/* #region Head */ // #include #include #include #include #include // assert.h #include // math.h #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair; template using vc = vector; template using vvc = vc>; using vll = vc; using vvll = vvc; using vld = vc; using vvld = vvc; using vs = vc; using vvs = vvc; template using um = unordered_map; template using pq = priority_queue; template using pqa = priority_queue, greater>; template using us = unordered_set; #define TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i)) #define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i)) #define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i)) #define TREPD(T, i, m, n, d) for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d)) #define TREPMD(T, i, m, n, d) for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d)) #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 REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); 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 CEIL(a, b) (((a) + (b)-1) / (b)) #define endl '\n' constexpr ll INF = 1'010'000'000'000'000'017LL; constexpr int IINF = 1'000'000'007LL; constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7 // constexpr ll MOD = 998244353; constexpr ld EPS = 1e-12; constexpr ld PI = 3.14159265358979323846; template istream &operator>>(istream &is, vc &vec) { // vector 入力 for (T &x : vec) is >> x; return is; } template ostream &operator<<(ostream &os, const vc &vec) { // vector 出力 (for dump) os << "{"; REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template ostream &operator>>(ostream &os, const vc &vec) { // vector 出力 (inline) REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " "); return os; } template istream &operator>>(istream &is, array &arr) { // array 入力 REP(i, 0, SIZE(arr)) is >> arr[i]; return is; } template ostream &operator<<(ostream &os, const array &arr) { // array 出力 (for dump) os << "{"; REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template istream &operator>>(istream &is, pair &pair_var) { // pair 入力 is >> pair_var.first >> pair_var.second; return is; } template ostream &operator<<(ostream &os, const pair &pair_var) { // pair 出力 os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // map, um, set, us 出力 template ostream &out_iter(ostream &os, const T &map_var) { os << "{"; REPI(itr, map_var) { os << *itr; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } return os << "}"; } template ostream &operator<<(ostream &os, const map &map_var) { return out_iter(os, map_var); } template ostream &operator<<(ostream &os, const um &map_var) { os << "{"; REPI(itr, map_var) { auto [key, value] = *itr; os << "(" << key << ", " << value << ")"; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } os << "}"; return os; } template ostream &operator<<(ostream &os, const set &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const us &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const pq &pq_var) { pq 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 << "}"; } void pprint() { cout << endl; } template void pprint(Head &&head, Tail &&...tail) { cout << head; if (sizeof...(Tail) > 0) cout << ' '; pprint(move(tail)...); } // dump #define DUMPOUT cerr void dump_func() { DUMPOUT << endl; } template 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 > 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 > bool chmin(T &xmin, const U &x, Comp comp = {}) { if (comp(x, xmin)) { xmin = x; return true; } return false; } // ローカル用 #ifndef ONLINE_JUDGE #define DEBUG_ #endif #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 #define VAR(type, ...) \ type __VA_ARGS__; \ cin >> __VA_ARGS__; template istream &operator,(istream &is, T &rhs) { return is >> rhs; } template ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; } 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; void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; } void YN(bool p) { cout << (p ? "YES" : "NO") << endl; } /* #endregion */ // #include // using namespace atcoder; /* #region Graph */ // エッジ(本来エッジは双方向だが,ここでは単方向で管理) template 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_t weight; // 重み flow_t cap; Edge() : src(0), dst(0), weight(0) {} Edge(ll src, ll dst, weight_t weight) : src(src), dst(dst), weight(weight) {} Edge(ll src, ll dst, weight_t weight, flow_t cap) : src(src), dst(dst), weight(weight), cap(cap) {} // Edge 標準出力 friend ostream &operator<<(ostream &os, Edge &edge) { os << "(" << edge.src << " -> " << edge.dst << ", " << edge.weight << ")"; return os; } }; // 同じ頂点を始点とするエッジ集合 template class Node : public vc> { public: ll idx; Node() : vc>() {} // void add(int a, int b, weight_t w, flow_t cap) { this->emplace_back(a, b, w, cap); }; }; // graph[i] := 頂点 i を始点とするエッジ集合 template class Graph : public vc> { public: Graph() : vc>() {} Graph(int n) : vc>(n) { REP(i, 0, n)(*this)[i].idx = i; } // 単方向 void add_arc(int a, int b, weight_t w = 1, flow_t cap = 