//L=28
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef __int128 lll;
using ull = unsigned long long;
typedef pair<ll,ll> pll;
typedef vector<ll> vll;
typedef vector<pll> vpll;
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define all(x) x.begin(),x.end()
#define si(x) ll(x.size())
#define rep(i,n) for(ll i=0;i<n;i++)
#define per(i,n) for(ll i=n-1;i>=0;i--)
#define rng(i,l,r) for(ll i=l;i<r;i++)
#define gnr(i,l,r) for(ll i=r-1;i>=l;i--)
#define fore(i, a) for(auto &&i : a)
#define fore2(a, b, v) for(auto &&[a, b] : v)
#define fore3(a, b, c, v) for(auto &&[a, b, c] : v)
#include "Anna.h"
namespace{
vector<int> de_Bruijn(int typ){
//ternaries of 3 digits
//except numbers whose digits are all (1 or 2) (ex. 121)
//also exept
//typ=0:
//typ=1: 010,101
//typ=2: 000,010,101
//typ=3: 010,101,020,202
ll len=3;
//make graph
ll n=pow(3,len-1);
vector<vector<pair<ll,ll> > >g(n);
auto valid=[&](ll x){
//valid as an edge?
if(typ>=1&&x==3)return 0;
if(typ>=1&&x==9+1)return 0;
if(typ==2&&x==0)return 0;
if(typ==3&&x==2*3)return 0;
if(typ==3&&x==2*9+2*1)return 0;
rep(_,len){
if(x%3==0)return 1;
x/=3;
}
return 0;
};
rep(i,3*n)if(valid(i)){
ll x=i/3;
ll y=i%n;
g[x].eb(y,i%3);
}
// {
// vector<int> cnt(n,0);
// rep(i,n)rep(j,si(g[i]))cnt[g[i][j].first]++;
// rep(i,n)if(cnt[i]!=si(g[i])){
// cout<<"invalid graph: degree sum is not 0"<<endl;
// }
// }
//generate sequence (get an euler cycle of the graph)
vector<int> ans;
function<void(ll,ll)> dfs=[&](ll x,ll col){
while(si(g[x])){
auto [nxt,ncol]=g[x].back();
g[x].pop_back();
dfs(nxt,ncol);
}
ans.pb(col);
};
ll start_vertex=0;
dfs(start_vertex,-1);
ans.pop_back();
reverse(all(ans));
return ans;
}
}
pair<string,int> anna(int N,string S){
string str="RGB";
int B=9,L=28;
const int TYP=4;
string T;
rep(i,N+B)T+='#';
ll id=0;
//make 4 de_Bruijn-like sequences of period 19, 17, 16, 15
//they make a de_Bruijn-like sequence of period LCM(19,17,16,15)
vector<int> seq[TYP];
rep(typ,TYP)seq[typ]=de_Bruijn(typ);
rep(i,N/B+1){
//repeat blocks
//control differnce of adjacent digits mod 3
//a block is: (?) * ? * ? * ? * (1 or 2)
// ?: over control
// *: fully under control (either 0,1,2)
rep(typ,TYP){
//write de Bruijn_like sequences at *s
rep(x,3)if(str[x]!=S[id]){
rep(y,3)if(str[y]!=S[id+1]){
if((x-y+3)%3==seq[typ][i%si(seq[typ])]){
T[id++]=str[x];
T[id++]=str[y];
x=y=3;
}
}
}
}
rep(x,3)if(str[x]!=S[id]&&str[x]!=T[id-1]){
T[id++]=str[x];
break;
}
}
while(si(T)>N)T.pop_back();
if(L>N)L=N;
return {T,L};
}
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef __int128 lll;
using ull = unsigned long long;
typedef pair<ll,ll> pll;
typedef vector<ll> vll;
typedef vector<pll> vpll;
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define all(x) x.begin(),x.end()
#define si(x) ll(x.size())
#define rep(i,n) for(ll i=0;i<n;i++)
#define per(i,n) for(ll i=n-1;i>=0;i--)
#define rng(i,l,r) for(ll i=l;i<r;i++)
#define gnr(i,l,r) for(ll i=r-1;i>=l;i--)
#define fore(i, a) for(auto &&i : a)
#define fore2(a, b, v) for(auto &&[a, b] : v)
#define fore3(a, b, c, v) for(auto &&[a, b, c] : v)
#include "Bruno.h"
namespace{
int N,L;
const int B=9,TYP=4;
//same as Anna
vector<int> de_Bruijn(int typ){
//ternaries of 3 digits
//except numbers whose digits are all (1 or 2) (ex. 121)
//also exept
//typ=0:
//typ=1: 010,101
//typ=2: 000,010,101
//typ=3: 010,101,020,202
ll len=3;
//make graph
ll n=pow(3,len-1);
vector<vector<pair<ll,ll> > >g(n);
auto valid=[&](ll x){
//valid as an edge?
