#include "teams.h"
#include <bits/stdc++.h>
using namespace std;
#define v vector
#define ii pair<int,int>
#define fi first
#define se second
struct node{
node* l;
node* r;
int sum;
node(int val){
l=nullptr;
r=nullptr;
sum=val;
}
node(node* lll, node* rr){
l=lll;
r=rr;
sum=l->sum + r->sum;
}
};
node* build(int l, int r){
if(l==r) return new node(0);
int m=(l+r)/2;
return new node(build(l,m), build(m+1,r));
}
node* update(node* cur, int l, int r, int tar){
if(l==r) return new node(cur->sum+1);
int m=(l+r)/2;
if(tar<=m) return new node(update(cur->l, l, m, tar), cur->r);
return new node(cur->l, update(cur->r, m+1, r, tar));
}
int query(node* cur, int l, int r, int ql){
if(ql<=l) return cur->sum;
int m=(l+r)/2, ret=0;
if(ql<=m) ret += query(cur->l, l, m, ql);
ret += query(cur->r, m+1, r, ql);
return ret;
}
int binSearchQuery(node* curl, node* curr, int l, int r, int num){
//returns last place where num<amount holds
if(l==r) return l;
int m=(l+r)/2;
int amount = curr->r->sum - curl->r->sum;
if(num >= amount) return binSearchQuery(curl->l, curr->l, l,m, num - amount);
return binSearchQuery(curl->r, curr->r, m+1, r, num);
}
int n;
v<ii> points;
v<node*> roots;
int getRect(int x1, int x2, int y){
ii p1 = {x1, -1}, p2 = {x2+1, -1};
int ind1 = distance(points.begin(), lower_bound(points.begin(), points.end(), p1));
int ind2 = distance(points.begin(), lower_bound(points.begin(), points.end(), p2));
return query(roots[ind2], 1, n, y) - query(roots[ind1], 1, n, y);
}
int getSplit(int x1, int x2, int num){
ii p1 = {x1, -1}, p2 = {x2+1, -1};
int ind1 = distance(points.begin(), lower_bound(points.begin(), points.end(), p1));
int ind2 = distance(points.begin(), lower_bound(points.begin(), points.end(), p2));
return binSearchQuery(roots[ind1], roots[ind2], 1, n, num) + 1;//the first place where the suffix sum is >= num
}
void init(int N, int A[], int B[]) {
n=N;
for(int i=0; i<n; i++) points.push_back({A[i], B[i]});
roots.push_back(build(1,n));
sort(points.begin(), points.end());
for(ii it:points) roots.push_back(update(roots.back(), 1, n, it.se));
}
int cnt=0;
int can(int M, int K[]) {
sort(K, K+M);
if(M>400){
priority_queue<ii> pq;
int j=0;
for(int i=0; i<M; i++){
while(j<n && points[j].fi<=K[i]){
pq.push({-points[j].se, points[j].fi});
j++;
}
while(pq.size()>0 && -pq.top().fi<K[i]) pq.pop();
if(pq.size()<K[i]) return 0;
for(int k=0; k<K[i]; k++) pq.pop();
}
return 1;
}
v<int> dp(M);
set<int> opt;
priority_queue<pair<int,ii>> pq;
for(int i=0; i<M; i++){
dp[i] = getRect(0, K[i], K[i]) - K[i];
int cnt=0;
while(pq.size()>0 && pq.top().fi<=K[i]){
int j1=pq.top().se.fi;
int j2=pq.top().se.se;
pq.pop();
if(opt.find(j1)==opt.end() || opt.find(j2)==opt.end()) continue;
opt.erase(j2);
}
if(opt.size()>0){
auto it=opt.end();
it--;
int j=*it;
dp[i] = min(dp[i], dp[j] + (K[i]==K[j] ? 0 : getRect(K[j]+1, K[i], K[i])) - K[i]);
}
if(dp[i]<0) return 0;
opt.insert(i);
if(opt.size()>1){
auto it = opt.end();
it--;
it--;
int j1=*it;
int j2=i;
int k = (K[j1]==K[j2]) ? 0 : getSplit(K[j1]+1, K[j2], dp[j2]-dp[j1]);
if(K[j1]==K[j2]) k= (dp[j2] - dp[j1] < 0) ? K[M-1]+1 : K[j2]+1;
pq.push({k, {j1,j2}});
}
}
return 1;
}
