#include <bits/stdc++.h>
#include "wall.h"
using namespace std;
using ll = long long;
using ld = long double;
using db = double;
using str = string; // yay python!
using pi = pair<int,int>;
using pl = pair<ll,ll>;
using pd = pair<db,db>;
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>;
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
#define tcT template<class T
// ^ lol this makes everything look weird but I'll try it
tcT> using V = vector<T>;
tcT, size_t SZ> using AR = array<T,SZ>;
// pairs
#define mp make_pair
#define f first
#define s second
// vectors
#define sz(x) (int)(x).size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pf push_front
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
// loops
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
const ll N = 4e7;
class SegmentTree {
const ll inf = 1e18;
int n, n0;
ll max_v[4*N], smax_v[4*N], max_c[4*N];
ll min_v[4*N], smin_v[4*N], min_c[4*N];
ll sum[4*N];
void update_node_max(int k, ll x) {
sum[k] += (x - max_v[k]) * max_c[k];
if(max_v[k] == min_v[k]) {
max_v[k] = min_v[k] = x;
} else if(max_v[k] == smin_v[k]) {
max_v[k] = smin_v[k] = x;
} else {
max_v[k] = x;
}
}
void update_node_min(int k, ll x) {
sum[k] += (x - min_v[k]) * min_c[k];
if(max_v[k] == min_v[k]) {
max_v[k] = min_v[k] = x;
} else if(smax_v[k] == min_v[k]) {
min_v[k] = smax_v[k] = x;
} else {
min_v[k] = x;
}
}
void push(int k) {
if(max_v[k] < max_v[2*k+1]) {
update_node_max(2*k+1, max_v[k]);
}
if(min_v[2*k+1] < min_v[k]) {
update_node_min(2*k+1, min_v[k]);
}
if(max_v[k] < max_v[2*k+2]) {
update_node_max(2*k+2, max_v[k]);
}
if(min_v[2*k+2] < min_v[k]) {
update_node_min(2*k+2, min_v[k]);
}
}
void update(int k) {
sum[k] = sum[2*k+1] + sum[2*k+2];
if(max_v[2*k+1] < max_v[2*k+2]) {
max_v[k] = max_v[2*k+2];
max_c[k] = max_c[2*k+2];
smax_v[k] = max(max_v[2*k+1], smax_v[2*k+2]);
} else if(max_v[2*k+1] > max_v[2*k+2]) {
max_v[k] = max_v[2*k+1];
max_c[k] = max_c[2*k+1];
smax_v[k] = max(smax_v[2*k+1], max_v[2*k+2]);
} else {
max_v[k] = max_v[2*k+1];
max_c[k] = max_c[2*k+1] + max_c[2*k+2];
smax_v[k] = max(smax_v[2*k+1], smax_v[2*k+2]);
}
if(min_v[2*k+1] < min_v[2*k+2]) {
min_v[k] = min_v[2*k+1];
min_c[k] = min_c[2*k+1];
smin_v[k] = min(smin_v[2*k+1], min_v[2*k+2]);
} else if(min_v[2*k+1] > min_v[2*k+2]) {
min_v[k] = min_v[2*k+2];
min_c[k] = min_c[2*k+2];
smin_v[k] = min(min_v[2*k+1], smin_v[2*k+2]);
} else {
min_v[k] = min_v[2*k+1];
min_c[k] = min_c[2*k+1] + min_c[2*k+2];
smin_v[k] = min(smin_v[2*k+1], smin_v[2*k+2]);
}
}
void _update_min(ll x, int a, int b, int k, int l, int r) {
if(b <= l || r <= a || max_v[k] <= x) {
return;
}
if(a <= l && r <= b && smax_v[k] < x) {
update_node_max(k, x);
return;
}
push(k);
_update_min(x, a, b, 2*k+1, l, (l+r)/2);
_update_min(x, a, b, 2*k+2, (l+r)/2, r);
update(k);
}
void _update_max(ll x, int a, int b, int k, int l, int r) {
