// Begin include: "../../template/template.hpp" using namespace std; // intrinstic #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // utility // Begin include: "util.hpp" namespace yamada { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; using lld = long double; template using V = vector; template using VV = vector>; template using VVV = vector>>; template using VVVV = vector>>>; using vl = vector; using vd = V; using vs = V; using vvl = vector>; using vvvl = vector>>; using vvvvl = vector>>>; template using minpq = priority_queue, greater>; template using maxpq = priority_queue, less>; template struct P : pair { template P(Args... args) : pair(args...) {} using pair::first; using pair::second; P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } template P &operator*=(const S &r) { first *= r, second *= r; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } template P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P; using vp = V; using vvp = VV; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline T Max(const vector &v) { return *max_element(begin(v), end(v)); } template inline T Min(const vector &v) { return *min_element(begin(v), end(v)); } template inline long long Sum(const vector &v) { return accumulate(begin(v), end(v), T(0)); } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template vector mkrui(const vector &v, bool rev = false) { vector ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N, F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector mkinv(vector &v) { int max_val = *max_element(begin(v), end(v)); vector inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector mkiota(int n) { vector ret(n); iota(begin(ret), end(ret), 0); return ret; } template T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template bool nxp(T &v) { return next_permutation(begin(v), end(v)); } // 返り値の型は入力の T に依存 // i 要素目 : [0, a[i]) template vector> product(const vector &a) { vector> ret; vector v; auto dfs = [&](auto rc, int i) -> void { if (i == (int)a.size()) { ret.push_back(v); return; } for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back(); }; dfs(dfs, 0); return ret; } template vector Digit(T a, const U &x, int siz = -1) { vector ret; while (a > 0) { ret.emplace_back(a % x); a /= x; } if (siz >= 0) while ((int)ret.size() < siz) ret.emplace_back(0); return ret; } // F : function(void(T&)), mod を取る操作 // T : 整数型のときはオーバーフローに注意する template T Power(T a, long long n, const T &I, const function &f) { T res = I; for (; n; f(a = a * a), n >>= 1) { if (n & 1) f(res = res * a); } return res; } // T : 整数型のときはオーバーフローに注意する template T Power(T a, long long n, const T &I = T{1}) { return Power(a, n, I, function{[](T &) -> void {}}); } template T Rev(const T &v) { T res = v; reverse(begin(res), end(res)); return res; } template vector Transpose(const vector &v) { using U = typename T::value_type; if(v.empty()) return {}; int H = v.size(), W = v[0].size(); vector res(W, T(H, U{})); for (int i = 0; i < H; i++) for (int j = 0; j < W; j++) res[j][i] = v[i][j]; return res; } template vector Rotate(const vector &v, int clockwise = true) { using U = typename T::value_type; int H = v.size(), W = v[0].size(); vector res(W, T(H, U{})); for (int i = 0; i < H; i++) for (int j = 0; j < W; j++) { if (clockwise) res[W - 1 - j][i] = v[i][j]; else res[j][H - 1 - i] = v[i][j]; } return res; } template T bisect(T ok, T bad, F pred) { if (ok == bad) return ok; if (!pred(ok)) return ok; while (bad - ok > 1) { T mid = ok + (bad - ok) / 2; (pred(mid) ? ok : bad) = mid; } return bad; } template T bisect_double(T ok, T bad, F pred, int iter = 100) { if (ok == bad) return ok; if (!pred(ok)) return ok; while (iter--) { T mid = ok + (bad - ok) / 2; (pred(mid) ? ok : bad) = mid; } return bad; } template bool inLR(T L, T x, T R){ return (L <= x && x < R); } bool YESNO(bool b) { cout << (b ? "YES\n" : "NO\n"); return b; } bool YesNo(bool b) { cout << (b ? "Yes\n" : "No\n"); return b; } template void mout(mint