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)

// Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools

#include <bits/stdc++.h>

using namespace std;

using i64 = long long;

const i64 MOD = 1e9 + 7;
const i64 INF = i64(1e18) + 7;


template <typename T>
bool chmin(T& x, T y){
    if(x > y){
        x = y;
        return true;
    }
    return false;
}

template <typename T>
bool chmax(T& x, T y){
    if(x < y){
        x = y;
        return true;
    }
    return false;
}

int n;
vector<int> a;
vector<int> path;
multiset<int> ign;
set<int> used;
clock_t st;

void solve(int idx, int now){
    path[idx] = now;
    if((double(clock()) - st) / CLOCKS_PER_SEC >= 2){
        cout << -1 << endl;
        exit(0);
    }
    if(idx == n - 1){
        for(int i = 0; i < n; ++i)
            cout << path[i] + 1 << " \n"[i == n - 1];
        exit(0);
    }

    used.erase(now);

    if(*ign.begin() == *ign.rbegin() && used.find(*ign.begin()) != used.end()){
        cout << "hoge" << endl;
        used.emplace(now);
        return;
    }

    ign.erase(ign.find(a[now]));

    for(auto it = used.begin(); it != used.end(); ++it){
        if(*it != a[now])
            solve(idx + 1, *it);
    }
    used.emplace(now);
    ign.insert(a[now]);
}


signed main(){
    long long N;
    st = clock();
    scanf("%lld",&N);
    std::vector<int> A(N);
    for(int i = 0 ; i < N ; i++){
        scanf("%d",&A[i]);
    }
    n = move(N);
    a = move(A);
    path.assign(n, 150);
    for(int i = 0; i < n; ++i){
        used.emplace(i);
        --a[i];
        ign.insert(a[i]);
    }
    return 0;
    for(int i = 0; i < n; ++i)
        solve(0, i);
    cout << -1 << endl;
    return 0;
}