if(typ>=1&&x==3)return 0;
if(typ>=1&&x==9+1)return 0;
if(typ==2&&x==0)return 0;
if(typ==3&&x==2*3)return 0;
if(typ==3&&x==2*9+2*1)return 0;
rep(_,len){
if(x%3==0)return 1;
x/=3;
}
return 0;
};
rep(i,3*n)if(valid(i)){
ll x=i/3;
ll y=i%n;
g[x].eb(y,i%3);
}
// {
// vector<int> cnt(n,0);
// rep(i,n)rep(j,si(g[i]))cnt[g[i][j].first]++;
// rep(i,n)if(cnt[i]!=si(g[i])){
// cout<<"invalid graph: degree sum is not 0"<<endl;
// }
// }
//generate sequence (get an euler cycle of the graph)
vector<int> ans;
function<void(ll,ll)> dfs=[&](ll x,ll col){
while(si(g[x])){
auto [nxt,ncol]=g[x].back();
g[x].pop_back();
dfs(nxt,ncol);
}
ans.pb(col);
};
ll start_vertex=0;
dfs(start_vertex,-1);
ans.pop_back();
reverse(all(ans));
return ans;
}
vector<int> seq[TYP];
map<ll,ll> rv[TYP];
map<tuple<ll,ll,ll,ll>,ll> block_id;
}
void init(int n,int l){
N=n,L=l;
//pre-calculate the difference sequence Anna generates
ll bruijn_len=3;
rep(typ,TYP){
seq[typ]=de_Bruijn(typ);
ll x=0;
rep(i,si(seq[typ])+bruijn_len-1){
x%=(ll)pow(3,bruijn_len-1);
x=x*3+seq[typ][i%si(seq[typ])];
if(i-(bruijn_len-1)>=0){
rv[typ][x]=i-(bruijn_len-1);
}
}
}
rep(i,N/B+1){
block_id[make_tuple(i%si(seq[0]),i%si(seq[1]),i%si(seq[2]),i%si(seq[3]))]=i;
}
}
int bruno(string U){
string str="RGB";
if(N==L)return 1;
//calculate difference sequence
vll v;
rep(i,L-1){
rep(x,3)if(str[x]==U[i]){
rep(y,3)if(str[y]==U[i+1]){
v.pb((x-y+3)%3);
}
}
}
int s; // s...where a block starts at
{
//for each remainder mod B(block size), see whether 0s exist in the given defference sequence (length L-1).
//It can be "No" for only 0,2,4,6,8th places (cf. a block is: ? * ? * ? * ? * (1 or 2) )
//always "Yes" for 1,3,5,7th places, since we generated de_Bruijn-like sequences in that way
//always "No" for 8th place.
//we can determine which is the 8th place, seeing the distance parities of "No" places.
vector<int> exzero(B,0);
rep(i,si(v)){
exzero[i%B]|=v[i]==0;
}
vll nonzeros;
rep(i,B)if(!exzero[i])nonzeros.pb(i);
if(si(nonzeros)==1){
s=nonzeros[0];
}
else{
s=nonzeros.back();
rep(i,si(nonzeros)-1){
if((nonzeros[i+1]-nonzeros[i])%2==1){
s=nonzeros[i];
break;
}
}
}
}
//calculate block's place using pre-calculated dictionary (patterns -> number)
vll pos;
rep(typ,TYP){
ll x=0;
rep(i,si(v))if(i%B==(s+2+2*typ)%B){
x=x*3+v[i];
}
ll pos_=rv[typ][x];
if(s+2+2*typ-B<0)pos_=(pos_-1+si(seq[typ]))%si(seq[typ]);
pos.pb(pos_);
}
ll res=block_id[make_tuple(pos[0],pos[1],pos[2],pos[3])];
return res*B+B-2-s+1;
}
