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:warning: sorted_set
(competitive/data_structure/sorted_set.hpp)

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#pragma once
#include "competitive/std/std.hpp"
template<typename T> struct SortedSet {
    protected:
    static const int BUCKET_RATIO = 50;
    static const int REBUILD_RATIO = 170;

    public:
    vector<vector<T>> a;
    protected:
    int _sz;
    void build(const vector<T> &ai) {
        _sz = sz(ai);
        int bucket_size = max<int>(sqrtll(_sz / BUCKET_RATIO), 1);
        a = vector<vector<T>>(bucket_size);
        rep(i, bucket_size) {
            ll s = _sz * i / bucket_size;
            ll t = min<int>(_sz * (i+1) / bucket_size, _sz);
            rep(j, s, t) a[i].push_back(ai[j]);
        }
    }
    void build() {
        vector<T> ai;
        rep(i, sz(a)) rep(j, sz(a[i])) ai.push_back(a[i][j]);
        build(ai);
    }
    int find_bucket(T x) {
        if (sz(a) == 0) return 0;
        rep(i, sz(a)) {
            if (x <= a[i].back()) return i;
        }
        return sz(a) - 1;
    }

    struct Iterator {
        SortedSet<T>& ss;
        int p1, p2;
        Iterator() = delete;
        Iterator(SortedSet<T>& _ss, int _p1, int _p2) : ss(_ss), p1(_p1), p2(_p2) {}
        const T& operator*() const { return ss.a[p1][p2]; }
        Iterator& operator++() {
            assert(p1 != sz(ss.a));
            p2++;
            if (p2 == sz(ss.a[p1])) {p1++; p2 = 0;}
            return *this;
        }
        Iterator& operator--() {
            assert(p1 != 0 || p2 != 0);
            p2--;
            if(p2 < 0) {p1--; p2 = sz(ss.a[p1]) - 1;}
            return *this;
        }
        Iterator operator++(int) { Iterator iter(*this); ++(*this); return iter;}
        Iterator operator--(int) { Iterator iter(*this); --(*this); return iter;}
        Iterator& operator+=(int rhs) {
            p2 += rhs;
            while (p1 < sz(ss.a) && p2 >= sz(ss.a[p1])) { p2 -= sz(ss.a[p1++]); }
            return *this;
        }
        Iterator& operator-=(int rhs) {
            p2 -= rhs;
            while (p1 >= 0 && p2 < 0) { p2 += sz(ss.a[--p1]); }
            return *this;
        }
        friend Iterator operator+(const Iterator& iter, int x) { return Iterator(iter) += x; }
        friend Iterator operator+(int x, const Iterator& iter) { return Iterator(iter) += x; }
        friend Iterator operator-(const Iterator& iter, int x) { return Iterator(iter) -= x; }
        friend Iterator operator-(int x, const Iterator& iter) { return Iterator(iter) -= x; }
        friend int operator-(const Iterator& lhs, const Iterator& rhs) {
            int rev = 0;
            int lp1 = lhs.p1;
            int lp2 = lhs.p2;
            while (rhs.p1 > lp1) { lp2 -= sz(lhs.ss.a[lp1++]); }
            while (rhs.p1 < lp1) { lp2 += sz(lhs.ss.a[--lp1]); }
            return lp2 - rhs.p2;
        }
        bool operator==(const Iterator& iter) { return this->p1 == iter.p1 && this->p2 == iter.p2; }
        bool operator!=(const Iterator& iter) { return !(*this == iter); }
        Iterator& operator=(const Iterator& iter) { ss = iter.ss; p1 = iter.p1; p2 = iter.p2; return *this; }
    };

    public:
    SortedSet() = default;
    template<typename Iterable>
    explicit SortedSet(const Iterable& _a) : _sz(sz(_a)) {
        vector<T> ai(_sz);
        auto iter = _a.begin();
        rep(i, _sz) ai[i] = *iter++;
        sort(all(ai));
        uniq(ai);
        build(ai);
    };
    explicit SortedSet(int n) : _sz(n) {
        vector<T> ai(n);
        build(ai);
    }
    explicit SortedSet(ll n) : _sz(n) {
        vector<T> ai(n);
        build(ai);
    }
    template<typename Iterator>
    SortedSet(const Iterator& begin, const Iterator end) {
        vector<T> ai;
        auto iter = begin;
        while(iter != end) ai.push_back(*iter++);
        size = sz(ai);
        sort(all(ai));
        build(ai);
    };

