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#include "../template.hh"
template<typename T, typename F>
struct ST {
using value_type = T;
using merge_type = F;
const int n;
const T e;
F merge;
vector<T> data;
ST(int sz, T _e, F m) : n{sz}, e{_e}, merge{m}, data(2 * n, e) {}
void build() {
for (int i = n - 1; i; --i)
data[i] = merge(data[i << 1], data[i << 1 | 1]);
}
T query(int l, int r) {
T li = e, ri = e;
for (l += n, r += n; l < r; r >>= 1, l >>= 1) {
if (l & 1) li = merge(li, data[l++]);
if (r & 1) ri = merge(data[--r], ri);
}
return merge(li, ri);
}
void update(int i, T val) {
for (data[i += n] = val; i > 1; i >>= 1)
data[i >> 1] = merge(data[i & ~1], data[i | 1]);
}
};
#line 1 "code/template.cc"
// this line is here for a reason
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> ii;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<vi> vvi;
typedef vector<vii> vvii;
#define fi first
#define se second
#define eb emplace_back
#define pb push_back
#define mp make_pair
#define mt make_tuple
#define endl '\n'
#define ALL(x) (x).begin(), (x).end()
#define RALL(x) (x).rbegin(), (x).rend()
#define SZ(x) (int)(x).size()
#define FOR(a, b, c) for (auto a = (b); (a) < (c); ++(a))
#define F0R(a, b) FOR (a, 0, (b))
template <typename T>
bool ckmin(T& a, const T& b) { return a > b ? a = b, true : false; }
template <typename T>
bool ckmax(T& a, const T& b) { return a < b ? a = b, true : false; }
#ifndef DEBUG
#define DEBUG 0
#endif
#define dout if (DEBUG) cerr
#define dvar(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
#line 2 "code/dataStructures/STIT.cc"
template<typename T, typename F>
struct ST {
using value_type = T;
using merge_type = F;
const int n;
const T e;
F merge;
vector<T> data;
ST(int sz, T _e, F m) : n{sz}, e{_e}, merge{m}, data(2 * n, e) {}
void build() {
for (int i = n - 1; i; --i)
data[i] = merge(data[i << 1], data[i << 1 | 1]);
}
T query(int l, int r) {
T li = e, ri = e;
for (l += n, r += n; l < r; r >>= 1, l >>= 1) {
if (l & 1) li = merge(li, data[l++]);
if (r & 1) ri = merge(data[--r], ri);
}
return merge(li, ri);
}
void update(int i, T val) {
for (data[i += n] = val; i > 1; i >>= 1)
data[i >> 1] = merge(data[i & ~1], data[i | 1]);
}
};