Problem:
Score : 800 points

Problem Statement

Niwango has N cards, numbered 1,2,\ldots,N.
He will now arrange these cards in a row.

Niwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below.
To help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.

To the immediate right of Card 1 (if any) is NOT Card a_1.

To the immediate right of Card 2 (if any) is NOT Card a_2.

\vdots

To the immediate right of Card N (if any) is NOT Card a_N.

Constraints

2 \leq N \leq 10^{5}

1 \leq a_i \leq N

a_i \neq i

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 \ldots a_N

Output

If no arrangements satisfy the conditions, print -1. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:

b_1 b_2 \ldots b_N

Here, b_i represents the i-th card from the left.

Sample Input 1

4
2 3 4 1

Sample Output 1

1 3 2 4

The arrangement (1,2,3,4) is lexicographically smaller than (1,3,2,4), but is invalid, since it violates the condition "to the immediate right of Card 1 is not Card 2."

Sample Input 2

2
2 1

Sample Output 2

-1

If no arrangements satisfy the conditions, print -1.

Sample Input 3

13
2 3 4 5 6 7 8 9 10 11 12 13 12

Sample Output 3

1 3 2 4 6 5 7 9 8 10 12 11 13

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Runtime.CompilerServices;
using System.Text;
using static Template;
using static System.Console;
using static System.Convert;
using static System.Math;
using Pi = Pair<int, int>;

class Solver
{
    public void Solve(Scanner sc)
    {
        var N = sc.Int;
        var A = new int[N];
        var ct = new int[N];
        for (var i = 0; i < N; i++)
        {
            A[i] = sc.Next<int>() - 1;
            ct[A[i]]++;
        }
        var q = new PriorityQueue<int>();
        for (var i = 0; i < N; i++) q.Push(i);
        var use = new bool[N];
        var res = new List<int>();
        for (var i = 0; i < N-5; i++)
        {
            var p = q.Pop();
            while (q.Any() && use[q.Top]) q.Pop(); 
            if (i > 0 && A[res[i - 1] - 1] == p)
            {
                var t = p;
                p = q.Pop();
                while (q.Any() && use[q.Top]) q.Pop();
                q.Push(t);
            }
            if (!use[A[p]]&&ct[A[p]] == N - i - 1)
            {
                q.Push(p);
                p = A[p];
            }
            use[p] = true;
            ct[A[p]]--;
            res.Add(p + 1);
            while (q.Any() && use[q.Top]) q.Pop();
        }
        var a = q.data.Where(v=>!use[v]).ToList();a.Sort();
        foreach (var p in Permutations(Enumerable.Range(0, a.Count).ToArray()))
        {
            var b = true;
            if (res.Count > 0)
                b = A[res.Last() - 1] != a[p[0]];
            for (var j = 0; j < a.Count - 1; j++)
                b &= A[a[p[j]]] != a[p[j + 1]];
            if (b) { res.AddRange(Enumerable.Range(0, a.Count).Select(v => a[p[v]] + 1).ToArray()); Console.WriteLine(string.Join(" ", res)); return; }
        }
        WriteLine(-1);
    }
    static IEnumerable<T[]> Permutations<T>(T[] array) where T : IComparable<T>
    {
        int index = 0;
        yield return array;
        while (true)
        {
            for (int i = array.Length - 1; i > 0; i--)
            {
                if (array[i - 1].CompareTo(array[i]) >= 0) continue;
                int j = Array.FindLastIndex(array, x => array[i - 1].CompareTo(x) < 0);
                T tmp = array[i - 1]; array[i - 1] = array[j]; array[j] = tmp;
                Array.Reverse(array, i, array.Length - i);
                yield return array;
                goto end;
            }
            Array.Reverse(array, index, array.Length);
            yield break;
        end:;
        }
    }
}

public class PriorityQueue<T>
{
    public List<T> data = new List<T>();
    private Comparison<T> cmp;
    public int Count { get { return data.Count; } }
    public T Top { get { return data[0]; } }
    public PriorityQueue() { cmp = cmp ?? Comparer<T>.Default.Compare; }