1) { (*this)[a].emplace_back(a, b, w, cap); } // 双方向 void add_edge(int a, int b, weight_t w = 1, flow_t cap = 1) { add_arc(a, b, w, cap), add_arc(b, a, w, cap); } }; // using Array = vc; // using Matrix = vc; /* #endregion */ /* #region DINIC_SPARSE */ // using flow_type = int; template struct dinic_sparse { struct edge { int src, dst; flow_type cap, flow; int rev_idx; bool is_rev; }; int n, s, t; std::vector> g; std::vector level, prog, que; std::vector, flow_type>> edges; dinic_sparse(int n_ = 0) : n(n_) {} // Compute the maximum-flow from `s_` to `t_` by Dinic's algorithm. flow_type maximum_flow(int s_, int t_) { s = s_; t = t_; make_graph(); que.resize(n); flow_type res = 0; while (levelize()) { prog.assign(n, 0); res += augment(s, std::numeric_limits::max()); } return res; } // Add an edge from `u` to `v` with capacity `c`. Note that it will be added // to `g` when `make_graph` is called instead of just after calling this // function. void add_edge(int u, int v, flow_type c) { if (u != v && c != 0) { edges.emplace_back(std::make_pair(u, v), c); } } void make_graph() { g.assign(n, {}); if (true) { std::sort(edges.begin(), edges.end()); for (auto it = edges.begin(); it != edges.end();) { flow_type c = 0; auto uv = it->first; while (it != edges.end() && it->first == uv) { c += it->second; ++it; } int u = uv.first, v = uv.second; g[u].push_back({u, v, c, 0, (int)g[v].size(), false}); g[v].push_back({v, u, c, c, (int)g[u].size() - 1, true}); } } else { for (auto &e : edges) { auto uv = e.first; int u = uv.first, v = uv.second; flow_type c = e.second; g[u].push_back({u, v, c, 0, (int)g[v].size(), false}); g[v].push_back({v, u, c, c, (int)g[u].size() - 1, true}); } } } bool levelize() { int fst = 0, lst = 0; que[lst++] = s; level.assign(n, -1); level[s] = 0; while (fst != lst) { int v = que[fst++]; if (v == t) break; for (auto &e : g[v]) { if (level[e.dst] == -1 && residue(e) != 0) { level[e.dst] = level[v] + 1; que[lst++] = e.dst; } } } return level[t] != -1; } flow_type augment(int v, flow_type lim) { flow_type res = 0; if (v == t) return lim; for (int &i = prog[v]; i < (int)g[v].size(); ++i) { if (lim == 0) break; auto &e = g[v][i]; if (level[v] < level[e.dst] && residue(e) != 0) { flow_type aug = augment(e.dst, std::min(lim, residue(e))); if (aug == 0) continue; e.flow += aug; reverse(e).flow -= aug; res += aug; lim -= aug; } } return res; } flow_type residue(const edge &e) { return e.cap - e.flow; } edge &reverse(const edge &e) { return g[e.dst][e.rev_idx]; } // Output current flow by graphviz dot language. // Run `dot $filename -o out.png -T png` on shell. void show(const std::string &filename = "out.dot") { int fst = 0, lst = 0; que[lst++] = s; level.assign(n, -1); level[s] = 0; while (fst != lst) { int v = que[fst++]; for (auto &e : g[v]) { if (!e.is_rev && level[e.dst] == -1 && e.flow) { level[e.dst] = level[v] + 1; que[lst++] = e.dst; } } } std::map> rank_to_vertices; for (int i = 0; i < n; ++i) { rank_to_vertices[level[i]].push_back(i); } std::ostringstream oss; oss << "digraph {" << '\n'; for (int i = 0; i < n; ++i) { oss << "\t" << i; if (i == s || i == t) { oss << " [ peripheries = 2 ]"; } oss << ";\n"; for (auto &e : g[i]) { if (!e.is_rev) { const char *color = e.flow ? "black" : "gray"; oss << "\t" << e.src << " -> " << e.dst << "\t[ " << "label = \"" << e.flow << "/" << e.cap << "\", " << "color = \"" << color << "\", " << "fontcolor = \"" << color << "\"];\n"; } } } for (auto &p : rank_to_vertices) { const char *rank = p.first != -1 ? "same" : "sink"; oss << "\t{ rank = " << rank << "; "; for (int v : p.second) { if (v != s && v != t) { oss << v << "; "; } } oss << "}\n"; } oss << "\t{ rank = same; " << s << "; }\n"; oss << "\t{ rank = same; " << t << "; }\n"; oss << "}\n"; std::ofstream ofs(filename); ofs << oss.str(); } }; /* #endregion */ // Problem void solve() { VAR(ll, n); // vll row_caps, col_caps; REPM(i, 1, 2 * n) { if (i % 4 == 1 || i % 4 == 0) { row_caps.push_back(i); } else { col_caps.push_back(i); } } ll sum = accumulate(ALL(row_caps), 0LL); // dump(rows, cols); using Flow = ll; dinic_sparse dn(n * n + 2 * n + 2); auto idx = [&](ll r, ll c) -> ll { return n * r + c; }; auto row = [&](ll r) -> ll { return n * n + r; }; auto col = [&](ll c) -> ll { return n * n + n + c; }; ll S = n * n + 2 * n; ll T = S + 1; REP(i, 0, n) REP(j, 0, n) { dn.add_edge(row(i), idx(i, j), 2); dn.add_edge(idx(i, j), col(j), 2); } REP(i, 0, n) dn.add_edge(S, row(i), row_caps[i]); REP(j, 0, n) dn.add_edge(col(j), T, col_caps[j]); ll f = dn.maximum_flow(S, T); // dump(f); if (f != sum) { Yn(false); return; } vvll ans(n, vll(n, INF)); for (auto &edges : dn.g) { for (auto &edge : edges) { if (edge.src < n * n) { ll i = edge.src / n; ll j = edge.src % n; if (edge.dst != col(j)) continue; // dump(i, j, edge.src, edge.dst, edge.flow); ans[i][j] = edge.flow; } } } // dump(ans); REP(i, 0, n) { REP(j, 0, n) cout << ans[i][j]; cout << endl; } } // entry point int main() { solve(); return 0; }