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 <iostream>
#include <cassert>
#include <queue>
#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define trav(a, x) for(auto& a : x)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
using namespace std;

using ll = long long;
const ll mod = 1e9 + 7;

void print(priority_queue<int, vector<int>, greater<int>> pq) {
	while (!pq.empty()) cout << pq.top(), pq.pop();
}

signed main() {
	cin.sync_with_stdio(false); cin.tie(nullptr);
	cin.exceptions(cin.failbit);

	int n; cin >> n;
	int nxt[n], indeg[n];
	rep(i, 0, n)
		cin >> nxt[i], --nxt[i];
	rep(i, 0, n) indeg[i] = 0;
	rep(i, 0, n) ++indeg[nxt[i]];
	if (n == 2) return cout << -1, 0;
		
	queue<int> q;
	priority_queue<int, vector<int>, greater<int>> pq;

	int u = 0;
	rep(i, 0, n) if (indeg[i] == n - 1) u = i;
	q.push(u);
	rep(i, 0, n) if (i != u) pq.push(i);
	while (!pq.empty()) {
		int v = -1;
		if (pq.top() == nxt[u]) {
			v = nxt[u]; pq.pop();
		}
		u = pq.top();
		q.push(u);
		pq.pop();
		if (v != -1) pq.push(v);
	}
	while (!q.empty()) cout << q.front() + 1 << ' ', q.pop();
}