#include<iostream>
#include<string>
#include<algorithm>
#include<cstdlib>
#include<cstdio>
#include<set>
#include<map>
#include<vector>
#include<cstring>
#include<stack>
#include<cmath>
#include<queue>
using namespace std;
#define CL(x,v); memset(x,v,sizeof(x));
#define INF 0x3f3f3f3f
#define LL long long
#define REP(i,r,n) for(int i=r;i<=n;i++)
#define RREP(i,n,r) for(int i=n;i>=r;i--)
const int MAXN=8e4+100;
const int mod=1000000;
struct SplayTree {
int sz[MAXN];
int ch[MAXN][2];
int pre[MAXN];
int rt,top;
inline void up(int x){
sz[x] = cnt[x] + sz[ ch[x][0] ] + sz[ ch[x][1] ];
}
inline void Rotate(int x,int f){
int y=pre[x];
ch[y][!f] = ch[x][f];
pre[ ch[x][f] ] = y;
pre[x] = pre[y];
if(pre[x]) ch[ pre[y] ][ ch[pre[y]][1] == y ] =x;
ch[x][f] = y;
pre[y] = x;
up(y);
}
inline void Splay(int x,int goal){//将x旋转到goal的下面
while(pre[x] != goal){
if(pre[pre[x]] == goal) Rotate(x , ch[pre[x]][0] == x);
else {
int y=pre[x],z=pre[y];
int f = (ch[z][0]==y);
if(ch[y][f] == x) Rotate(x,!f),Rotate(x,f);
else Rotate(y,f),Rotate(x,f);
}
}
up(x);
if(goal==0) rt=x;
}
inline void RTO(int k,int goal){//将第k位数旋转到goal的下面
int x=rt;
while(sz[ ch[x][0] ] != k-1) {
if(k < sz[ ch[x][0] ]+1) x=ch[x][0];
else {
k-=(sz[ ch[x][0] ]+1);
x = ch[x][1];
}
}
Splay(x,goal);
}
inline void vist(int x){
if(x){
printf("结点%2d : 左儿子 %2d 右儿子 %2d %2d sz=%d\n",x,ch[x][0],ch[x][1],val[x],sz[x]);
vist(ch[x][0]);
vist(ch[x][1]);
}
}
inline void Newnode(int &x,int c){
x=++top;
ch[x][0] = ch[x][1] = pre[x] = 0;
sz[x]=1; cnt[x]=1;
val[x] = c;
}
inline void init(){
ans=0;type=-1;
ch[0][0]=ch[0][1]=pre[0]=sz[0]=0;
rt=top=0; cnt[0]=0;
Newnode(rt,-INF);
Newnode(ch[rt][1],INF);
pre[top]=rt;
sz[rt]=2;
}
inline void Insert(int &x,int key,int f){
if(!x) {
Newnode(x,key);
pre[x]=f;
Splay(x,0);
return ;
}
if(key==val[x]){
cnt[x]++;
sz[x]++;
return ;
}else if(key<val[x]) {
Insert(ch[x][0],key,x);
} else {
Insert(ch[x][1],key,x);
}
up(x);
}
void Del(){ //删除根结点
int t=rt;
if(ch[rt][1]) {
rt=ch[rt][1];
RTO(1,0);
ch[rt][0]=ch[t][0];
if(ch[rt][0]) pre[ch[rt][0]]=rt;
}
else rt=ch[rt][0];
pre[rt]=0;
up(rt);
}
void findpre(int x,int key,int &ans){ //找key前趋
if(!x) return ;
if(val[x] <= key){
ans=x;
findpre(ch[x][1],key,ans);
} else
findpre(ch[x][0],key,ans);
}
void findsucc(int x,int key,int &ans){ //找key后继
if(!x) return ;
if(val[x]>=key) {
ans=x;
findsucc(ch[x][0],key,ans);
} else
findsucc(ch[x][1],key,ans);
}