// Copyright © 2022 Youngmin Park. All rights reserved.
//#pragma GCC optimize("O3")
//#pragma GCC target("avx2")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<int>;
using pii = pair<int, int>;
using vpi = vector<pii>;
using pll = pair<ll, ll>;
using vl = vector<ll>;
using vpl = vector<pll>;
using ld = long double;
template <typename T, size_t SZ>
using ar = array<T, SZ>;
template <typename T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define all(v) (v).begin(), (v).end()
#define pb push_back
#define sz(x) (int)(x).size()
#define fi first
#define se second
#define lb lower_bound
#define ub upper_bound
constexpr int INF = 1e9;
constexpr ll LINF = 1e18;
const ld PI = acos((ld)-1.0);
constexpr int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
template <typename T>
constexpr bool ckmin(T &a, const T &b) { return b < a ? a = b, 1 : 0; }
template <typename T>
constexpr bool ckmax(T &a, const T &b) { return b > a ? a = b, 1 : 0; }
template <typename A, typename B>
ostream &operator<<(ostream &os, const pair<A, B> &p)
{
return os << '(' << p.first << ", " << p.second << ')';
}
template <typename T_container, typename T = typename enable_if<!is_same<T_container, string>::value, typename T_container::value_type>::type>
ostream &operator<<(ostream &os, const T_container &v)
{
os << '{';
string sep;
for (const T &x : v)
os << sep << x, sep = ", ";
return os << '}';
}
template <typename T>
ostream &operator<<(ostream &os, const deque<T> &v) {
os << vector<T>(all(v));
return os;
}
template <typename T, typename S, typename C>
ostream &operator<<(ostream &os, priority_queue<T, S, C> pq) {
vector<T> v;
while (sz(pq)) {
v.pb(pq.top());
pq.pop();
}
os << v;
return os;
}
void dbg_out()
{
cerr << "\033[0m" << endl;
}
template <typename Head, typename... Tail>
void dbg_out(Head H, Tail... T)
{
cerr << ' ' << H;
dbg_out(T...);
}
#ifdef LOCAL
#define dbg(...) cerr << "\033[1;35m(" << #__VA_ARGS__ << "):\033[33m", dbg_out(__VA_ARGS__)
#else
#define dbg(...) 42
#endif
inline namespace RecursiveLambda
{
template <typename Fun>
struct y_combinator_result
{
Fun fun_;
template <typename T>
explicit y_combinator_result(T &&fun) : fun_(forward<T>(fun)) {}
template <typename... Args>
decltype(auto) operator()(Args &&...args)
{
return fun_(ref(*this), forward<Args>(args)...);
}
};
template <typename Fun>
decltype(auto) y_combinator(Fun &&fun)
{
return y_combinator_result<decay_t<Fun>>(forward<Fun>(fun));
}
};
class Range {
struct Iter
{
int iter;
constexpr Iter(int it) noexcept : iter(it) {}
constexpr void operator++() noexcept { iter++; }
constexpr bool operator!=(const Iter &other) const noexcept { return iter != other.iter; }
constexpr int operator*() const noexcept { return iter; }
};
const Iter first, last;
public:
explicit constexpr Range(const int f, const int l) noexcept : first(f), last(max(f, l)) {}
constexpr Iter begin() const noexcept { return first; }
constexpr Iter end() const noexcept { return last; }
};
constexpr Range rep(const int l, const int r) noexcept { return Range(l, r); }
constexpr Range rep(const int n) noexcept { return Range(0, n); }
class ReversedRange {
struct Iter {
int itr;
constexpr Iter(const int pos) noexcept : itr(pos) {}
constexpr void operator++() noexcept { --itr; }
constexpr bool operator!=(const Iter& other) const noexcept { return itr != other.itr; }
constexpr int operator*() const noexcept { return itr; }
};
const Iter first, last;
public:
explicit constexpr ReversedRange(const int f, const int l) noexcept
: first(l - 1), last(min(f, l) - 1) {}
constexpr Iter begin() const noexcept { return first; }
constexpr Iter end() const noexcept { return last; }
};