    int size() const {return _sz;}
    Iterator begin() {return Iterator(*this, 0, 0);}
    Iterator end() {return Iterator(*this, sz(a), 0);}

    bool insert(T x) {
        if (_sz == 0) {
            a = {{x}};
            _sz++;
            return true;
        }
        int pos = find_bucket(x);
        auto iter = std::lower_bound(all(a[pos]), x);
        if (iter != a[pos].end() && *iter == x) return false;
        a[pos].insert(iter, x);
        _sz++;
        if (sz(a[pos]) > sz(a) * REBUILD_RATIO) build();
        return true;
    }

    bool erase(T x) {
        if (_sz == 0) return false;
        int pos = find_bucket(x);
        auto iter = std::lower_bound(all(a[pos]), x);
        if (iter == a[pos].end() && *iter != x) return false;
        a[pos].erase(iter);
        _sz--;
        if (sz(a[pos]) == 0) build();
        return true;
    }

    bool contains(T x) {
        if (_sz == 0) return false;
        int pos = find_bucket(x);
        auto iter = lower_bound(all(a[pos]), x);
        return iter != a[pos].end() && *iter == x;
    }

    T operator[](int x) {
        assert(0 <= x && x < _sz);
        rep(i, sz(a)) {
            if (x < sz(a[i])) return a[i][x];
            x -= sz(a[i]);
        }
        return -1;
    }
    Iterator lower_bound(T x) {
        rep(i, sz(a)) {
            if (a[i].back() >= x) {
                auto iter = std::lower_bound(all(a[i]), x);
                return Iterator(*this, i, distance(a[i].begin(), iter));
            }
        }
        return end();
    }
    Iterator upper_bound(T x) {
        rep(i, sz(a)) {
            if (a[i].back() > x) {
                auto iter = std::upper_bound(all(a[i]), x);
                return Iterator(*this, i, distance(a[i].begin(), iter));
            }
        }
        return end();
    }
};
template<typename T> struct SortedMultiSet : public SortedSet<T> {
    using SortedSet<T>::SortedSet;
    template<typename Iterable>
    explicit SortedMultiSet(const Iterable& _a) {
        SortedSet<T>::_sz = sz(_a);
        vector<T> ai(SortedSet<T>::_sz);
        auto iter = _a.begin();
        rep(i, SortedSet<T>::_sz) ai[i] = *iter++;
        sort(all(ai));
        SortedSet<T>::build(ai);
    };

