CF913B.Christmas Spruce

普及/提高-

通过率：0%

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题目描述

Consider a rooted tree. A rooted tree has one special vertex called the root. All edges are directed from the root. Vertex $u$ is called a child of vertex $v$ and vertex $v$ is called a parent of vertex $u$ if there exists a directed edge from $v$ to $u$ . A vertex is called a leaf if it doesn't have children and has a parent.

Let's call a rooted tree a spruce if its every non-leaf vertex has at least $3$ leaf children. You are given a rooted tree, check whether it's a spruce.

The definition of a rooted tree can be found here.

输入格式

The first line contains one integer $n$ — the number of vertices in the tree ( $3<=n<=1000$ ). Each of the next $n-1$ lines contains one integer $p_{i}$ ( $1<=i<=n-1$ ) — the index of the parent of the $i+1$ -th vertex ( $1<=p_{i}<=i$ ).

Vertex $1$ is the root. It's guaranteed that the root has at least $2$ children.

输出格式

Print "Yes" if the tree is a spruce and "No" otherwise.

输入输出样例

输入#1
```
4
1
1
1
```
输出#1
```
Yes
```
输入#2
```
7
1
1
1
2
2
2
```
输出#2
```
No
```
输入#3
```
8
1
1
1
1
3
3
3
```
输出#3
```
Yes
```

说明/提示

The first example:

The second example:

It is not a spruce, because the non-leaf vertex $1$ has only $2$ leaf children.

The third example:

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