#include "teams.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll linf = ll(1e18);
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<int, int> p2;
#define rep(i, high) for (int i = 0; i < high; i++)
#define repp(i, low, high) for (int i = low; i < high; i++)
#define repe(i, container) for (auto& i : container)
#define sz(container) ((int)container.size())
#define all(x) begin(x),end(x)
#if _LOCAL
#define assert(x) if (!(x)) __debugbreak()
#endif
struct node
{
int lc=-1, rc=-1;
int sum = 0;
node(int lc, int rc, int s) : lc(lc), rc(rc), sum(s) {}
node() {}
};
int psc = 0;
node pnodes[int(2e7)];
int build(int l, int r)
{
if (l==r)
{
return psc++;
}
else
{
int mid = (l + r) / 2;
int ind = psc++;
pnodes[ind].lc = build(l, mid);
pnodes[ind].rc = build(mid + 1, r);
return ind;
}
}
int update(int x, int l, int r, int i, int s)
{
if (l==r)
{
int ind = psc++;
pnodes[ind].sum = pnodes[x].sum + s;
return ind;
}
else
{
int mid = (l + r) / 2;
int ind = psc++;
pnodes[ind].lc = pnodes[x].lc;
pnodes[ind].rc = pnodes[x].rc;
if (i <= mid) pnodes[ind].lc = update(pnodes[x].lc, l, mid, i, s);
else pnodes[ind].rc = update(pnodes[x].rc, mid + 1, r, i, s);
pnodes[ind].sum = pnodes[pnodes[ind].lc].sum + pnodes[pnodes[ind].rc].sum;
return ind;
}
}
int query(int x, int l, int r, int ql, int qr)
{
if (l > qr || r < ql) return 0;
if (l >= ql && r <= qr) return pnodes[x].sum;
int mid = (l + r) / 2;
return query(pnodes[x].lc, l, mid, ql, qr) + query(pnodes[x].rc, mid + 1, r, ql, qr);
}
int n;
typedef pair<double, int> pt;
vector<p2> pts;
int roots[int(5e5)];
void init(int N, int A[], int B[])
{
n = N;
vi a(n);
vi b(n);
rep(i, N) a[i] = A[i], b[i] = B[i];
rep(i, n)
{
pts.emplace_back(a[i], b[i]);
}
sort(all(pts), [](p2 a, p2 b)
{
return a.second < b.second;
});
int root = build(0, n - 1);
rep(i, n)
{
root = roots[i] = update(root, 0, n - 1, pts[i].first, 1);
}
}
int rectangle_sum(int xlo, int xhi, int yhi)
{
return query(roots[yhi], 0, n - 1, xlo, xhi);
}
struct tnode
{
p2 corner;
int value, sum=0, prio, cnt=1;
tnode *l=0, *r=0;
tnode(p2 corner, int value) : corner(corner), prio(rand()), value(value) {}
tnode() {}
};
int node_cnt = 0;
tnode nodes[int(4e5)];
typedef tnode* pnode;
int get_sum(pnode x) { return x ? x->sum : 0; }
int get_cnt(pnode x) { return x ? x->cnt : 0; }
void pull(pnode x)
{
if (!x) return;
x->sum = get_sum(x->l) + get_sum(x->r) + x->value;
x->cnt = get_cnt(x->l) + get_cnt(x->r) + 1;
}
void split(pnode x, pnode& l, pnode& r, int s)
{
if (!x) return void(l = r = 0);
if (x->corner.first > s)
split(x->l, l, x->l, s), r = x;
else
split(x->r, x->r, r, s), l = x;
pull(x);
}
void merge(pnode& x, pnode l, pnode r)
{
if (!l || !r)
x = l ? l : r;
else if (l->prio < r->prio)
merge(r->l, l, r->l), x = r;
else
merge(l->r, l->r, r), x = l;
pull(x);
}
p2 get_corner(pnode x, int i, int add = 0)
{
int node_i = add + get_cnt(x->l);
if (node_i == i) return x->corner;
if (node_i > i) return get_corner(x->l, i, add);
return get_corner(x->r, i, add + get_cnt(x->l) + 1);
}
int sum(pnode& root, int xhi, int yhi)
{
int prev = -1;
int taken = 0;
int lo = -1;
int hi = get_cnt(root);
while (lo + 1 < hi)
{
int mid = (lo + hi) / 2;
if (get_corner(root, mid).second <= yhi)
{
hi = mid;
}
else lo = mid;
}
int s = 0;
if (root)
{
pnode l, r;
int lo = -2;
if (hi) lo = get_corner(root, hi - 1).first;
split(root, l, r, lo);
if (r) s = r->sum;
merge(root, l, r);
}
if (hi > 0 && get_cnt(root))
{
s += rectangle_sum(0, get_corner(root, hi-1).first, yhi);
}
return rectangle_sum(0, xhi, yhi) - s;
}
const int inf = int(2e9);
p2 invalid = p2(-inf, -inf);
p2 lower_bound(pnode root, int x)
{
if (!root) return invalid;
if (root->corner.first >= x)
{
p2 left_result = lower_bound(root->l, x);
if (left_result != invalid) return left_result;
else return root->corner;
}
else
{
return lower_bound(root->r, x);
}
}
p2 rev_bound(pnode root, int x)
{
if (!root) return invalid;
p2 result = invalid;
if (root->corner.first <= x) {
result = root->corner;
p2 right_result = rev_bound(root->r, x);
if (right_result != invalid) result = right_result;
}
else result = rev_bound(root->l, x);
return result;
}
void del(pnode x)
{
if (!x) return;
del(x->l);
del(x->r);
delete x;
}
int can(int m, int K[]) {
int t = 0;
int t2 = 0;
node_cnt = 0;
vi k(m);
rep(i, m) k[i] = K[i];
sort(all(k));
pnode hull = 0;
auto insert = [&](p2 new_corner)
{
p2 lo = lower_bound(hull, new_corner.first);
if ((new_corner.first <= lo.first && new_corner.second <= lo.second))
{
// dominated
}
else
{
while (1)
{
p2 p = rev_bound(hull, new_corner.first);
if (p == invalid) break;
assert(p.first <= new_corner.first);
if (p.second <= new_corner.second)
{
pnode l, mid, r;
split(hull, l, r, p.first);
split(hull, l, mid, p.first - 1);
merge(hull, l, r);
}
else break;
}
p2 lo = rev_bound(hull, new_corner.first);
int s = rectangle_sum((lo.first!=-inf)?lo.first+1:0, new_corner.first, new_corner.second);
pnode new_node = &nodes[node_cnt++];
new_node->cnt = 1;
new_node->corner = new_corner;
new_node->value = s;
new_node->sum = 0;
new_node->l = 0;
new_node->r = 0;
pnode l, r;
split(hull, l, r, new_corner.first);
merge(hull, l, new_node);
merge(hull, hull, r);
}
};
int lo = 0;
rep(i, m)
{
lo = lower_bound(pts.begin() + lo, pts.end(), p2(0, k[i]), [](p2 a, p2 b) {
return a.second < b.second;
}) - pts.begin();
if (lo) insert(p2(k[i], lo-1));
if (sum(hull, k[i], n-1)<k[i])
{
return 0;
}
int lob = lo-1;
int hib = n;
while (lob+1<hib)
{
int mid = (lob + hib) / 2;
if (sum(hull, k[i], mid) < k[i])
{
lob = mid;
}
else hib = mid;
}
p2 new_corner = p2(k[i], hib);
insert(new_corner);
}
return 1;
}
