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#include<cstdio>
#include<algorithm>
using namespace std;
const int inf=~0U>>1;
struct node {
    int key,size;
    node*c[2];
    node(int _key,int _size,node*_c)
        :key(_key),size(_size) {
        c[0]=c[1]=_c;
    }
    void rz() {
        size=c[0]->size+c[1]->size+1;
    }
} TNull(0,0,0),*Null=&TNull;
int n,a;
char c;
node*root;
void rot(node*&t,bool d) {
    node*p=t->c[d];
    t->c[d]=p->c[!d];
    p->c[!d]=t;
    t->rz();
    p->rz();
    t=p;
}
void maintain(node*&t,bool d) {
    if(t==Null) return;
    node*&p=t->c[d];
    if(p->c[d]->size>t->c[!d]->size)
        rot(t,d);
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