#include <iostream>
#include <fstream>
#include <cstdio>
#include <vector>
#include <algorithm>
#include <queue>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <cstring>
#include <cmath>
#include <stack>
#include <deque>
#include <iomanip>
#include <cassert>
#include <bitset>
#include <tuple>
using namespace std;

inline void operator delete(void * A) {}
inline void operator delete[](void * A) {}

#define _U unsigned
#define ll long long

typedef pair<int,int> pii;
typedef pair<pii,int> ppi;
typedef pair<ll,ll> pll;


#define F first
#define S second

#define GET(I,N) get<N>(I)

#define ll long long

#define  FOR(I,N) for (auto I=0;I <N;++I)
#define BFOR(I,N) for (auto I=N;I>=0;--I)

int DATE[]= {-1,31,29,31,30,31,30,31,31,30,31,30,31};

#define ld long double
#define _FL_ setprecision

const ld PI = 3.14159265358979323846;
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;

typedef
tree<
  int,  //!
  null_type,
  less<int>, //!
  rb_tree_tag,
  tree_order_statistics_node_update>
ordered_set;

ordered_set t;

// t.order_of_key(2)
// *t.find_by_order(0)