#include <bits/stdc++.h>
#include "toxic.h"
using namespace std;
#define forn(i,n) for(int i=0;i<int(n);i++)
#define forsn(i,s,n) for(int i=int(s);i<int(n);i++)
#define dforn(i,n) for(int i=int(n)-1;i>=0;i--)
#define dforsn(i,s,n) for(int i=int(n)-1;i>=int(s);i--)
#define fst first
#define snd second
#define pb push_back
#define eb emplace_back
#define sz(x) (int)x.size()
#define all(x) x.begin(), x.end()
typedef long long ll;
typedef vector<ll> vll;
typedef vector<int> vi;
typedef pair<int,int> ii;
map<vi,int> memo;
int cnt=0;
int query(vi v){
if(memo.count(v)) return memo[v];
return memo[v]=query_sample(v);
}
vi perm;
int find_toxic(int l, int r){
if(l>r) return -1;
vi vec(r-l+1);
forsn(i,l,r+1) vec[i-l]=perm[i];
if(query(vec)==r-l+1) return -1;
int lo=l-1,hi=r;
while(hi-lo>1){
int mid=(lo+hi)/2;
if(query(vi(begin(vec),begin(vec)+mid-l+1))<mid-l+1) hi=mid;
else lo=mid;
}
return hi;
}
vi find_all_toxic(int l, int r){
int first=find_toxic(l,r);
if(first==-1) return {};
vi ret=find_all_toxic(first+1,r);
ret.pb(perm[first]);
return ret;
}
const int k=10;
void determine_type(int n){
memo.clear();
perm=vi(n);
forn(i,n) perm[i]=i+1;
srand(time(0)^clock());
random_shuffle(all(perm));
int t=find_toxic(0,n-1);
t=perm[t];
answer_type(t,'T');
queue<int> q;
forsn(i,1,n+1){
if(i!=t) q.push(i);
}
vi v;
while(!q.empty()){
vi type(8,-1);
forn(i,8){
if(q.empty()) break;
type[i]=q.front(); q.pop();
}
vi sample{t};
forn(i,8) if(type[i]!=-1){
forn(_,1<<i) sample.eb(type[i]);
}
int x=query(sample);
forn(i,8) if(type[i]!=-1){
if(x>>i&1) answer_type(type[i],'S');
else v.pb(type[i]);
}
}
perm=v;
random_shuffle(all(perm));
vi toxic;
for(int l=0,r=l+k-1;l<sz(perm);l=r+1,r=l+k-1){
for(int x:find_all_toxic(l,min(r,sz(perm)-1))) toxic.pb(x);
}
sort(all(toxic));
for(int x:toxic) answer_type(x,'T');
int j=0;
sort(all(v));
forn(i,sz(v)){
if(j<sz(toxic)&&v[i]==toxic[j]) j++;
else answer_type(v[i],'R');
}
}
