#include <cstdio>
#include <cstring>
#include <cstdlib>
using namespace std;
struct Node
{
Node *ch[2];
int r;
int v;
int s;
Node(int v): v(v) {
ch[0] = ch[1] = NULL; r = rand(); s = 1;
}
bool operator < (const Node& rhs) const{
return r < rhs.r;
}
int cmp(int x) const{
if(x == v) return -1;
return x < v ? 0 : 1;
}
void maintain(){
s = 1;
if(ch[0] != NULL) s += ch[0]->s;
if(ch[1] != NULL) s += ch[1]->s;
}
};
void rotate(Node* &o, int d){
Node* k = o->ch[d^1]; o->ch[d^1] = k->ch[d]; k->ch[d] = 0;
o->maintain(); k->maintain(); o = k;
}
void insert(Node* &o, int x){
if(o == NULL){
o = new Node(x);
}
else{
int d = (x < o->v ? 0 : 1);
insert(o->ch[d], x);
if(o->ch[d] > o) rotate(o, d^1);
}
}
void remove(Node* &o, int x){
int d= o->cmp(x);
if(d == -1){
Node* u = o;
if(o->ch[0] != NULL && o->ch[1] != NULL){
int d2 = o->ch[0] > o->ch[1] ? 1 : 0;
rotate(o, d2); remove(o->ch[d2], x);
}
else{
if(o->ch[0] == NULL) o = o->ch[1];
else o = o->ch[0];
delete u;
}
}
else
remove(o->ch[d], x);
if(o != NULL) o->maintain();
}