#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;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int cnt=0;
int query(vi v){
if(memo.count(v)) return memo[v];
return memo[v]=query_sample(v);
}
vector<vi> g1,g2;
vi v;
vi perm;
int query2(vi vec){
if(g1.empty()) return query(vec);
vi g=g1.back();
int prev=sz(vec);
forn(i,sz(g)){
forn(_,1<<i) vec.pb(g[i]);
}
int x=query(vec);
if(x==sz(vec)) return prev;
g1.pop_back();
forn(i,sz(g)){
if(x>>i&1) answer_type(g[i],'S');
else v.pb(g[i]);
}
return 0;
}
vi find_toxic(int l, int r, bool flag){
if(l>r) return {};
vi vec(r-l+1);
forsn(i,l,r+1) vec[i-l]=perm[i];
if(!flag&&query2(vec)) return {};
int lo=l-1,hi=r;
while(hi-lo>1){
int mid=(lo+hi)/2;
if(!query2(vi(begin(vec),begin(vec)+mid-l+1))) hi=mid;
else lo=mid;
}
vi res=find_toxic(hi+1,r,0);
res.pb(perm[hi]);
return res;
}
void determine_type(int n){
memo.clear(),g1.clear(),g2.clear();
v.clear();
perm=vi(n);
forn(i,n) perm[i]=i+1;
shuffle(all(perm),rng);
int j=0;
vi t;
while(j<n){
vi type(8,-1);
forn(i,8){
if(j>=n) break;
type[i]=perm[j++];
}
vi sample;
forn(i,8) if(type[i]!=-1){
forn(_,1<<i) sample.pb(type[i]);
}
int x=query(sample);
if(x==sz(sample)){
g1.pb(type);
while(g1.back().back()==-1) g1.back().pop_back();
continue;
}
vi lol;
forn(i,8) if(type[i]!=-1){
if(x>>i&1) answer_type(type[i],'S');
else lol.pb(type[i]);
}
if(!lol.empty()){
if(sz(lol)==1) t.pb(lol[0]),v.pb(lol[0]);
else g2.pb(lol);
}
}
for(vi g:g2){
perm=g;
shuffle(all(perm),rng);
for(int x:find_toxic(0,sz(g)-1,1)) t.pb(x);
v.insert(end(v),all(g));
}
assert(sz(t)>=1);
for(vi g:g1){
vi sample={t[0]};
forn(i,sz(g)){
forn(_,1<<i) sample.pb(g[i]);
}
int x=query(sample);
forn(i,sz(g)){
if(x>>i&1) answer_type(g[i],'S');
else v.pb(g[i]);
}
}
sort(all(v));
sort(all(t));
for(int x:t) answer_type(x,'T');
j=0;
forn(i,sz(v)){
if(j<sz(t)&&t[j]==v[i]) j++;
else answer_type(v[i],'R');
}
}