if(b <= l || r <= a || x <= min_v[k]) {
return;
}
if(a <= l && r <= b && x < smin_v[k]) {
update_node_min(k, x);
return;
}
push(k);
_update_max(x, a, b, 2*k+1, l, (l+r)/2);
_update_max(x, a, b, 2*k+2, (l+r)/2, r);
update(k);
}
ll _query_max(int a, int b, int k, int l, int r) {
if(b <= l || r <= a) {
return -inf;
}
if(a <= l && r <= b) {
return max_v[k];
}
push(k);
ll lv = _query_max(a, b, 2*k+1, l, (l+r)/2);
ll rv = _query_max(a, b, 2*k+2, (l+r)/2, r);
return max(lv, rv);
}
ll _query_min(int a, int b, int k, int l, int r) {
if(b <= l || r <= a) {
return inf;
}
if(a <= l && r <= b) {
return min_v[k];
}
push(k);
ll lv = _query_min(a, b, 2*k+1, l, (l+r)/2);
ll rv = _query_min(a, b, 2*k+2, (l+r)/2, r);
return min(lv, rv);
}
ll _query_sum(int a, int b, int k, int l, int r) {
if(b <= l || r <= a) {
return 0;
}
if(a <= l && r <= b) {
return sum[k];
}
push(k);
ll lv = _query_sum(a, b, 2*k+1, l, (l+r)/2);
ll rv = _query_sum(a, b, 2*k+2, (l+r)/2, r);
return lv + rv;
}
public:
SegmentTree(int n) {
SegmentTree(n, nullptr);
}
SegmentTree(int n, ll *a) : n(n) {
n0 = 1;
while(n0 < n) n0 <<= 1;
for(int i=0; i<n; ++i) {
max_v[n0-1+i] = min_v[n0-1+i] = sum[n0-1+i] = (a != nullptr ? a[i] : 0);
smax_v[n0-1+i] = -inf;
smin_v[n0-1+i] = inf;
max_c[n0-1+i] = min_c[n0-1+i] = 1;
}
for(int i=n; i<n0; ++i) {
max_v[n0-1+i] = smax_v[n0-1+i] = -inf;
min_v[n0-1+i] = smin_v[n0-1+i] = inf;
max_c[n0-1+i] = min_c[n0-1+i] = 0;
}
for(int i=n0-2; i>=0; i--) update(i);
}
void update_min(int a, int b, ll x) {
return _update_min(x, a, b, 0, 0, n0);
}
void update_max(int a, int b, ll x) {
return _update_max(x, a, b, 0, 0, n0);
}
ll query_max(int a, int b) {
return _query_max(a, b, 0, 0, n0);
}
ll query_min(int a, int b) {
return _query_min(a, b, 0, 0, n0);
}
ll query_sum(int a, int b) {
return _query_sum(a, b, 0, 0, n0);
}
};
void buildWall(int n, int k, int op[], int left[], int right[],
int height[], int finalHeight[]){
ll v[n];
for(int i = 0;i<n;i++) v[i] = 0;
SegmentTree stb(n,v);
for(int i = 0;i<k;i++){
int l = left[i];
int r = right[i];
int h = height[i];
r++;
if(op[i] == 1){
stb.update_max(l,r,h);
}
else stb.update_min(l,r,h);
}
for(int i = 0;i<n;i++){
finalHeight[i] = stb.query_max(i,i+1);
// cout<<finalHeight[i] << " ";
}
// cout << endl;
}
// int main() {
// setIO();
// int n;
// cin>>n;
// int q;
// cin>>q;
// int op[q],left[q],right[q],height[q],finalHeight[n];
// for(int i = 0;i<q;i++){
// cin >> op[i];
// cin >> left[i] >> right[i] >> height[i];
// }
// for(int i = 0;i<n;i++) finalHeight[i] = 0;
// buildWall(n,q,op,left,right,height,finalHeight);
// // you should actually read the stuff at the bottom
// }
/* stuff you should look for
* read the probem 3 more times in case of WA :)
* int overflow, array bounds
* special cases (n=1?)
* do smth instead of nothing and stay organized
* WRITE STUFF DOWN
* DON'T GET STUCK ON ONE APPROACH
*/