    bool insert(T x) {
        if (SortedSet<T>::_sz == 0) {
            SortedSet<T>::a = {{x}};
            SortedSet<T>::_sz++;
            return true;
        }
        int pos = SortedSet<T>::find_bucket(x);
        auto iter = std::lower_bound(all(SortedSet<T>::a[pos]), x);
        SortedSet<T>::a[pos].insert(iter, x);
        SortedSet<T>::_sz++;
        if (sz(SortedSet<T>::a[pos]) > sz(SortedSet<T>::a) * SortedSet<T>::REBUILD_RATIO) SortedSet<T>::build();
        return true;
    }
};
template <typename T> ostream &operator<<(ostream &os, SortedSet<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, SortedMultiSet<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
/**
 * @brief sorted_set
 * @docs docs/data_structure/sorted_set.md
 */
#line 2 "competitive/std/std.hpp"
#include <bits/stdc++.h>
#ifndef LOCAL_TEST
#pragma GCC target ("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#endif // LOCAL_TEST
using namespace std;
// 型名の短縮
using ll = long long;
using pii = pair<int, int>; using pll = pair<ll, ll>;
using vi = vector<int>;  using vvi = vector<vi>; using vvvi = vector<vvi>;
using vl = vector<ll>;  using vvl = vector<vl>; using vvvl = vector<vvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
using vs = vector<string>; using vvs = vector<vector<string>>; using vvvs = vector<vector<vector<string>>>;
template<typename T> vector<vector<T>> vv(int h, int w, T val = T()) { return vector(h, vector<T>(w, val)); }
template<typename T> vector<vector<vector<T>>> vvv(int h1, int h2, int h3, T val = T()) { return vector(h1, vector(h2, vector<T>(h3, val))); }
template<typename T> vector<vector<vector<vector<T>>>> vvvv(int h1, int h2, int h3, int h4, T val = T()) { return vector(h1, vector(h2, vector(h3, vector<T>(h4, val)))); }
template <class T> using priority_queue_min = priority_queue<T, vector<T>, greater<T>>;
// 定数の定義
constexpr double PI = 3.14159265358979323;
constexpr int INF = 100100111; constexpr ll INFL = 3300300300300300491LL;
float EPS = 1e-8; double EPSL = 1e-16;
template<typename T> bool eq(const T x, const T y) { return x == y; }
template<> bool eq<double>(const double x, const double y) { return abs(x - y) < EPSL; }
template<> bool eq<float>(const float x, const float y) { return abs(x - y) < EPS; }
template<typename T> bool neq(const T x, const T y) { return !(eq<T>(x, y)); }
template<typename T> bool ge(const T x, const T y) { return (eq<T>(x, y) || (x > y)); }
template<typename T> bool le(const T x, const T y) { return (eq<T>(x, y) || (x < y)); }
template<typename T> bool gt(const T x, const T y) { return !(le<T>(x, y)); }
template<typename T> bool lt(const T x, const T y) { return !(ge<T>(x, y)); }
constexpr int MODINT998244353 = 998244353;
constexpr int MODINT1000000007 = 1000000007;
// 入出力高速化
struct Nyan { Nyan() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } nyan;
// 汎用マクロの定義
#define all(a) (a).begin(), (a).end()
#define sz(x) ((ll)(x).size())
#define rep1(n) for(ll dummy_iter = 0LL; dummy_iter < n; ++dummy_iter) // 0 から n-1 まで昇順
#define rep2(i, n) for(ll i = 0LL, i##_counter = 0LL; i##_counter < ll(n); ++(i##_counter), (i) = i##_counter) // 0 から n-1 まで昇順
#define rep3(i, s, t) for(ll i = ll(s), i##_counter = ll(s); i##_counter < ll(t); ++(i##_counter), (i) = (i##_counter)) // s から t まで昇順
#define rep4(i, s, t, step) for(ll i##_counter = step > 0 ? ll(s) : -ll(s), i##_end = step > 0 ? ll(t) : -ll(t), i##_step = abs(step), i = ll(s); i##_counter < i##_end; i##_counter += i##_step, i = step > 0 ? i##_counter : -i##_counter) // s から t まで stepずつ
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define repe(a, v) for(auto& a : (v)) // v の全要素（変更可能）
#define smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod
#define sdiv(n, m) (((n) - smod(n, m)) / (m)) // 非負div
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去
int Yes(bool b=true) { cout << (b ? "Yes\n" : "No\n"); return 0; };
int YES(bool b=true) { cout << (b ? "YES\n" : "NO\n"); return 0; };
int No(bool b=true) {return Yes(!b);};
int NO(bool b=true) {return YES(!b);};
template<typename T, size_t N> T max(array<T, N>& a) { return *max_element(all(a)); };
template<typename T, size_t N> T min(array<T, N>& a) { return *min_element(all(a)); };
template<typename T> T max(vector<T>& a) { return *max_element(all(a)); };
template<typename T> T min(vector<T>& a) { return *min_element(all(a)); };
template<typename T> vector<T> vec_slice(const vector<T>& a, int l, int r) { vector<T> rev; rep(i, l, r) rev.push_back(a[i]); return rev; };
template<typename T> T sum(vector<T>& a, T zero = T(0)) { T rev = zero; rep(i, sz(a)) rev += a[i]; return rev; };
template<typename T> bool in_range(const T& val, const T& s, const T& t) { return s <= val && val < t; };

template <class T> inline vector<T>& operator--(vector<T>& v) { repe(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repe(x, v) ++x; return v; }

