int &i = prog[v]; i < (int)g[v].size(); i++) {
      const int &d = g[v][i];
      if (residue(v, d) == 0 || level[v] >= level[d])
        continue;
      const Flow aug = augment(d, std::min(lim, residue(v, d)));
      flow[v][d] += aug;
      flow[d][v] -= aug;
      res += aug;
      lim -= aug;
      if (lim == 0)
        break;
    }
    return res;
  }
};

/* #endregion */

// Problem
void solve() {
  ll n;
  cin >> n;

  vll s(n), t(n); // 0, 1
  vc<ull> u(n), v(n);
  cin >> s >> t >> u >> v;

  ull whole = 0;
  REP(i, 0, n) whole |= u[i] | v[i];
  ll maxdigit = 64 - __builtin_clzll(whole);
  // dump(maxdigit);

  vc<vc<ull>> ret(n, vc<ull>(n, 0));

  REP(digit, 0, maxdigit) {

    Graph g(2 * n + 4);
    ll start = 2 * n, sink = start + 1, super_start = start + 2,
       super_sink = start + 3;
    auto line = [](ll linenum) { return linenum; };
    auto row = [&n](ll rownum) { return rownum + n; };
    Weight w = 1;
    REP(i, 0, n) REP(j, 0, n) add_arc(g, line(i), row(j), w, 1);
    // add_arc(g, super_start, start, w, INF);
    // add_arc(g, sink, super_sink, w, INF);

    auto add_arc_minmax = [&](ll src, ll dst, ll cap_mi, ll cap_ma) {
      if (cap_mi == 0) {
        if (cap_ma > 0)
          add_arc(g, src, dst, w, cap_ma);
      } else if (cap_mi == cap_ma) {
        add_arc(g, super_start, dst, w, cap_ma);
        add_arc(g, src, super_sink, w, cap_ma);
      } else {
        add_arc(g, super_start, dst, w, cap_mi);
        add_arc(g, src, super_sink, w, cap_mi);
        add_arc(g, src, dst, w, cap_ma - cap_mi);
      }
    };

    REP(i, 0, n) {
      if (s[i] == 0) { // i 行目の AND が u[i]
        if (u[i] & (1ULL << digit))
          add_arc_minmax(start, line(i), n, n); // n bit 全て立っていてほしい
        else
          add_arc_minmax(start, line(i), 0,
                         n - 1); // n bit 全て立っていたら駄目
      } else {                   // i 行目の OR が u[i]
        if (u[i] & (1ULL << digit))
          add_arc_minmax(start, line(i), 1, n); // 1 bit は立っていてほしい
        // else add_arc_minmax(start, line(i), 0, 0); // 1 bit
        // も立っていたら駄目
      }
    }
    REP(j, 0, n) {
      if (t[j] == 0) { // j 列目の AND が v[j]
        if (v[j] & (1ULL << digit))
          add_arc_minmax(row(j), sink, n, n); // n bit 全て立っていてほしい
        else
          add_arc_minmax(row(j), sink, 0, n - 1); // n bit 全て立っていたら駄目
      } else {                                    // j 列目の OR が v[j]
        if (v[j] & (1ULL << digit))
          add_arc_minmax(row(j), sink, 1, n); // 1 bit は立っていてほしい
        // else // 1 bit も立っていたら駄目
      }
    }

    dinic dn(g);
    dn.solve(super_start, super_sink);
    dn.solve(start, super_sink);
    dn.solve(super_start, sink);
    dn.solve(start, sink);

    REP(i, 0, n)
    REP(j, 0, n) if (dn.flow[line(i)][row(j)] == 1) ret[i][j] += 1ULL << digit;
  }

  // dump(ret);

  // validate
  bool ok = true;
  // ull and_init = 0;
  // REP(i, 0, maxdigit) and_init |= 1ULL << i;
  ull and_init = -1;
  // dump(and_init);

  REP(i, 0, n) {
    if (s[i] == 0) { // i 行目の AND が u[i]
      ull acc = and_init;
      REP(j, 0, n) acc &= ret[i][j];
      if (acc != u[i]) {
        ok = false;
        // dump(i, acc, u[i]);
        break;
      }
    } else { // i 行目の OR が u[i]
      ull acc = 0;
      REP(j, 0, n) acc |= ret[i][j];
      if (acc != u[i]) {
        ok = false;
        // dump(i, acc, u[i]);
        break;
      }
    }
  }
  REP(j, 0, n) {
    if (t[j] == 0) { // j 列目の AND が v[j]
      ull acc = and_init;
      REP(i, 0, n) acc &= ret[i][j];
      if (acc != v[j]) {
        ok = false;
        // dump(j, acc, v[j]);
        break;
      }
    } else { // j 列目の OR が v[j]
      ull acc = 0;
      REP(i, 0, n) acc |= ret[i][j];
      if (acc != v[j]) {
        ok = false;
        // dump(j, acc, v[j]);
        break;
      }
    }
  }
  if (!ok) {
    cout << -1 << endl;
    return;
  }
  REP(i, 0, n) cout >> ret[i];
}

