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)

#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>

#include <iostream>
#include <complex>
#include <string>
#include <algorithm>
#include <numeric>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>

#include <functional>
#include <cassert>

typedef long long ll;
using namespace std;

#ifndef LOCAL
#define debug(x) ;
#else
#define debug(x) cerr << __LINE__ << " : " << #x << " = " << (x) << endl;

template <typename T1, typename T2>
ostream &operator<<(ostream &out, const pair<T1, T2> &p) {
  out << "{" << p.first << ", " << p.second << "}";
  return out;
}

template <typename T>
ostream &operator<<(ostream &out, const vector<T> &v) {
  out << '{';
  for (const T &item : v) out << item << ", ";
  out << "\b\b}";
  return out;
}
#endif

#define mod 1000000007 //1e9+7(prime number)
#define INF 1000000000 //1e9
#define LLINF 2000000000000000000LL //2e18
#define SIZE 200010

set<int> rs[SIZE];

int main() {
  int N;
  int a[SIZE], counter[SIZE] = {};

  scanf("%d", &N);

  set<int> ss;

  for (int i=0; i<N; i++) ss.insert(i);

  for (int i=0; i<N; i++) {
    scanf("%d", a+i);
    a[i]--;
    counter[a[i]]++;
    rs[a[i]].insert(i);
  }

  set<int> v;

  for (int i=0; i<N; i++)
    if (rs[i].size()) v.insert(i);

  if (N == 2) {
    puts("-1");
    return 0;
  }

  int now = -1;

  vector<int> ans;

  for (int i=0; i<N-3; i++) {
    auto it = ss.begin();
    int p1 = *it; it++;
    int p2 = *it; it++;
    int p3 = *it;

    set<int> tmp;
    tmp.insert(p1);
    tmp.insert(p2);
    tmp.insert(p3);

    auto it2 = v.begin();
    int t1 = *it2; it2++;
    int t2 = *it2;

    tmp.insert(*rs[t1].begin());
    tmp.insert(*rs[t2].begin());

    for (auto pp : tmp) {
      debug(pp);
      if (now != -1 && a[now] == pp) continue;
      if (rs[a[pp]].size() == 1 && v.size() == 2) continue;

      ans.push_back(pp);
      ss.erase(pp);
      now = pp;
      rs[a[pp]].erase(pp);

      if (rs[a[pp]].size() == 0) {
        v.erase(a[pp]);
      }
      break;
    }

    debug(ans);
  }

  int vv[3];
  auto it = ss.begin();
  for (int i=0; i<3; i++) {
    vv[i] = *it;
    it++;
  }

  do{
    bool ok = N <= 3 || a[*ans.rbegin()] != vv[0];

    for (int i=0; i<2; i++) {
      ok &= a[vv[i]] != vv[i+1];
    }

    if (ok) {
      ans.push_back(vv[0]);
      ans.push_back(vv[1]);
      ans.push_back(vv[2]);
      break;
    }

  }while(next_permutation(vv, vv+3));

  assert(ans.size() == N);

  for (int i=0; i<N; i++) {
    printf("%d%c", ans[i]+1, " \n"[N==i+1]);
  }

  return 0;
}