#include "doll.h"
#include<bits/stdc++.h>
using namespace std;
typedef vector<int> vi;
#define pb emplace_back
#define SZ(x) (int)x.size()
inline int MSB(unsigned int x){
return 32-__builtin_clz(x);
}
#define INF 1e9
vi occ[130100];
int c=-1;
vi X,Y;
void fill(int sizes, int numfill, int rt){
// cout<<sizes<<' '<<numfill<<' '<<exit<<'\n';
if (sizes == numfill){
if (sizes == 2){
X.pb(1);Y.pb(1);
return;
}
int t=SZ(X);
X.pb(c--);
Y.pb(0);
fill (sizes/2,numfill/2,rt);
Y[t] = c--;
fill(sizes/2,numfill/2,rt);
return;
}
if (numfill == 2){
if (sizes == 1){
X.pb(rt);
Y.pb(1);
}else{
X.pb(1);
Y.pb(1);
}
return;
}
if (sizes*2 <= numfill){
X.pb(rt);
Y.pb(c--);
fill (sizes, numfill/2,rt);
return;
}else{
int t=SZ(X);
X.pb(c--);
Y.pb(0);
fill (sizes-numfill/2, numfill/2, rt);
Y[t] = c--;
fill (numfill/2,numfill/2,rt);
return;
}
}
void f2(int sizes, int numf2, int exit, int rt){
// cout<<sizes<<' '<<numf2<<' '<<exit<<'\n';
if (sizes == numf2){
if (sizes == 2){
if (exit){
X.pb(1);
Y.pb(0);
}else{
X.pb(1);
Y.pb(1);
}
return;
}
int t=SZ(X);
X.pb(c--);
Y.pb(0);
f2 (sizes/2,numf2/2,0,rt);
Y[t] = c--;
if (exit)f2 (sizes/2,numf2/2,1,rt);
else f2(sizes/2,numf2/2,0,rt);
return;
}
if (numf2 == 2){
if (sizes == 1){
X.pb(rt);
Y.pb(1-exit);
}else{
X.pb(1);
Y.pb(1-exit);
}
return;
}
if (sizes*2 <= numf2){
X.pb(rt);
Y.pb(c--);
f2 (sizes, numf2/2, 0, rt);
return;
}else{
int t=SZ(X);
X.pb(c--);
Y.pb(0);
f2 (sizes-numf2/2, numf2/2, 0, rt);
Y[t] = c--;
f2 (numf2/2,numf2/2,exit,rt);
return;
}
}
vi C;
int states[270100];
void simulate(int x){
map<int,int> states;
for (int t=0;t<SZ(occ[x]);++t){
int cur=C[x];
// cout<<"Simulate with dest "<<occ[x][t]<< " from "<<cur<<'\n';
while (1){
int nxt = X[-1-cur];
if (states[-1-cur] == 1){
nxt = Y[-1-cur];
}
// cout<<"At "<<cur<<" aka "<<-1-cur<<" next is "<<nxt<<'\n';
if (nxt == 1){
// cout<<"Change "<<-1-cur<<" when the state is "<<cur<<'\n';
if (states[-1-cur] == 1){
Y[-1-cur] = occ[x][t];
}else{
X[-1-cur] = occ[x][t];
}
states[-1-cur] = 1-states[-1-cur];
break;
}else{
states[-1-cur] = 1-states[-1-cur];
cur = nxt;
}
}
}
}
void create_circuit(int M, std::vector<int> A) {
int N = A.size();
C.resize(M+1,-1);
if (M == 1){
int t = MSB(N-1);
int l = (1<<t);
C[1] = c--;
C[0]=1;
f2(N,l,1,-1);
answer(C,X,Y);
return;
}
occ[0].pb(A[0]);
for (int i=0;i<N-1;++i){
occ[A[i]].pb(A[i+1]);
}
occ[A[N-1]].pb(0);
for (int i=0;i<=M;++i){
if (SZ(occ[i]) == 0){
C[i]=0;
}else if(SZ(occ[i]) == 1){
C[i]=occ[i][0];
}else if (SZ(occ[i]) == 2){
C[i] = c;
--c;
X.pb(occ[i][0]);
Y.pb(occ[i][1]);
}else if (SZ(occ[i]) == 3){
int a = c;
C[i] = a;
c -= 3;
X.pb(a-1);
Y.pb(a-2);
X.pb(occ[i][0]);
Y.pb(a);
X.pb(occ[i][1]);
Y.pb(occ[i][2]);
}else if (SZ(occ[i]) == 4){
int a = c;
C[i] = a;
c -= 3;
X.pb(a-1);
Y.pb(a-2);
X.pb(occ[i][0]);
Y.pb(occ[i][2]);
X.pb(occ[i][1]);
Y.pb(occ[i][3]);
}else{
int N = SZ(occ[i]);
int t = MSB(N-1);
int l = (1<<t);
int cc=c;
C[i] = c--;
fill(N,l,cc);
}
// cout<<"Value "<<i<<" ends at "<<c<<'\n';
// for (int i=0;i<SZ(X);++i)cout<<X[i]<<' '<<Y[i]<<'\n';
}
// for (int i=0;i<=M;++i)cout<<C[i]<<' ';cout<<"\n\n";
// for (int i=0;i<SZ(X);++i)cout<<X[i]<<' '<<Y[i]<<'\n';
for (int i=0;i<=M;++i){
if (SZ(occ[i]) > 4)simulate(i);
}
// for (int i=0;i<=M;++i)cout<<C[i]<<' ';cout<<"\n\n";
// for (int i=0;i<SZ(X);++i)cout<<X[i]<<' '<<Y[i]<<'\n';
// for (int i=0;i<=M;++i)cout<<C[i]<<' ';cout<<'\n';
answer(C,X,Y);
}