// entry point
int main() {
  solve();
  return 0;
}


Error: TLE

Fixed submission:

/* #region Head */

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

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;

#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d)                                                       \\
  for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d)                                                      \\
  for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define PERM(c)                                                                \\
  sort(ALL(c));                                                                \\
  for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());

// #define endl '\\n'
#define sqrt sqrtl
#define floor floorl
#define log2 log2l

constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;

template <typename T>
istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
  for (T &x : vec)
    is >> x;
  return is;
}
template <typename T>
ostream &operator<<(ostream &os, vc<T> &vec) { // vector 出力 (for dump)
  os << "{";
  REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
  os << "}";
  return os;
}
template <typename T>
ostream &operator>>(ostream &os, vc<T> &vec) { // vector 出力 (inline)
  REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\\n" : " ");
  return os;
}

template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
  is >> pair_var.first >> pair_var.second;
  return is;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, pair<T, U> &pair_var) { // pair 出力
  os << "(" << pair_var.first << ", " << pair_var.second << ")";
  return os;
}

// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, T &map_var) {
  os << "{";
  REPI(itr, map_var) {
    os << *itr;
    auto itrcp = itr;
    if (++itrcp != map_var.end())
      os << ", ";
  }
  return os << "}";
}
template <typename T, typename U>
ostream &operator<<(ostream &os, map<T, U> &map_var) {
  return out_iter(os, map_var);
}
template <typename T, typename U>
ostream &operator<<(ostream &os, um<T, U> &map_var) {
  return out_iter(os, map_var);
}
template <typename T> ostream &operator<<(ostream &os, set<T> &set_var) {
  return out_iter(os, set_var);
}
template <typename T> ostream &operator<<(ostream &os, us<T> &set_var) {
  return out_iter(os, set_var);
}
template <typename T> ostream &operator<<(ostream &os, pq<T> &pq_var) {
  pq<T> pq_cp(pq_var);
  os << "{";
  if (!pq_cp.empty()) {
    os << pq_cp.top(), pq_cp.pop();
    while (!pq_cp.empty())
      os << ", " << pq_cp.top(), pq_cp.pop();
  }
  return os << "}";
}

// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail>
void dump_func(Head &&head, Tail &&...tail) {
  DUMPOUT << head;
  if (sizeof...(Tail) > 0)
    DUMPOUT << ", ";
  dump_func(move(tail)...);
}

// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>>
bool chmax(T &xmax, const U &x, Comp comp = {}) {
  if (comp(xmax, x)) {
    xmax = x;
    return true;
  }
  return false;
}

// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>>
bool chmin(T &xmin, const U &x, Comp comp = {}) {
  if (comp(x, xmin)) {
    xmin = x;
    return true;
  }
  return false;
}

// ローカル用
#define DEBUG_

#ifdef DEBUG_
#define DEB
#define dump(...)                                                              \\
  DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                              \\
          << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl  \\
          << "    ",                                                           \\
      dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif

struct AtCoderInitialize {
  static constexpr int IOS_PREC = 15;
  static constexpr bool AUTOFLUSH = false;
  AtCoderInitialize() {
    ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
    cout << fixed << setprecision(IOS_PREC);
    if (AUTOFLUSH)
      cout << unitbuf;
  }
} ATCODER_INITIALIZE;

string yes = "Yes", no = "No";
// string yes = "YES", no = "NO";
void yn(bool p) { cout << (p ? yes : no) << endl; }

/* #endregion */

/* #region FLOW_LR */

template <typename flow_t> struct Dinic {
  const flow_t INF;

  struct edge {
    int to;
    flow_t cap;
    int rev;
    bool isrev;
    int idx;
  };

  vector<vector<edge>> graph;
  vector<int> min_cost, iter;

