You 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.
The first line contains integer n (1 ≤ n ≤ 2·105) — 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.
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.
0 1 2 1 2
0 1 2 3
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.