// modでのpow
ll powm(ll a, ll n, ll mod=INFL) {
    ll res = 1;
    while (n > 0) {
        if (n & 1) res = (res * a) % mod;
        if (n > 1) a = (a * a) % mod;
        n >>= 1;
    }
    return res;
}
// 整数Sqrt
ll sqrtll(ll x) {
    assert(x >= 0);
    ll rev = sqrt(x);
    while(rev * rev > x) --rev;
    while((rev+1) * (rev+1)<=x) ++rev;
    return rev;
}
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新（更新されたら true を返す）
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新（更新されたら true を返す）
int digit(ll x, int d=10) { int rev=0; while (x > 0) { rev++; x /= d;}; return rev; } // xのd進数桁数
/**
 * @brief std.hpp
 * @docs docs/std/std.md
 */
#line 3 "competitive/data_structure/sorted_set.hpp"
template<typename T> struct SortedSet {
    protected:
    static const int BUCKET_RATIO = 50;
    static const int REBUILD_RATIO = 170;

    public:
    vector<vector<T>> a;
    protected:
    int _sz;
    void build(const vector<T> &ai) {
        _sz = sz(ai);
        int bucket_size = max<int>(sqrtll(_sz / BUCKET_RATIO), 1);
        a = vector<vector<T>>(bucket_size);
        rep(i, bucket_size) {
            ll s = _sz * i / bucket_size;
            ll t = min<int>(_sz * (i+1) / bucket_size, _sz);
            rep(j, s, t) a[i].push_back(ai[j]);
        }
    }
    void build() {
        vector<T> ai;
        rep(i, sz(a)) rep(j, sz(a[i])) ai.push_back(a[i][j]);
        build(ai);
    }
    int find_bucket(T x) {
        if (sz(a) == 0) return 0;
        rep(i, sz(a)) {
            if (x <= a[i].back()) return i;
        }
        return sz(a) - 1;
    }

    struct Iterator {
        SortedSet<T>& ss;
        int p1, p2;
        Iterator() = delete;
        Iterator(SortedSet<T>& _ss, int _p1, int _p2) : ss(_ss), p1(_p1), p2(_p2) {}
        const T& operator*() const { return ss.a[p1][p2]; }
        Iterator& operator++() {
            assert(p1 != sz(ss.a));
            p2++;
            if (p2 == sz(ss.a[p1])) {p1++; p2 = 0;}
            return *this;
        }
        Iterator& operator--() {
            assert(p1 != 0 || p2 != 0);
            p2--;
            if(p2 < 0) {p1--; p2 = sz(ss.a[p1]) - 1;}
            return *this;
        }
        Iterator operator++(int) { Iterator iter(*this); ++(*this); return iter;}
        Iterator operator--(int) { Iterator iter(*this); --(*this); return iter;}
        Iterator& operator+=(int rhs) {
            p2 += rhs;
            while (p1 < sz(ss.a) && p2 >= sz(ss.a[p1])) { p2 -= sz(ss.a[p1++]); }
            return *this;
        }
        Iterator& operator-=(int rhs) {
            p2 -= rhs;
            while (p1 >= 0 && p2 < 0) { p2 += sz(ss.a[--p1]); }
            return *this;
        }
        friend Iterator operator+(const Iterator& iter, int x) { return Iterator(iter) += x; }
        friend Iterator operator+(int x, const Iterator& iter) { return Iterator(iter) += x; }
        friend Iterator operator-(const Iterator& iter, int x) { return Iterator(iter) -= x; }
        friend Iterator operator-(int x, const Iterator& iter) { return Iterator(iter) -= x; }
        friend int operator-(const Iterator& lhs, const Iterator& rhs) {
            int rev = 0;
            int lp1 = lhs.p1;
            int lp2 = lhs.p2;
            while (rhs.p1 > lp1) { lp2 -= sz(lhs.ss.a[lp1++]); }
            while (rhs.p1 < lp1) { lp2 += sz(lhs.ss.a[--lp1]); }
            return lp2 - rhs.p2;
        }
        bool operator==(const Iterator& iter) { return this->p1 == iter.p1 && this->p2 == iter.p2; }
        bool operator!=(const Iterator& iter) { return !(*this == iter); }
        Iterator& operator=(const Iterator& iter) { ss = iter.ss; p1 = iter.p1; p2 = iter.p2; return *this; }
    };

