#include "teams.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef double db;
typedef string str;
typedef pair<int,int> pi;
typedef pair<ll,ll> pl;
typedef pair<db,db> pd;
typedef vector<int> vi;
typedef vector<bool> vb;
typedef vector<ll> vl;
typedef vector<db> vd;
typedef vector<str> vs;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<pd> vpd;
#define mp make_pair
#define f first
#define s second
#define sz(x) (int)(x).size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pf push_front
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5;
const ll INF = 1e18;
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1};
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
template<class T> bool ckmin(T& a, const T& b) {
return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) {
return a < b ? a = b, 1 : 0; }
constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int bits(int x) { return 31-__builtin_clz(x); } // floor(log2(x))
ll cdiv(ll a, ll b) { return a/b+((a^b)>0&&a%b); } // divide a by b rounded up
ll fdiv(ll a, ll b) { return a/b-((a^b)<0&&a%b); } // divide a by b rounded down
ll half(ll x) { return fdiv(x,2); }
template<class T, class U> T fstTrue(T lo, T hi, U f) {
// note: if (lo+hi)/2 is used instead of half(lo+hi) then this will loop infinitely when lo=hi
hi ++; assert(lo <= hi); // assuming f is increasing
while (lo < hi) { // find first index such that f is true
T mid = half(lo+hi);
f(mid) ? hi = mid : lo = mid+1;
}
return lo;
}
template<class T, class U> T lstTrue(T lo, T hi, U f) {
lo --; assert(lo <= hi); // assuming f is decreasing
while (lo < hi) { // find first index such that f is true
T mid = half(lo+hi+1);
f(mid) ? lo = mid : hi = mid-1;
}
return lo;
}
template<class T> void remDup(vector<T>& v) {
sort(all(v)); v.erase(unique(all(v)),end(v)); }
// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);
template<class T> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }
template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }
// TO_STRING
#define ts to_string
str ts(char c) { return str(1,c); }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
str ts(bool b) {
#ifdef LOCAL
return b ? "true" : "false";
#else
return ts((int)b);
#endif
}
template<class A> str ts(complex<A> c) {
stringstream ss; ss << c; return ss.str(); }
str ts(vector<bool> v) {
str res = "{"; F0R(i,sz(v)) res += char('0'+v[i]);
res += "}"; return res; }
template<size_t SZ> str ts(bitset<SZ> b) {
str res = ""; F0R(i,SZ) res += char('0'+b[i]);
return res; }
template<class A, class B> str ts(pair<A,B> p);
template<class T> str ts(T v) { // containers with begin(), end()
#ifdef LOCAL
bool fst = 1; str res = "{";
for (const auto& x: v) {
if (!fst) res += ", ";
fst = 0; res += ts(x);
}
res += "}"; return res;
#else
bool fst = 1; str res = "";
for (const auto& x: v) {
if (!fst) res += " ";
fst = 0; res += ts(x);
}
return res;
#endif
}
template<class A, class B> str ts(pair<A,B> p) {
#ifdef LOCAL
return "("+ts(p.f)+", "+ts(p.s)+")";
#else
return ts(p.f)+" "+ts(p.s);
#endif
}
// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) {
pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) {
pr(h); if (sizeof...(t)) pr(" "); ps(t...); }
// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
cerr << ts(h); if (sizeof...(t)) cerr << ", ";
DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL, chk -> fake assert
#define dbg(...) cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#define chk(...) if (!(__VA_ARGS__)) cerr << "Line(" << __LINE__ << ") -> function(" \
<< __FUNCTION__ << ") -> CHK FAILED: (" << #__VA_ARGS__ << ")" << "\n", exit(0);
#else
#define dbg(...) 0
#define chk(...) 0
#endif
// FILE I/O
void setIn(str s) { freopen(s.c_str(),"r",stdin); }
void setOut(str s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
void setIO(str s = "") {
unsyncIO();
// cin.exceptions(cin.failbit);
// throws exception when do smth illegal
// ex. try to read letter into int
if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}
const int mx = 500005;
int N;
vpi students;
int pref[mx];
int suf[mx];
/**
* Description: point update and rectangle sum with offline 2D BIT.
* For each of the points to be updated, $x\in (0,SZ)$ and $y\neq 0$.
