#include "teams.h"
#include "bits/stdc++.h"
#define rep(i, n) for(ll i = 0; i < ll(n); ++i)
#define rep2(i, s, n) for(ll i = ll(s); i < ll(n); ++i)
#define rrep(i, n) for(ll i = ll(n)-1; i >= 0; --i)
#define pb push_back
#define eb emplace_back
#define all(a) a.begin(),a.end()
#define SZ(a) int(a.size())
using namespace std;
using ll = long long;
using P = pair<int, int>;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vp = vector<P>;
using vvp = vector<vp>;
using vb = vector<bool>;
using vvb = vector<vb>;
using vs = vector<string>;
const int inf = 1001001001;
const ll linf = 1001001001001001001;
template<class T>
bool chmin(T &a, T b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template<class T>
bool chmax(T &a, T b) {
if (a < b) {
a = b;
return true;
}
return false;
}
class segtree {
struct node {
ll lrd;
node *cl;
node *cr;
node(int l, int r, int d) : lrd((ll(l) << 40) + (ll(r) << 20) + d), cl(nullptr), cr(nullptr) {}
};
int n;
node *root;
node *build(int l, int r, const vi::iterator &a, const vi::iterator &b) {
if (a == b) return nullptr;
node *res = new node(l, r, b - a);
if (r - l > 1) {
int m = (l + r) / 2;
auto c = lower_bound(a, b, m);
res->cl = build(l, m, a, c);
res->cr = build(m, r, c, b);
}
return res;
}
int count(int l, int r, node *nd) {
if (nd == nullptr) return 0;
int nl = nd->lrd >> 40;
int nr = (nd->lrd >> 20) - (nl << 20);
if (r <= nl or nr <= l) return 0;
if (l <= nl and nr <= r) return nd->lrd - (nd->lrd >> 20 << 20);
return count(l, r, nd->cl) + count(l, r, nd->cr);
}
public:
segtree(int _n, const vi::iterator &a, const vi::iterator &b) : n(_n) {
root = build(0, n, a, b);
}
int count(int l, int r) {
assert(0 <= l and l <= r and r <= n);
return count(l, r, root);
}
};
vector<segtree> st;
int sz = 1;
void merge(vi &v, const vi &a, const vi &b) {
int ai = 0, bi = 0;
v.reserve(SZ(a) + SZ(b));
while (ai < SZ(a) or bi < SZ(b)) {
if (ai < SZ(a) and bi < SZ(b)) {
if (a[ai] < b[bi]) v.pb(a[ai++]);
else v.pb(b[bi++]);
} else if (ai < SZ(a)) {
v.pb(a[ai++]);
} else {
v.pb(b[bi++]);
}
}
}
void build(const vvi &v) {
vvi ls(2 * sz);
rep(i, sz) ls[sz + i] = v[i];
for (int i = sz - 1; i >= 1; --i) {
merge(ls[i], ls[2 * i], ls[2 * i + 1]);
}
rep(i, 2 * sz) st.eb(sz, all(ls[i]));
}
int n;
vi a, b;
int count(int xl, int xr, int yl, int yr) {
assert(0 <= xl and xl <= xr and xr <= sz);
assert(0 <= yl and yl <= yr and yr <= sz);
// cerr << xl << ' ' << xr << ' ' << yl << ' ' << yr << ' ';
yl += sz, yr += sz;
int res = 0;
while (yl < yr) {
if (yl & 1) res += st[yl++].count(xl, xr);
if (yr & 1) res += st[--yr].count(xl, xr);
yl >>= 1, yr >>= 1;
}
// cerr << res << endl;
// int res = 0;
// rep(i, n) if (xl <= a[i] and a[i] < xr and yl <= b[i] and b[i] < yr) ++res;
return res;
}
void init(int N, int A[], int B[]) {
n = N;
a = vi(A, A + N);
b = vi(B, B + N);
for (int &i: b) ++i;
while (sz <= n + 1) sz *= 2;
vvi v(sz);
rep(i, n) v[b[i]].pb(a[i]);
rep(i, sz) sort(all(v[i]));
build(v);
// cerr << "init : " << N << endl;
}
int max_yr(int xl, int xr, int yl, int ub) {
assert(0 <= xl and xl <= xr and xr <= sz);
assert(0 <= yl and yl <= sz);
assert(ub > 0);
yl += sz;
while (true) {
if ((yl & -yl) == yl) return sz;
while (~yl & 1) yl >>= 1;
int now = st[yl].count(xl, xr);
if (now < ub) {
ub -= now;
++yl;
continue;
}
while (yl < sz) {
yl *= 2;
now = st[yl].count(xl, xr);
if (now < ub) {
ub -= now;
++yl;
}
}
return yl - sz;
}
}
int can(int m, int K[]) {
vi k = vi(K, K + m);
sort(all(k));
// {x, max_y, rem in max_y}
vvi v;
v.pb({0, n + 1, 0});
for (int i: k) {
// cerr << "i : " << i << endl;
// for (auto t: v) cerr << "v : " << t[0] << ' ' << t[1] << ' ' << t[2] << endl;
while (v.back()[1] < i + 1) v.pop_back();
int now = i + 1;
int rem = i;
while (true) {
if (now > n + 1) return 0;
assert(v.back()[1] >= now);
int sum = count(v.back()[0] + 1, i + 1, now, v.back()[1] + 1) + v.back()[2];
if (sum < rem) {
rem -= sum;
now = v.back()[1] + 1;
v.pop_back();
continue;
}
int psum = count(v.back()[0] + 1, i + 1, now, v.back()[1]);
if (psum < rem) {
v.back()[0] = i;
v.back()[2] = sum - rem;
} else {
int ok = max_yr(v.back()[0] + 1, i + 1, now, rem) + 1;
v.eb(vi{i, ok - 1, count(v.back()[0] + 1, i + 1, now, ok) - rem});
}
break;
}
}
// cerr << "i : end" << endl;
// for (auto t: v) cerr << "v : " << t[0] << ' ' << t[1] << ' ' << t[2] << endl;
return 1;
}
