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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

//Link : https://codeforces.com/contest/1194/problem/B

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define N 100005
int a[N];

vector<int> bestFactorial(int ban,vector<int>v) {
  vector<int> ret;

  assert(v.size()<=4 && v.size()>=3);
  do {
    if(v[0]==ban) {
      continue;
    }
    bool isGood = true;
    for(int i=0;i<v.size()-1;++i) {
      if(a[v[i]]==v[i+1]) {
        isGood = false;
        break;
      }
    }
    if(isGood) {
      if(ret.size()==0) {
        ret = v;
      } else {
        ret = min(ret,v);
      }
    }
  } while(next_permutation(v.begin(),v.end()));
  assert(ret.size()!=0);
  return ret;
}

set<int> rem;
void printBest(int ban) {
  if(rem.size()<=4) {
    vector<int> v;
    for(int node : rem) {
      v.push_back(node);
    }
    vector<int> r = bestFactorial(ban,v);
    for(int i=0;i<r.size();++i) {
      printf("%d ", r[i]);
    }
    putchar('\n');
    return;
  }
  for(int node : rem) {
    if(node==ban) {
      continue;
    }
    rem.erase(node);
    printf("%d ", node);
    rem.erase(node);
    printBest(a[node]);
    break;
  }
}
void solve() {
  int n;scanf("%d ", &n);
  for(int i=1;i<=n;++i) {
    scanf("%d ", &a[i]);
    rem.insert(i);
  }
  if(n==2) {
    printf("-1\n");
    return;
  }
  printBest(0);
}

int main() {
    //freopen("input.txt","r",stdin);
    solve();
    return 0;
}