//Challenge: Accepted
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
using namespace std;
#ifdef zisk
void debug(){cout << endl;}
template<class T, class ... U> void debug(T a, U ... b){cout << a << " ", debug(b...);}
template<class T> void pary(T l, T r){
while (l != r) cout << *l << " ", l++;
cout << endl;
}
#else
#define debug(...) 0
#define pary(...) 0
#endif
#define ll long long
#define maxn 500005
#define pii pair<int, int>
#define ff first
#define ss second
#include "teams.h"
struct segtree{
vector<int> seg[4*maxn];
void build(int cur, int l, int r, vector<pii> a) {
if (r <= l || a.size() == 0) return;
if (r - l == 1) {
for (auto p:a) seg[cur].push_back(p.ss);
sort(seg[cur].begin(), seg[cur].end());
return;
}
int m = (l + r) / 2;
vector<pii> lef, rig;
for (auto p:a) {
if (p.ff < m)lef.push_back(p);
else rig.push_back(p);
}
build(cur*2, l, m, lef), build(cur*2+1, m, r, rig);
int ls = seg[cur*2].size(), rs = seg[cur*2+1].size();
vector<int> &le = seg[cur*2], &ri = seg[cur*2+1];
int ind = 0;
for (int i = 0;i < ls;i++) {
while (ind < rs && ri[ind] < le[i]) seg[cur].push_back(ri[ind++]);
seg[cur].push_back(le[i]);
}
while (ind < rs) seg[cur].push_back(ri[ind++]);
}
int query(int cur, int l, int r, int ql, int qr) {
//number of segments covering [ql, qr]
if (r <= l || l > ql) return 0;
if (r-1 <= ql) {
int ind = lower_bound(seg[cur].begin(), seg[cur].end(), qr) - seg[cur].begin();
return (int)seg[cur].size() - ind;
}
int m = (l + r) / 2;
return query(cur*2, l, m, ql, qr) + query(cur*2+1, m, r, ql, qr);
}
} tr;
int v[maxn];
int n;
void init(signed N, signed A[], signed B[]) {
n = N;
vector<pii> a(n);
for (int i = 0;i < n;i++) {
a[i] = {A[i], B[i]};
v[A[i]]++;
v[B[i] + 1]--;
}
tr.build(1, 1, N+1, a);
for (int i = 1;i <= n;i++) v[i] += v[i-1]; //number of segments covering i
}
signed can(signed m, signed num[]) {
sort(num, num + m);
vector<int> c(m, 0), dp(m, 0);
int tot = 0;
for (int i = 0;i < m;i++) {
tot += num[i];
c[i] = v[num[i]] - num[i];
dp[i] = c[i];
if (c[i] < 0 || tot > n) return 0;
}
vector<int> stk, pnt;
auto f = [&] (int l, int r){
return c[r] + dp[l] - tr.query(1, 1, n+1, num[l], num[r]);
};
for (int i = 0;i < m;i++) {
while (stk.size() > 1 && pnt.back() < i) {
stk.pop_back();
pnt.pop_back();
}
if (stk.size()) {
dp[i] = min(dp[i], f(stk.back(), i));
if (dp[i] < 0) return 0;
}
if (i < m - 1) {
bool done = 0;
while (stk.size()) {
if (f(stk.back(), pnt.back()) >= f(i, pnt.back())) {
stk.pop_back();
pnt.pop_back();
continue;
}
if (f(stk.back(), i+1) <= f(i, i+1)) {
done = 1;
break;
}
int low = i+1, up = pnt.back();
while (low < up - 1) {
int mid = (low + up) / 2;
if (f(stk.back(), mid) > f(i, mid)) low = mid;
else up = mid;
}
stk.push_back(i);
pnt.push_back(low);
done = 1;
break;
}
if (!done && stk.size() == 0) {
stk.push_back(i);
pnt.push_back(m-1);
}
}
}
return 1;
}
/*
4
2 3 1 1
3 4 4 4
1
4
*/
