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 Rust (1.15.1) (judge verdict: Wrong Answer)

//https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 より
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

//

use std::io::Write;

fn valid(a: &[usize], ans: &[usize]) -> bool {
    for i in 1..ans.len() {
        if a[ans[i - 1]] == ans[i] {
            return false;
        }
    }
    true
}

fn run() {
    let out = std::io::stdout();
    let mut out = std::io::BufWriter::new(out.lock());
    input! {
        n: usize,
        a: [usize; n],
    }
    if n == 2 {
        println!("-1");
        return;
    }
    let mut a = a;
    a.reverse();
    a.push(0);
    a.reverse();
    let mut ans = vec![0; n + 1];
    let mut set = std::collections::BTreeSet::new();
    for i in 1..(n + 1) {
        set.insert(i);
    }
    for i in 1..(n + 1 - 3) {
        let mut v = 0;
        for &k in set.iter() {
            if a[ans[i - 1]] != k {
                v = k;
                break;
            }
        }
        set.remove(&v);
        ans[i] = v;
    }
    let b: Vec<usize> = set.into_iter().collect();
    let (x, y, z) = (b[0], b[1], b[2]);
    for &(x, y, z) in [(x, y, z), (x, z, y), (y, x, z), (y, z, x), (z, x, y), (z, y, x)].iter() {
        ans[n - 2] = x;
        ans[n - 1] = y;
        ans[n - 0] = z;
        if valid(&a, &ans) {
            for (i, a) in ans.into_iter().skip(1).enumerate() {
                if i > 0 {
                    write!(out, " ").ok();
                }
                write!(out, "{}", a).ok();
            }
            writeln!(out, "").ok();
            return;
        }
    }
}

fn main() {
    run();
}