    public:
    SortedSet() = default;
    template<typename Iterable>
    explicit SortedSet(const Iterable& _a) : _sz(sz(_a)) {
        vector<T> ai(_sz);
        auto iter = _a.begin();
        rep(i, _sz) ai[i] = *iter++;
        sort(all(ai));
        uniq(ai);
        build(ai);
    };
    explicit SortedSet(int n) : _sz(n) {
        vector<T> ai(n);
        build(ai);
    }
    explicit SortedSet(ll n) : _sz(n) {
        vector<T> ai(n);
        build(ai);
    }
    template<typename Iterator>
    SortedSet(const Iterator& begin, const Iterator end) {
        vector<T> ai;
        auto iter = begin;
        while(iter != end) ai.push_back(*iter++);
        size = sz(ai);
        sort(all(ai));
        build(ai);
    };

    int size() const {return _sz;}
    Iterator begin() {return Iterator(*this, 0, 0);}
    Iterator end() {return Iterator(*this, sz(a), 0);}

    bool insert(T x) {
        if (_sz == 0) {
            a = {{x}};
            _sz++;
            return true;
        }
        int pos = find_bucket(x);
        auto iter = std::lower_bound(all(a[pos]), x);
        if (iter != a[pos].end() && *iter == x) return false;
        a[pos].insert(iter, x);
        _sz++;
        if (sz(a[pos]) > sz(a) * REBUILD_RATIO) build();
        return true;
    }

    bool erase(T x) {
        if (_sz == 0) return false;
        int pos = find_bucket(x);
        auto iter = std::lower_bound(all(a[pos]), x);
        if (iter == a[pos].end() && *iter != x) return false;
        a[pos].erase(iter);
        _sz--;
        if (sz(a[pos]) == 0) build();
        return true;
    }

    bool contains(T x) {
        if (_sz == 0) return false;
        int pos = find_bucket(x);
        auto iter = lower_bound(all(a[pos]), x);
        return iter != a[pos].end() && *iter == x;
    }

    T operator[](int x) {
        assert(0 <= x && x < _sz);
        rep(i, sz(a)) {
            if (x < sz(a[i])) return a[i][x];
            x -= sz(a[i]);
        }
        return -1;
    }
    Iterator lower_bound(T x) {
        rep(i, sz(a)) {
            if (a[i].back() >= x) {
                auto iter = std::lower_bound(all(a[i]), x);
                return Iterator(*this, i, distance(a[i].begin(), iter));
            }
        }
        return end();
    }
    Iterator upper_bound(T x) {
        rep(i, sz(a)) {
            if (a[i].back() > x) {
                auto iter = std::upper_bound(all(a[i]), x);
                return Iterator(*this, i, distance(a[i].begin(), iter));
            }
        }
        return end();
    }
};
template<typename T> struct SortedMultiSet : public SortedSet<T> {
    using SortedSet<T>::SortedSet;
    template<typename Iterable>
    explicit SortedMultiSet(const Iterable& _a) {
        SortedSet<T>::_sz = sz(_a);
        vector<T> ai(SortedSet<T>::_sz);
        auto iter = _a.begin();
        rep(i, SortedSet<T>::_sz) ai[i] = *iter++;
        sort(all(ai));
        SortedSet<T>::build(ai);
    };

    bool insert(T x) {
        if (SortedSet<T>::_sz == 0) {
            SortedSet<T>::a = {{x}};
            SortedSet<T>::_sz++;
            return true;
        }
        int pos = SortedSet<T>::find_bucket(x);
        auto iter = std::lower_bound(all(SortedSet<T>::a[pos]), x);
        SortedSet<T>::a[pos].insert(iter, x);
        SortedSet<T>::_sz++;
        if (sz(SortedSet<T>::a[pos]) > sz(SortedSet<T>::a) * SortedSet<T>::REBUILD_RATIO) SortedSet<T>::build();
        return true;
    }
};
template <typename T> ostream &operator<<(ostream &os, SortedSet<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, SortedMultiSet<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
/**
 * @brief sorted_set
 * @docs docs/data_structure/sorted_set.md
 */
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