    public PriorityQueue(Comparison<T> comparison) { cmp = comparison; }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    private int Parent(int i)
        => (i - 1) >> 1;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    private int Left(int i)
        => (i << 1) + 1;
    public T Push(T val)
    {
        int i = data.Count;
        data.Add(val);
        while (i > 0)
        {
            int p = Parent(i);
            if (cmp(data[p], val) <= 0)
                break;
            data[i] = data[p];
            i = p;
        }
        data[i] = val;
        return val;
    }
    public T Pop()
    {
        var ret = data[0];
        var p = 0;
        var x = data[data.Count - 1];
        while (Left(p) < data.Count - 1)
        {
            var l = Left(p);
            if (l < data.Count - 2 && cmp(data[l + 1], data[l]) < 0) l++;
            if (cmp(data[l], x) >= 0)
                break;
            data[p] = data[l];
            p = l;
        }
        data[p] = x;
        data.RemoveAt(data.Count - 1);
        return ret;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public bool Any() => data.Count > 0;
}
#region Template
public static class Template
{
    static void Main(string[] args)
    {
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        new Solver().Solve(new Scanner());
        Console.Out.Flush();
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmin<T>(ref T a, T b) where T : IComparable<T>
    { if (a.CompareTo(b) == 1) { a = b; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmax<T>(ref T a, T b) where T : IComparable<T>
    { if (a.CompareTo(b) == -1) { a = b; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(ref T a, ref T b)
    { var t = b; b = a; a = t; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static T[] Create<T>(int n, Func<T> f)
    {
        var rt = new T[n];
        for (var i = 0; i < rt.Length; ++i)
            rt[i] = f();
        return rt;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static T[] Create<T>(int n, Func<int, T> f)
    {
        var rt = new T[n];
        for (var i = 0; i < rt.Length; ++i)
            rt[i] = f(i);
        return rt;
    }
    public static T[] Copy<T>(this T[] A)
        => Create(A.Length, i => A[i]);
    public static void Fail<T>(T s) { Console.WriteLine(s); Console.Out.Close(); Environment.Exit(0); }
}

public class Scanner
{
    public string Str => Console.ReadLine().Trim();
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public int[] ArrInt => Str.Split(' ').Select(int.Parse).ToArray();
    public long[] ArrLong => Str.Split(' ').Select(long.Parse).ToArray();
    public char[][] Grid(int n) => Create(n, () => Str.ToCharArray());
    public int[] ArrInt1D(int n) => Create(n, () => Int);
    public long[] ArrLong1D(int n) => Create(n, () => Long);
    public int[][] ArrInt2D(int n) => Create(n, () => ArrInt);
    public long[][] ArrLong2D(int n) => Create(n, () => ArrLong);
    public Pair<T1, T2> PairMake<T1, T2>() => new Pair<T1, T2>(Next<T1>(), Next<T2>());
    public Pair<T1, T2, T3> PairMake<T1, T2, T3>() => new Pair<T1, T2, T3>(Next<T1>(), Next<T2>(), Next<T3>());
    private Queue<string> q = new Queue<string>();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public T Next<T>() { if (q.Count == 0) foreach (var item in Str.Split(' ')) q.Enqueue(item); return (T)Convert.ChangeType(q.Dequeue(), typeof(T)); }
    public void Make<T1>(out T1 v1) => v1 = Next<T1>();
    public void Make<T1, T2>(out T1 v1, out T2 v2) { v1 = Next<T1>(); v2 = Next<T2>(); }
    public void Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3) { Make(out v1, out v2); v3 = Next<T3>(); }
    public void Make<T1, T2, T3, T4>(out T1 v1, out T2 v2, out T3 v3, out T4 v4) { Make(out v1, out v2, out v3); v4 = Next<T4>(); }
    public void Make<T1, T2, T3, T4, T5>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5) { Make(out v1, out v2, out v3, out v4); v5 = Next<T5>(); }
    public void Make<T1, T2, T3, T4, T5, T6>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6) { Make(out v1, out v2, out v3, out v4, out v5); v6 = Next<T6>(); }
}

public class Pair<T1, T2> : IComparable<Pair<T1, T2>>
{
    public T1 v1;
    public T2 v2;
    public Pair() { }
    public Pair(T1 v1, T2 v2)
    { this.v1 = v1; this.v2 = v2; }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int CompareTo(Pair<T1, T2> p)
    {
        var c = Comparer<T1>.Default.Compare(v1, p.v1);
        if (c == 0)
            c = Comparer<T2>.Default.Compare(v2, p.v2);
        return c;
    }
    public override string ToString() => $"{v1.ToString()} {v2.ToString()}";
    public void Tie(out T1 a, out T2 b) { a = v1; b = v2; }
}

public class Pair<T1, T2, T3> : Pair<T1, T2>, IComparable<Pair<T1, T2, T3>>
{
    public T3 v3;
    public Pair() : base() { }
    public Pair(T1 v1, T2 v2, T3 v3) : base(v1, v2)
    { this.v3 = v3; }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int CompareTo(Pair<T1, T2, T3> p)
    {
        var c = base.CompareTo(p);
        if (c == 0)
            c = Comparer<T3>.Default.Compare(v3, p.v3);
        return c;
    }
    public override string ToString() => $"{base.ToString()} {v3.ToString()}";
    public void Tie(out T1 a, out T2 b, out T3 c) { Tie(out a, out b); c = v3; }
}
#endregion