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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.

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