CF963B.Destruction of a Tree

普及/提高-

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题目描述

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.

输入格式

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.

输出格式

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.

输入输出样例

输入#1
```
5
0 1 2 1 2
```
输出#1
```
YES
1
2
3
5
4
```
输入#2
```
4
0 1 2 3
```
输出#2
```
NO
```

说明/提示

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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