  Dinic(int V) : INF(numeric_limits<flow_t>::max()), graph(V) {}

  void add_edge(int from, int to, flow_t cap, int idx = -1) {
    graph[from].emplace_back(
        (edge){to, cap, (int)graph[to].size(), false, idx});
    graph[to].emplace_back(
        (edge){from, 0, (int)graph[from].size() - 1, true, idx});
  }

  bool bfs(int s, int t) {
    min_cost.assign(graph.size(), -1);
    queue<int> que;
    min_cost[s] = 0;
    que.push(s);
    while (!que.empty() && min_cost[t] == -1) {
      int p = que.front();
      que.pop();
      for (auto &e : graph[p]) {
        if (e.cap > 0 && min_cost[e.to] == -1) {
          min_cost[e.to] = min_cost[p] + 1;
          que.push(e.to);
        }
      }
    }
    return min_cost[t] != -1;
  }

  flow_t dfs(int idx, const int t, flow_t flow) {
    if (idx == t)
      return flow;
    for (int &i = iter[idx]; i < graph[idx].size(); i++) {
      edge &e = graph[idx][i];
      if (e.cap > 0 && min_cost[idx] < min_cost[e.to]) {
        flow_t d = dfs(e.to, t, min(flow, e.cap));
        if (d > 0) {
          e.cap -= d;
          graph[e.to][e.rev].cap += d;
          return d;
        }
      }
    }
    return 0;
  }

  flow_t max_flow(int s, int t) {
    flow_t flow = 0;
    while (bfs(s, t)) {
      iter.assign(graph.size(), 0);
      flow_t f = 0;
      while ((f = dfs(s, t, INF)) > 0)
        flow += f;
    }
    return flow;
  }

  void output() {
    for (int i = 0; i < graph.size(); i++) {
      for (auto &e : graph[i]) {
        if (e.isrev)
          continue;
        auto &rev_e = graph[e.to][e.rev];
        cout << i << "->" << e.to << " (flow: " << rev_e.cap << "/"
             << e.cap + rev_e.cap << ")" << endl;
      }
    }
  }
};

template <typename flow_t, template <typename> class F>
struct MaxFlowLowerBound {
  F<flow_t> flow;
  vector<flow_t> in, up;
  typename F<flow_t>::edge *latte, *malta;
  int X, Y, V;
  flow_t sum;

  MaxFlowLowerBound(int V) : V(V), flow(V + 2), X(V), Y(V + 1), sum(0), in(V) {}

  void add_edge(int from, int to, flow_t low, flow_t high) {
    assert(from != to);
    flow.add_edge(from, to, high - low, up.size());
    in[from] -= low;
    in[to] += low;
    up.emplace_back(high);
  }

  void build() {
    for (int i = 0; i < V; i++) {
      if (in[i] > 0) {
        flow.add_edge(X, i, in[i]);
        sum += in[i];
      } else if (in[i] < 0) {
        flow.add_edge(i, Y, -in[i]);
      }
    }
  }

  bool can_flow(int s, int t) {
    assert(s != t);
    flow.add_edge(t, s, flow.INF);
    latte = &flow.graph[t].back();
    malta = &flow.graph[s].back();
    return can_flow();
  }

  bool can_flow() {
    build();
    auto ret = flow.max_flow(X, Y);
    return ret >= sum;
  }

  flow_t max_flow(int s, int t) {
    if (can_flow(s, t)) {
      return flow.max_flow(s, t);
    } else {
      return -1;
    }
  }

  flow_t min_flow(int s, int t) {
    if (can_flow(s, t)) {
      auto ret = flow.INF - latte->cap;
      latte->cap = malta->cap = 0;
      return ret - flow.max_flow(t, s);
    } else {
      return -1;
    }
  }

  void output(int M) {
    vector<flow_t> ans(M);
    for (int i = 0; i < flow.graph.size(); i++) {
      for (auto &e : flow.graph[i]) {
        if (!e.isrev && ~e.idx)
          ans[e.idx] = up[e.idx] - e.cap;
      }
    }
    for (flow_t &p : ans)
      cout << p << endl;
  }
};

/* #endregion */

// Problem
void solve() {
  ll n;
  cin >> n;

  vll s(n), t(n); // 0, 1
  vc<ull> u(n), v(n);
  cin >> s >> t >> u >> v;

  ull whole = 0;
  REP(i, 0, n) whole |= u[i] | v[i];
  ll maxdigit = 64 - __builtin_clzll(whole);
  // dump(maxdigit);

  vc<vc<ull>> ret(n, vc<ull>(n, 0));

  REP(digit, 0, maxdigit) {

    MaxFlowLowerBound<ll, Dinic> mf(2 * n + 2);
    // MF mf(2 * n + 2);
    // Graph g(2 * n + 4);
    // ll start = 2 * n, sink = start + 1, super_start = start + 2, super_sink =
    // start + 3;
    ll start = 2 * n, sink = start + 1;
    auto line = [](ll linenum) { return linenum; };
    auto row = [&n](ll rownum) { return rownum + n; };
    // Weight w = 1;
    // REP(i, 0, n) REP(j, 0, n) add_arc(g, line(i), row(j), w, 1);
    REP(i, 0, n) REP(j, 0, n) mf.add_edge(line(i), row(j), 0, 1);
    // add_arc(g, super_start, start, w, INF);
    // add_arc(g, sink, super_sink, w, INF);

