Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

B. Destruction of a Tree

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a tree (a graph with *n* vertices and *n* - 1 edges in which it's possible to reach any vertex from any other vertex using only its edges).

A vertex can be destroyed if this vertex has even degree. If you destroy a vertex, all edges connected to it are also deleted.

Destroy all vertices in the given tree or determine that it is impossible.

Input

The first line contains integer *n* (1 ≤ *n* ≤ 2·10^{5}) — number of vertices in a tree.

The second line contains *n* integers *p*_{1}, *p*_{2}, ..., *p*_{n} (0 ≤ *p*_{i} ≤ *n*). If *p*_{i} ≠ 0 there is an edge between vertices *i* and *p*_{i}. It is guaranteed that the given graph is a tree.

Output

If it's possible to destroy all vertices, print "YES" (without quotes), otherwise print "NO" (without quotes).

If it's possible to destroy all vertices, in the next *n* lines print the indices of the vertices in order you destroy them. If there are multiple correct answers, print any.

Examples

Input

5

0 1 2 1 2

Output

YES

1

2

3

5

4

Input

4

0 1 2 3

Output

NO

Note

In the first example at first you have to remove the vertex with index 1 (after that, the edges (1, 2) and (1, 4) are removed), then the vertex with index 2 (and edges (2, 3) and (2, 5) are removed). After that there are no edges in the tree, so you can remove remaining vertices in any order.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/16/2018 01:31:46 (d3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|