* Time: O(N\log^2 N)
* Memory: O(N\log N)
* Source: Own
* Verification:
* https://dmoj.ca/problem/occ19g4
* http://www.usaco.org/index.php?page=viewproblem2&cpid=722 (753 ms)
* http://www.usaco.org/index.php?page=viewproblem2&cpid=601 (679 ms)
*/
template<class T, int SZ> struct OffBIT2D {
bool mode = 0; // mode = 1 -> initialized
vpi todo; // locations of updates to process
int cnt[SZ], st[SZ];
vi val; vector<T> bit; // store all BITs in single vector
void init() { assert(!mode); mode = 1;
int lst[SZ]; F0R(i,SZ) lst[i] = cnt[i] = 0;
sort(all(todo),[](const pi& a, const pi& b) {
return a.s < b.s; });
trav(t,todo) for (int x = t.f; x < SZ; x += x&-x)
if (lst[x] != t.s) lst[x] = t.s, cnt[x] ++;
int sum = 0; F0R(i,SZ) lst[i] = 0, st[i] = (sum += cnt[i]);
val.rsz(sum); bit.rsz(sum); reverse(all(todo));
trav(t,todo) for (int x = t.f; x < SZ; x += x&-x)
if (lst[x] != t.s) lst[x] = t.s, val[--st[x]] = t.s;
}
int rank(int y, int l, int r) {
return ub(begin(val)+l,begin(val)+r,y)-begin(val)-l; }
void UPD(int x, int y, T t) {
for (y = rank(y,st[x],st[x]+cnt[x]); y <= cnt[x]; y += y&-y)
bit[st[x]+y-1] += t; }
void upd(int x, int y, T t) {
if (!mode) todo.pb({x,y});
else for (;x<SZ;x+=x&-x) UPD(x,y,t); }
int QUERY(int x, int y) { T res = 0;
for (y = rank(y,st[x],st[x]+cnt[x]); y; y -= y&-y) res += bit[st[x]+y-1];
return res; }
T query(int x, int y) { assert(mode);
if(x == 0 || y == 0) return 0;
T res = 0; for (;x;x-=x&-x) res += QUERY(x,y);
return res; }
T query(int xl, int xr, int yl, int yr) {
return query(xr,yr)-query(xl-1,yr)
-query(xr,yl-1)+query(xl-1,yl-1); }
};
OffBIT2D<int, 500005> bt;
const int mx2 = 1505;
int precomp[mx2][mx2];
void init(int _N, int A[], int B[]) {
N = _N;
for(int i = 0; i < N; i++){
students.pb(mp(A[i], B[i]));
}
sort(all(students));
for(int i = 0; i < N; i++){
bt.upd(A[i], B[i], 1);
}
bt.init();
for(int i = 0; i < N; i++){
bt.upd(A[i], B[i], 1);
}
for(int i = 0; i < N; i++){
pref[students[i].s]++;
suf[students[i].f]++;
}
for(int i = N; i >= 1; i--){
suf[i]+=suf[i+1];
}
for(int i = 1; i <= N; i++){
pref[i]+=pref[i-1];
}
for(int i = 0; i < N; i++){
if(B[i] < mx2) precomp[A[i]][B[i]]++;
}
for(int i = mx2-1; i >= 0; i--){
for(int j = 0; j < mx2; j++){
if(i+1 < mx2) precomp[i][j]+=precomp[i+1][j];
if(j-1 >= 0) precomp[i][j]+=precomp[i][j-1];
if(i+1 < mx2 && j-1 >= 0) precomp[i][j]-=precomp[i+1][j-1];
}
}
// for(int k = 0; k < mx2; k++){
// for(int j = 1; j+k < mx2; j++){
// if(j-1 >= 1) precomp[j-1][j+k]+=precomp[j][j+k];
// if(j+k+1 < mx2) precomp[j][j+k+1]+=precomp[j][j+k];
// }
// }
}
int getInt(int a, int b){
if(a > b) return 0;
assert(1 <= a && a <= b && b <= N);
if(b < mx2) return precomp[a][b];
return bt.query(a, N, 1, b);
}
int can(int M, int _K[]) {
vi K;
int Ksum = 0;
for(int i = 0; i < M; i++){
K.pb(_K[i]);
Ksum+=K[i];
if(Ksum > N) return 0;
}
sort(all(K));
vpi pv; // position, value --> csum
for(int i = 0; i < M; i++){
pv.pb(mp(K[i], 0));
for(int j = i; j < M; j++){
if(K[j] == K[i]){
pv.bk.s+=K[j];
i = j;
}
else{
break;
}
}
}
M = sz(pv);
vi dp;
for(int i = 0; i < M; i++){
dp.pb(0);
dp[i] = max(dp[i], pref[pv[i].f-1]);
for(int j = 0; j < i; j++){
dp[i] = max(dp[i], dp[j]+getInt(pv[j].f+1, pv[i].f-1));
}
dp[i]+=pv[i].s;
if(dp[i]+suf[pv[i].f+1] > N) return 0;
}
return 1;
}