    // auto add_arc_minmax = [&](ll src, ll dst, ll cap_mi, ll cap_ma) {
    //     if (cap_mi == 0) {
    //         if (cap_ma > 0) add_arc(g, src, dst, w, cap_ma);
    //     } else if (cap_mi == cap_ma) {
    //         add_arc(g, super_start, dst, w, cap_ma);
    //         add_arc(g, src, super_sink, w, cap_ma);
    //     } else {
    //         add_arc(g, super_start, dst, w, cap_mi);
    //         add_arc(g, src, super_sink, w, cap_mi);
    //         add_arc(g, src, dst, w, cap_ma - cap_mi);
    //     }
    // };

    REP(i, 0, n) {
      if (s[i] == 0) { // i 行目の AND が u[i]
        if (u[i] & (1ULL << digit))
          mf.add_edge(start, line(i), n, n); // n bit 全て立っていてほしい
        else
          mf.add_edge(start, line(i), 0, n - 1); // n bit 全て立っていたら駄目
      } else {                                   // i 行目の OR が u[i]
        if (u[i] & (1ULL << digit))
          mf.add_edge(start, line(i), 1, n); // 1 bit は立っていてほしい
        // else add_arc_minmax(start, line(i), 0, 0); // 1 bit
        // も立っていたら駄目
      }
    }
    REP(j, 0, n) {
      if (t[j] == 0) { // j 列目の AND が v[j]
        if (v[j] & (1ULL << digit))
          mf.add_edge(row(j), sink, n, n); // n bit 全て立っていてほしい
        else
          mf.add_edge(row(j), sink, 0, n - 1); // n bit 全て立っていたら駄目
      } else {                                 // j 列目の OR が v[j]
        if (v[j] & (1ULL << digit))
          mf.add_edge(row(j), sink, 1, n); // 1 bit は立っていてほしい
        // else // 1 bit も立っていたら駄目
      }
    }

    // dinic dn(g);
    // dn.solve(super_start, super_sink);
    // dn.solve(start, super_sink);
    // dn.solve(super_start, sink);
    // dn.solve(start, sink);
    if (mf.max_flow(start, sink) == -1) {
      cout << -1 << endl;
      return;
    }

    // REP(i, 0, n) REP(j, 0, n) if (dn.flow[line(i)][row(j)] == 1) ret[i][j] +=
    // 1 << digit; REP(i, 0, n) {
    //     for (auto &e : mf.flow.g[i]) {
    //         if (!(e.dst >= n && e.dst < 2 * n)) continue;
    //         dump(i, e.dst - n, e.flow, e.cap);
    //         if (e.dst >= n && e.dst < 2 * n && e.flow == 0) {
    //             dump(i, e.dst - n);
    //             ret[i][e.dst - n] += 1 << digit;
    //         }
    //     }
    // }
    for (int i = 0; i < mf.flow.graph.size(); i++) {
      for (auto &e : mf.flow.graph[i]) {
        if (!e.isrev && ~e.idx) {
          if (e.idx >= n * n)
            continue;
          ll f = mf.up[e.idx] - e.cap;
          if (f == 1)
            ret[e.idx / n][e.idx % n] += 1ULL << digit;
        }
      }
    }
  }

  // validate
  bool ok = true;
  ull and_init = -1;
  // REP(i, 0, maxdigit) and_init |= 1ULL << i;
  // dump(and_init);
  // dump(ret);

  REP(i, 0, n) {
    if (s[i] == 0) { // i 行目の AND が u[i]
      ull acc = and_init;
      REP(j, 0, n) acc &= ret[i][j];
      if (acc != u[i]) {
        ok = false;
        dump(i, acc, u[i]);
        break;
      }
    } else { // i 行目の OR が u[i]
      ull acc = 0;
      REP(j, 0, n) acc |= ret[i][j];
      if (acc != u[i]) {
        ok = false;
        dump(i, acc, u[i]);
        break;
      }
    }
  }
  REP(j, 0, n) {
    if (t[j] == 0) { // j 列目の AND が v[j]
      ull acc = and_init;
      REP(i, 0, n) acc &= ret[i][j];
      if (acc != v[j]) {
        ok = false;
        dump(j, acc, v[j]);
        break;
      }
    } else { // j 列目の OR が v[j]
      ull acc = 0;
      REP(i, 0, n) acc |= ret[i][j];
      if (acc != v[j]) {
        ok = false;
        dump(j, acc, v[j]);
        break;
      }
    }
  }
  if (!ok) {
    cout << -1 << endl;
    return;
  }
  REP(i, 0, n) cout >> ret[i];
}

// entry point
int main() {
  solve();
  return 0;
}