#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{
int l;
int r;
int sum;
};
int nodecnt=0;
v<node> nodes;
int newNode(int l, int r){
int ndc = nodecnt++;
nodes.push_back(node());
nodes[ndc].l=l;
nodes[ndc].r=r;
nodes[ndc].sum = nodes[nodes[ndc].l].sum + nodes[nodes[ndc].r].sum;
return ndc;
}
int build(int l, int r){
if(l==r){
nodes.push_back(node());
nodes[nodecnt].l = -1;
nodes[nodecnt].r = -1;
nodes[nodecnt].sum=0;
return nodecnt++;
}
int m=(l+r)/2;
return newNode(build(l, m), build(m+1, r));
}
int update(int cur, int l, int r, int tar){
if(l==r) {
nodes.push_back(node());
nodes[nodecnt].l = -1;
nodes[nodecnt].r = -1;
nodes[nodecnt].sum=nodes[cur].sum+1;
return nodecnt++;
}
int m=(l+r)/2;
if(tar<=m){
return newNode(update(nodes[cur].l, l, m, tar), nodes[cur].r);
}
return newNode(nodes[cur].l, update(nodes[cur].r, m+1, r, tar));
}
int query(int cur, int l, int r, int ql){
if(ql<=l) return nodes[cur].sum;
int m=(l+r)/2, ret=0;
if(ql<=m) ret += query(nodes[cur].l, l, m, ql);
ret += query(nodes[cur].r, m+1, r, ql);
return ret;
}
int binSearchQuery(int curl, int 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 = nodes[nodes[curr].r].sum - nodes[nodes[curl].r].sum;
if(num >= amount) return binSearchQuery(nodes[curl].l, nodes[curr].l, l,m, num - amount);
return binSearchQuery(nodes[curl].r, nodes[curr].r, m+1, r, num);
}
int n;
ii points[500000];
v<int> roots;
int getRect(int x1, int x2, int y){
ii p1 = {x1, -1}, p2 = {x2+1, -1};
int ind1 = distance(points, lower_bound(points, points + n, p1));
int ind2 = distance(points, lower_bound(points, points + n, 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, lower_bound(points, points + n, p1));
int ind2 = distance(points, lower_bound(points, points + n, 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[i].fi=A[i];
points[i].se=B[i];
}
roots.push_back(build(1,n));
sort(points, points+n);
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;
v<v<ii>> pq(M+1);
dp[0] = getRect(0, K[0], K[0]) - K[0];
opt.insert(0);
if(dp[0]<0) return 0;
for(int i=1; i<M; i++){
dp[i] = getRect(0, K[i], K[i]) - K[i];
for(ii it:pq[i]){
int j1=it.fi;
int j2=it.se;
if(opt.find(j1)==opt.end() || opt.find(j2)==opt.end()) continue;
opt.erase(j2);
}
auto it=opt.end();
it--;
int j=*it;
for(j=max(0,*it-2); j<min(i,*it+3); j++)
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;
it = opt.end();
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;
auto it2 = lower_bound(K, K+M, k);
int l = distance(K, it2);
pq[l].push_back({j1,j2});
if(l>i) opt.insert(i);
}
return 1;
}