constexpr ReversedRange per(const int l, const int r) noexcept { return ReversedRange(l, r); }
constexpr ReversedRange per(const int n) noexcept { return ReversedRange(0, n); }
/**
* Description: Generic segment tree with lazy propagation
* Source: Inspired by Jiangly - https://codeforces.com//contest/1672/submission/154766851
* Verification: https://cses.fi/problemset/task/1735
* Time Complexity: O(n) build, O(log n) per update/query
*/
template<typename T, typename U, typename Merge = plus<T>>
struct LazySegTree{
int sz;
const Merge merge;
vector<T> t;
vector<U> lazy;
LazySegTree(int n) : merge(Merge()) {
sz = 1;
while (sz < n) sz *= 2;
t.assign(sz * 2, {0, 0});
lazy.resize(sz * 2);
}
void build(vector<T> &vec, int x, int l, int r)
{
if (r - l == 1)
{
if (l < (int)vec.size())
t[x] = vec[l];
return;
}
int mid = (l + r) / 2;
build(vec, 2 * x + 1, l, mid);
build(vec, 2 * x + 2, mid, r);
t[x] = merge(t[2 * x + 1], t[2 * x + 2]);
}
void build(vector<T> &vec)
{
build(vec, 0, 0, sz);
}
void upd(int i, const T& v, int x, int l, int r)
{
if (r - l == 1)
{
t[x] = v;
return;
}
int mid = (l + r) / 2;
if (i < mid)
upd(i, v, 2 * x + 1, l, mid);
else
upd(i, v, 2 * x + 2, mid, r);
t[x] = merge(t[2 * x + 1], t[2 * x + 2]);
}
void upd(int i, const T& v)
{
upd(i, v, 0, 0, sz);
}
void rangeUpd(int l, int r, U v, int x, int lx, int rx) {
push(x, lx, rx);
if (lx >= r || rx <= l) return;
if (lx >= l && rx <= r) {
lazy[x] = lazyOnLazy(lazy[x], v);
push(x, lx, rx);
return;
}
int mid = (lx + rx) / 2;
rangeUpd(l, r, v, 2 * x + 1, lx, mid);
rangeUpd(l, r, v, 2 * x + 2, mid, rx);
t[x] = merge(t[2 * x + 1], t[2 * x + 2]);
}
void rangeUpd(int l, int r, U v) {
rangeUpd(l, r, v, 0, 0, sz);
}
T query(int l, int r, int x, int lx, int rx)
{
push(x, lx, rx);
if (lx >= r || rx <= l)
return T();
if (lx >= l && rx <= r)
return t[x];
int mid = (lx + rx) / 2;
T a = query(l, r, 2 * x + 1, lx, mid);
T b = query(l, r, 2 * x + 2, mid, rx);
return merge(a, b);
}
T query(int l, int r)
{
return query(l, r, 0, 0, sz);
}
void push(int x, int l, int r) {
if (lazy[x] == U()) return;
t[x] = lazyOnVal(t[x], lazy[x], l, r);
if (r - l > 1) {
lazy[2 * x + 1] = lazyOnLazy(lazy[2 * x + 1], lazy[x]);
lazy[2 * x + 2] = lazyOnLazy(lazy[2 * x + 2], lazy[x]);
}
lazy[x] = U();
}
U lazyOnLazy(U oldV, U newV) {
return oldV + newV;
}
T lazyOnVal(T val, U la, int l, int r) {
if (la.lo >= val.ma) {
return {la.lo, la.lo};
}else if (la.hi <= val.mi) {
return {la.hi, la.hi};
}
return {max(val.mi, la.lo), min(val.ma, la.hi)};
}
};
struct MinMax {
int mi, ma;
MinMax(int mi_ = INF, int ma_ = 0) : mi(mi_), ma(ma_) {}
MinMax operator+(const MinMax& other) const {
return {
min(mi, other.mi),
max(ma, other.ma)
};
}
};
const MinMax ZERO = {0, 0};
struct Lazy {
int lo, hi;
Lazy(int lo_ = 0, int hi_ = INF) : lo(lo_), hi(hi_) {}
Lazy operator+(const Lazy& other) const {
if (other.lo >= hi) {
return {other.lo, other.lo};
}else if (other.hi <= lo) return {other.hi, other.hi};
return {max(lo, other.lo), min(hi, other.hi)};
}
bool operator==(const Lazy& other) const {
return lo == other.lo && hi == other.hi;
}
};
void buildWall(int n, int k, int op[], int left[], int right[], int height[], int finalHeight[]) {
LazySegTree<MinMax, Lazy> st(n);
for (int i : rep(k)) {
Lazy l{};
if (op[i] == 1) {
l.lo = height[i];
}else l.hi = height[i];
st.rangeUpd(left[i], right[i] + 1, l);
}
for (int i : rep(n)) {
finalHeight[i] = st.query(i, i + 1).mi;
}
}
// void solve()
// {
// }
// int main()
// {
// cin.tie(0)->sync_with_stdio(0);
// cin.exceptions(cin.failbit);
// int testcase = 1;
// cin >> testcase;
// while (testcase--)
// {
// solve();
// }
// #ifdef LOCAL
// cerr << "Time elapsed: " << 1.0 * (double)clock() / CLOCKS_PER_SEC << " s.\n";
// #endif
// }
