#include "doll.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
#define watch(x) cout<<(#x)<<"="<<(x)<<'\n'
#define mset(d,val) memset(d,val,sizeof(d))
#define setp(x) cout<<fixed<<setprecision(x)
#define forn(i,a,b) for(int i=(a);i<(b);i++)
#define fore(i,a,b) for(int i=(a);i<=(b);i++)
#define pb push_back
#define F first
#define S second
#define pqueue priority_queue
#define fbo find_by_order
#define ook order_of_key
typedef long long ll;
typedef pair<ll,ll> ii;
typedef vector<ll> vi;
typedef vector<ii> vii;
typedef long double ld;
typedef tree<ll, null_type, less<ll>, rb_tree_tag, tree_order_statistics_node_update> pbds;
void amin(ll &a, ll b){ a=min(a,b); }
void amax(ll &a, ll b){ a=max(a,b); }
void YES(){cout<<"YES\n";} void NO(){cout<<"NO\n";}
void SD(int t=0){ cout<<"PASSED "<<t<<endl; }
const ll INF = int(1e9);
const int MOD = 998244353;
const bool DEBUG = 0;
const int MAXN = 200005;
vector<int> c,x,y;
int dfs(int rt, vector<int> nxt)
{
if(nxt.size()==2)
{
if(nxt[0]==INF){
x.pb(rt);
y.pb(nxt[1]);
if(DEBUG) cout<<"Base 1: "<<-(int)x.size()<<" -> "<<x.back()<<", "<<y.back()<<'\n';
return -(int)x.size();
}
else{
x.pb(nxt[0]);
y.pb(nxt[1]);
if(DEBUG) cout<<"Base 2: "<<-(int)x.size()<<" -> "<<x.back()<<", "<<y.back()<<'\n';
return -(int)x.size();
}
}
if(nxt.size()%2) nxt.insert(nxt.begin(), INF);
if(DEBUG){
forn(z,0,2){
cout<<"nxt=";
for(int X: nxt) cout<<X<<" ";
cout<<'\n';
}
}
vector<int> tmp[2];
for(int i=0;i<nxt.size();i++) tmp[i%2].pb(nxt[i]);
nxt.clear();
if(DEBUG){
forn(z,0,2){
cout<<"tmp["<<z<<"]=";
for(int X: tmp[z]) cout<<X<<" ";
cout<<'\n';
}
}
x.emplace_back();
y.emplace_back();
int self = x.size();
int nxtx = dfs(rt, tmp[0]);
int nxty = dfs(rt, tmp[1]);
x[self-1]=nxtx;
y[self-1]=nxty;
if(DEBUG) cout<<"Normal: "<<-self<<" -> "<<nxtx<<", "<<nxty<<'\n';
return -self;
}
void create_circuit(int m, vector<int> a)
{
int n = a.size();
c.resize(m+1);
vector<int> nxt[m+1];
forn(i,0,n-1){
nxt[a[i]].pb(a[i+1]);
}
nxt[a[n-1]].pb(0);
if(DEBUG){
fore(i,1,m){
cout<<"nxt["<<i<<"]=";
for(int x: nxt[i]) cout<<x<<" ";
cout<<'\n';
}
}
c[0]=a[0];
if(DEBUG) cout<<"c["<<0<<"] -> "<<c[0]<<'\n';
fore(i,1,m){
if(nxt[i].empty()){
c[i]=i;
if(DEBUG) cout<<"c["<<i<<"] -> "<<c[i]<<" (to self)\n";
continue;
}
c[i]=dfs(-(int)x.size()-1, nxt[i]);
if(DEBUG) cout<<"c["<<i<<"] -> "<<c[i]<<'\n';
}
answer(c,x,y);
}