a, int M = 100) { if (a == 0) { cout << 0 << "\n"; return; } for (int i = 0; i <= M; i++) for (int j = 1; j <= M; j++) { mint val = (mint)i / j; if (val == a) { if (j == 1) cout << i << "\n"; else cout << i << "/" << j << "\n"; return; } else if (val == -a) { if (j == 1) cout << -i << "\n"; else cout << -i << "/" << j << "\n"; return; } } cout << "NF\n"; } template void mout(std::vector A, int M = 100) { int N = A.size(); for (int pos = 0; pos < N; pos++) { if (A[pos] == 0) { cout << 0 << (pos == N - 1 ? "\n" : " "); continue; } bool found = false; for (int i = 0; i <= M; i++) { for (int j = 1; j <= M; j++) { mint val = (mint)i / j; if (val == A[pos]) { if (j == 1) cout << i << (pos == N - 1 ? "\n" : " "); else cout << i << "/" << j << (pos == N - 1 ? "\n" : " "); found = true; break; } else if (val == -A[pos]) { if (j == 1) cout << -i << (pos == N - 1 ? "\n" : " "); else cout << -i << "/" << j << (pos == N - 1 ? "\n" : " "); found = true; break; } } if (found) break; } if (!found) cout << "NF" << (pos == N - 1 ? "\n" : " "); } } bool is_square(uint64_t n) { if (n < 2) return true; uint64_t r = static_cast(sqrtl(static_cast(n))); if (r * r == n) return true; ++r; return r * r == n; } template struct CumulativeSum { std::vector S; CumulativeSum(std::vector &A) { int N = A.size(); S.resize(N + 1); for (int i = 0; i < N; i++) S[i + 1] = S[i] + A[i]; } T query(int l, int r) { return (l <= r ? S[r] - S[l] : (T)0); } T get_val(int i) { return S[i + 1] - S[i]; } }; template T extgcd(T a, T b, T &x, T &y) { T d = a; if(b != 0) { d = extgcd(b, a % b, y, x); y -= (a / b) * x; } else x = 1, y = 0; return d; } // floor(sqrt(x)) long long isqrt (long long x) { long long y = sqrt(x); while (y * y > x) y--; while ((y + 1) * (y + 1) <= x) y++; return y; } } // namespace yamada // End include: "util.hpp" // bit operation // Begin include: "bitop.hpp" namespace yamada { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return __builtin_popcountll(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template inline int gbit(const T &a, int i) { return (a >> i) & 1; } template inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace yamada // End include: "bitop.hpp" // inout // Begin include: "inout.hpp" namespace yamada { template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } struct IoSetupYamada { IoSetupYamada() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupyamada; } // namespace yamada // End include: "inout.hpp" // macro // Begin include: "macro.hpp" #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define each3(x, y, z, v) for (auto&& [x, y, z] : v) #define all(v) (v).begin(), (v).end() #define rep1(a) for (long long _ = 0; _ < (long long)(a); ++_) #define rep2(i, a) for (long long i = 0; i < (long long)(a); ++i) #define rep3(i, a, b) for (long long i = a; i < (long long)(b); ++i) #define rep4(i, a, b, c) for (long long i = a; i < (long long)(b); i += c) #define overload4(a, b, c, d, e, ...) e #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rep1r(a) for (long long i = (long long)(a)-1; i >= 0LL; --i) #define rep2r(i, a) for (long long i = (long long)(a)-1; i >= 0LL; --i) #define rep3r(i, a, b) for (long long i = (long long)(b)-1; i >= (long long)(a); --i) #define overload3(a, b, c, d, ...) d #define repr(...) overload3(__VA_ARGS__, rep3r, rep2r, rep1r)(__VA_ARGS__) #define eb emplace_back #define mkp make_pair #define mkt make_tuple #define fi first #define se second #define vv(type, name, h, ...) \ vector > name(h, vector(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector>> name( \ h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name( \ a, vector>>( \ b, vector>(c, vector(__VA_ARGS__)))) #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ yamada::out(__VA_ARGS__);\ return; \ } while (0) // End include: "macro.hpp" namespace yamada { void solve(); } int main() { yamada::solve(); } // End include: "../../template/template.hpp" // Begin include: "../../atcoder/maxflow.hpp" #ifndef