#include "wall.h"
#include <bits/stdc++.h>
using namespace std;
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template<typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T, typename U> using ordered_map = tree<T, U, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<ll> vll;
#define FOR(i,j,k,in) for(int i=(j); i < (k);i+=in)
#define FORD(i,j,k,in) for(int i=(j); i >=(k);i-=in)
#define REP(i,b) FOR(i,0,b,1)
#define REPD(i,b) FORD(i,b,0,1)
#define pb push_back
#define mp make_pair
#define ff first
#define ss second
#define all(x) begin(x), end(x)
#define MANY_TESTS int tcase; cin >> tcase; while(tcase--)
const double EPS = 1e-9;
const int MOD = 1e9+7;
const ll INFF = 1e18;
const int INF = 1e9;
const ld PI = acos((ld)-1);
const vi dy = {1, 0, -1, 0, -1, 1, 1, -1};
const vi dx = {0, 1, 0, -1, -1, 1, -1, 1};
void DBG(){cout << "]" << endl;}
template<typename T, typename ...U> void DBG(const T& head, const U... args){ cout << head << "; "; DBG(args...); }
#define dbg(...) cout << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__);
#define chk() cout << "Check at line(" << __LINE__ << ") hit." << endl;
template<class T, unsigned int U>
ostream& operator<<(ostream& out, const array<T, U> &v){out << "["; REP(i, U) out << v[i] << ", "; out << "]"; return out;}
template <class T, class U>
ostream& operator<<(ostream& out, const pair<T, U> &par) {out << "[" << par.first << ";" << par.second << "]"; return out;}
template <class T>
ostream& operator<<(ostream& out, const set<T> &cont) { out << "{"; for( const auto &x:cont) out << x << ", "; out << "}"; return out; }
template <class T, class U>
ostream& operator<<(ostream& out, const map<T, U> &cont) {out << "{"; for( const auto &x:cont) out << x << ", "; out << "}"; return out; }
template<class T>
ostream& operator<<(ostream& out, const vector<T> &v){ out << "["; REP(i, v.size()) out << v[i] << ", "; out << "]"; return out;}
template<class T>
istream& operator>>(istream& in, vector<T> &v){ for(auto &x : v) in >> x; return in; }
// on segtree[TIME] is operation information
// I toggle operations as I scanline
int n, k;
vector<int> op, height;
struct node{
bool Sop = false;
int S = -1, D = INF, I = -1;
void apply(int _D, int _I){
Sop = false; D = _D; I = _I;
}
};
struct segtree{
node comb(const node& a, const node& b){
node res;
if(b.Sop){res = b; return res;}
res = a; // will be overwritten
if(res.Sop){
res.S = max(res.S, b.I);
res.S = min(res.S, b.D);
return res;
}
res.I = max(res.I, b.I);
res.D = min(res.D, b.D);
if(res.D <= res.I){
res.Sop = true;
res.S = ((res.I == b.I) ? res.I : res.D);
}
return res;
}
int n;
vector<node> tree;
segtree(int _n){
n = 1; while(n < _n) n*= 2;
tree.resize(2 * n);
}
void upd(int pos, int state){
int _D, _I;
if(state == 1){
if(op[pos] == 1){_I = height[pos]; _D = INF;}
else{_I = -1; _D = height[pos];}
}
else{
_D = INF;
_I = -1;
}
pos += n;
tree[pos].apply(_D, _I);
for(int i = pos / 2; i > 0; i/=2)
tree[i] = comb(tree[i<<1], tree[i<<1|1]);
}
int query(int value){ //what it gets transformed to
if(tree[1].Sop)
return tree[1].S;
value = max(value, tree[1].I);
value = min(value, tree[1].D);
return value;
}
};
void buildWall(int N, int K, int OP[], int LEFT[], int RIGHT[], int HEIGHT[], int finalHeight[]){
n = N; k = K;
op.resize(K); height.resize(K);
REP(i, k){
op[i] = OP[i]; height[i] = HEIGHT[i];
}
segtree st(k);
vector<array<int, 2>> ev(k);
REP(i, k) ev[i] = {LEFT[i], i};
sort(all(ev));
int pp = 0;
set<pair<int, int>> open;
REP(i, n){
while(pp < ev.size() && ev[pp][0] <= i){
st.upd(ev[pp][1], 1);
open.insert({RIGHT[ev[pp][1]], ev[pp][1]});
pp++;
}
while(!open.empty() && open.begin()->ff < i){
st.upd(open.begin()->ss, 0);
open.erase(open.begin());
}
finalHeight[i] = st.query(0);
}
return;
}
