/*
* Author: Nonoze
* Created: Sunday 11/08/2024
*/
#include <bits/stdc++.h>
#include "doll.h"
using namespace std;
#ifndef _IN_LOCAL
#define dbg(...)
#endif
#define endl '\n'
#define endlfl '\n' << flush
#define quit(x) return (void)(cout << x << endl)
template<typename T> void read(T& x) { cin >> x;}
template<typename T1, typename T2> void read(pair<T1, T2>& p) { read(p.first), read(p.second);}
template<typename T> void read(vector<T>& v) { for (auto& x : v) read(x); }
template<typename T1, typename T2> void read(T1& x, T2& y) { read(x), read(y); }
template<typename T1, typename T2, typename T3> void read(T1& x, T2& y, T3& z) { read(x), read(y), read(z); }
template<typename T1, typename T2, typename T3, typename T4> void read(T1& x, T2& y, T3& z, T4& zz) { read(x), read(y), read(z), read(zz); }
template<typename T> void print(vector<T>& v) { for (auto& x : v) cout << x << ' '; cout << endl; }
#define sz(x) (int)(x.size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define cmin(a, b) a = min(a, b)
#define cmax(a, b) a = max(a, b)
// #define int long long
const int inf = numeric_limits<int>::max() / 4;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int MOD = 1e9+7, LOG=25;
int m, n, base=0;
vector<int> a, ans, x, y, state;
vector<pair<int, int>> par;
void build(int prec, bool left, int mx, int nb) {
if (nb==0) {
if (prec<=0) ans[-prec]=base;
else if (left) x[prec-1]=base;
else y[prec-1]=base;
return;
}
if (mx==2) {
if (nb==1) {
if (prec<=0) ans[-prec]=-sz(x)-1;
else if (left) x[prec-1]=-sz(x)-1;
else y[prec-1]=-sz(x)-1;
x.pb(base), y.pb(-inf), par.pb({prec, left});
return;
}
if (prec<=0) ans[-prec]=-sz(x)-1;
else if (left) x[prec-1]=-sz(x)-1;
else y[prec-1]=-sz(x)-1;
x.pb(-inf), y.pb(-inf), par.pb({prec, left});
return;
}
if (prec<=0) ans[-prec]=-sz(x)-1;
else if (left) x[prec-1]=-sz(x)-1;
else y[prec-1]=-sz(x)-1;
if (base==0) base=-sz(x)-1;
x.pb(inf), y.pb(inf), par.pb({prec, left});
int s=sz(x);
build(s, 1, mx/2, max(0, nb-mx/2));
build(s, 0, mx/2, min(nb, mx/2));
}
void simulate(int empl, int val) {
int nxt=(state[empl]?y[empl]:x[empl]);
if (nxt==-inf) {
if (state[empl]) y[empl]=val;
else x[empl]=val;
state[empl]^=1;
return;
}
nxt=-nxt-1;
state[empl]^=1;
simulate(nxt, val);
}
void create_circuit(int MM, vector<int> AA) { m=MM, a=AA, n=sz(a); ans.resize(m+1, inf); ans[0]=a[0];
state.resize(2*n);
vector<vector<int>> nxts(m+1);
vector<bool> done(m+1, 0);
for (int i=0; i<n; i++) nxts[a[i]].pb((i<n-1?a[i+1]:0));
vector<int> nxt;
int first=0;
for (int i=1; i<n; i++) {
if (sz(nxts[a[i-1]])>4) nxt.pb(a[i]), first=a[i-1];
}
if (sz(nxts[a.back()])>4) nxt.pb(0), first=a.back();
for (int i=1; i<=m; i++) if (sz(nxts[i])<=4) {
if (sz(nxts[i])<=1) {
if (sz(nxts[i])==1) ans[i]=nxts[i][0];
else ans[i]=0;
continue;
}
base=0;
int mx=1;
while (mx<sz(nxts[i])) mx*=2;
build(-i, 1, mx, sz(nxts[i]));
for (auto u: nxts[i]) simulate(-ans[i]-1, u);
}
if (sz(nxt)>=2) {
base=0;
int mx=1;
while (mx<sz(nxt)) mx*=2;
build(-first, 1, mx, sz(nxt));
for (auto u: nxt) simulate(-ans[first]-1, u);
}
for (auto &u: ans) if (u==inf) u=ans[first];
// for (int i=0; i<=m; i++) {
// cout << i << ' ' << ans[i] << endl;
// }
// for (int i=0; i<sz(x); i++) {
// cout << -i-1 << ' ' << x[i] << ' ' << y[i] << endl;
// }
answer(ans, x, y);
}
