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:heavy_check_mark: セグメント木（ラッパー）
(competitive/data_structure/segtree.hpp)

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#pragma once
#include "atcoder/segtree.hpp"
#include "competitive/std/std.hpp"
template <typename S, S (*op)(S, S), S (*e)()> std::ostream& operator<<(std::ostream& os, const atcoder::segtree<S, op, e> seg) {
    int n = seg.n();
    rep(i, n) { os << seg.get(i); if (i != n-1) os << " "; }
    return os;
};
namespace segtree_internal {
    template<typename T> T op_max(T x, T y) { return x > y? x : y; }
    template<typename T> T op_min(T x, T y) { return x < y? x : y; }
    template<typename T> T op_add(T x, T y) { return x + y; }

    template<typename T> T e_max() { return -INFL; }
    template<> int e_max() { return -INF; }
    template<typename T> T e_min() { return INFL; }
    template<> int e_min() { return INF; }
    template<typename T> T e_add() { return 0; }
}
template<class S, S (*op)(S,S), S(*e)()> using segtree = atcoder::segtree<S, op, e>;
template<typename T> using seg_add = segtree<T, segtree_internal::op_add<T>, segtree_internal::e_add<T>>;
template<typename T> using seg_max = segtree<T, segtree_internal::op_max<T>, segtree_internal::e_max<T>>;
template<typename T> using seg_min = segtree<T, segtree_internal::op_min<T>, segtree_internal::e_min<T>>;
/**
 * @brief セグメント木（ラッパー）
 * @docs docs/data_structure/segtree.md
 */
#line 2 "atcoder/segtree.hpp"
#include <algorithm>
#include <cassert>
#include <vector>

#line 2 "atcoder/internal_bit.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
constexpr int bsf_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

}  // namespace internal

}  // namespace atcoder
#line 7 "atcoder/segtree.hpp"

namespace atcoder {

template <class S, S (*_op)(S, S), S (*_e)()> struct segtree {
  public:
    S (*op)(S, S) = _op;
    S (*e)() = _e;
    segtree() : segtree(0) {}
    explicit segtree(const std::vector<S>& v) : _n(int(v.size())) {
        log = internal::ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }
    explicit segtree(int n) : segtree(std::vector<S>(n, _e())) {}

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    void add(int p, S x) {
        assert(0 <= p && p < _n);
        (*this).set(p, (*this).get(p) + x);
    }

    S get(int p) const {
        assert(0 <= p && p < _n);
        return d[p + size];
    }

    S prod(int l, int r) const {
        assert(0 <= l && l <= r && r <= _n);
        S sml = e(), smr = e();
        l += size;
        r += size;

        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }

    S all_prod() const { return d[1]; }

    template <bool (*f)(S)> int max_right(int l) const {
        return max_right(l, [](S x) { return f(x); });
    }
    template <class F> int max_right(int l, F f) const {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if (l == _n) return _n;
        l += size;
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, d[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (f(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*f)(S)> int min_left(int r) const {
        return min_left(r, [](S x) { return f(x); });
    }
    template <class F> int min_left(int r, F f) const {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if (r == 0) return 0;
        r += size;
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(d[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (f(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

    int n() const {return (*this)._n;}

  private:
    int _n, size, log;
    std::vector<S> d;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};

}  // namespace atcoder
#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 4 "competitive/data_structure/segtree.hpp"
template <typename S, S (*op)(S, S), S (*e)()> std::ostream& operator<<(std::ostream& os, const atcoder::segtree<S, op, e> seg) {
    int n = seg.n();
    rep(i, n) { os << seg.get(i); if (i != n-1) os << " "; }
    return os;
};
namespace segtree_internal {
    template<typename T> T op_max(T x, T y) { return x > y? x : y; }
    template<typename T> T op_min(T x, T y) { return x < y? x : y; }
    template<typename T> T op_add(T x, T y) { return x + y; }

    template<typename T> T e_max() { return -INFL; }
    template<> int e_max() { return -INF; }
    template<typename T> T e_min() { return INFL; }
    template<> int e_min() { return INF; }
    template<typename T> T e_add() { return 0; }
}
template<class S, S (*op)(S,S), S(*e)()> using segtree = atcoder::segtree<S, op, e>;
template<typename T> using seg_add = segtree<T, segtree_internal::op_add<T>, segtree_internal::e_add<T>>;
template<typename T> using seg_max = segtree<T, segtree_internal::op_max<T>, segtree_internal::e_max<T>>;
template<typename T> using seg_min = segtree<T, segtree_internal::op_min<T>, segtree_internal::e_min<T>>;
/**
 * @brief セグメント木（ラッパー）
 * @docs docs/data_structure/segtree.md
 */
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