ATCODER_MAXFLOW_HPP #define ATCODER_MAXFLOW_HPP 1 #include // Begin include: "internal_queue.hpp" #ifndef ATCODER_INTERNAL_QUEUE_HPP #define ATCODER_INTERNAL_QUEUE_HPP 1 #include namespace atcoder { namespace internal { template struct simple_queue { std::vector payload; int pos = 0; void reserve(int n) { payload.reserve(n); } int size() const { return int(payload.size()) - pos; } bool empty() const { return pos == int(payload.size()); } void push(const T& t) { payload.push_back(t); } T& front() { return payload[pos]; } void clear() { payload.clear(); pos = 0; } void pop() { pos++; } }; } // namespace internal } // namespace atcoder #endif // ATCODER_INTERNAL_QUEUE_HPP // End include: "internal_queue.hpp" #include #include #include #include namespace atcoder { template struct mf_graph { public: mf_graph() : _n(0) {} mf_graph(int n) : _n(n), g(n) {} int add_edge(int from, int to, Cap cap) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); assert(0 <= cap); int m = int(pos.size()); pos.push_back({from, int(g[from].size())}); int from_id = int(g[from].size()); int to_id = int(g[to].size()); if (from == to) to_id++; g[from].push_back(_edge{to, to_id, cap}); g[to].push_back(_edge{from, from_id, 0}); return m; } struct edge { int from, to; Cap cap, flow; }; edge get_edge(int i) { int m = int(pos.size()); assert(0 <= i && i < m); auto _e = g[pos[i].first][pos[i].second]; auto _re = g[_e.to][_e.rev]; return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap}; } std::vector edges() { int m = int(pos.size()); std::vector result; for (int i = 0; i < m; i++) { result.push_back(get_edge(i)); } return result; } void change_edge(int i, Cap new_cap, Cap new_flow) { int m = int(pos.size()); assert(0 <= i && i < m); assert(0 <= new_flow && new_flow <= new_cap); auto& _e = g[pos[i].first][pos[i].second]; auto& _re = g[_e.to][_e.rev]; _e.cap = new_cap - new_flow; _re.cap = new_flow; } Cap flow(int s, int t) { return flow(s, t, std::numeric_limits::max()); } Cap flow(int s, int t, Cap flow_limit) { assert(0 <= s && s < _n); assert(0 <= t && t < _n); assert(s != t); std::vector level(_n), iter(_n); internal::simple_queue que; auto bfs = [&]() { std::fill(level.begin(), level.end(), -1); level[s] = 0; que.clear(); que.push(s); while (!que.empty()) { int v = que.front(); que.pop(); for (auto e : g[v]) { if (e.cap == 0 || level[e.to] >= 0) continue; level[e.to] = level[v] + 1; if (e.to == t) return; que.push(e.to); } } }; auto dfs = [&](auto self, int v, Cap up) { if (v == s) return up; Cap res = 0; int level_v = level[v]; for (int& i = iter[v]; i < int(g[v].size()); i++) { _edge& e = g[v][i]; if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue; Cap d = self(self, e.to, std::min(up - res, g[e.to][e.rev].cap)); if (d <= 0) continue; g[v][i].cap += d; g[e.to][e.rev].cap -= d; res += d; if (res == up) break; } return res; }; Cap flow = 0; while (flow < flow_limit) { bfs(); if (level[t] == -1) break; std::fill(iter.begin(), iter.end(), 0); while (flow < flow_limit) { Cap f = dfs(dfs, t, flow_limit - flow); if (!f) break; flow += f; } } return flow; } std::vector min_cut(int s) { std::vector visited(_n); internal::simple_queue que; que.push(s); while (!que.empty()) { int p = que.front(); que.pop(); visited[p] = true; for (auto e : g[p]) { if (e.cap && !visited[e.to]) { visited[e.to] = true; que.push(e.to); } } } return visited; } private: int _n; struct _edge { int to, rev; Cap cap; }; std::vector> pos; std::vector> g; }; } // namespace atcoder #endif // ATCODER_MAXFLOW_HPP // End include: "../../atcoder/maxflow.hpp" void yamada::solve() { inl(N); const ll M=5000; vl cnt(M+1); rep(i,N){ inl(a); cnt[a]++; } auto check=[&](ll m)->bool{ atcoder::mf_graph g(M+m+2); ll st=M+m; ll go=st+1; rep(u,M)if(cnt[u+1])g.add_edge(st,u,cnt[u+1]); rep(j,1,m+1){ ll v=M+j-1; rep(i,j,M+1,j){ /* out("i,j:",i,j); */ ll u=i-1; g.add_edge(u,v,1); } g.add_edge(v,go,1); } ll f=g.flow(st,go); /* out(f,m); */ return f==m; }; out(bisect(1LL,N+1,check)-1); }