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: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;

#define range(i, m, n) for(int i = m; i < n; i++)
#define husk(i, m, n) for(int i = m; i > n; i--)

int n;

int main() {
  cin >> n;
  vector<int> cnt(n);
  vector<int> a(n);
  range(i, 0, n) {
    cin >> a[i];
    a[i]--;
    cnt[a[i]]++;
  }
  vector<int> pos;
  range(i, 0, n) if(cnt[i] == n - 1) {
    pos.push_back(i);
  }
  if(pos.size() > 1) {
    cout << -1;
    return 0;
  }
  if(!pos.empty()) {
    vector<int> res = {pos[0]};
    range(i, 0, n) if(i != pos[0]) res.push_back(i);
    if(a[res[0]] == res[1]) swap(res[1], res[2]);
    for(int i : res) cout << i + 1 << " ";
    return 0;
  }
  set<int> cur;
  vector<int> res;
  range(i, 0, n) cur.insert(i);
  while(cur.size() > 1) {
    auto it = cur.begin();
    if(!res.empty() && a[res.back()] == *it) it = next(it);
    res.push_back(*it);
    cur.erase(it);
  }
  int c = *cur.begin();
  cur.erase(c);
  while(res.size()) {
    if(a[res.back()] == c) {
      cur.insert(res.back());
      res.pop_back();
    }
    else break;
  }
  if(cur.size() == 1 && a[c] == *cur.begin()) {
    res.push_back(*cur.begin());
    vector<int> tt = res;
    int pos = -1;
    husk(i, res.size() - 3, -2) {
      if(i == -1 || a[res[i]] != c) {
        tt.insert(tt.begin() + i + 1, c);
        pos = i;
        break;
      }
    }
    int z = res[res.size() - 2];
    res.erase(res.begin() + res.size() - 2);
    husk(i, res.size() - 4, pos - 1) {
      if(i == -1 || a[res[i]] != z) {
        res.insert(res.begin() + i + 1, z);
        res.insert(res.begin() + i + 2, c);
        res = min(res, tt);
        break;
      }
    }
  } else {
    res.push_back(c);
    while(cur.size()) {
      int c = *cur.begin();
      if(a[res.back()] == c) c = *next(cur.begin());
      cur.erase(c);
      res.push_back(c);
    }
  }
  for(int i : res) cout << i + 1 << " ";
  return 0;
}