Christmas Spruce

题意翻译

题意 考虑一颗有根树。一颗有根树有一个叫做根的特殊顶点，所有边的方向都是从根来的。如果有一条从v到u的边，那么顶点v是u的父亲，u是v的孩子。如果一个顶点没有孩子并且有一个父亲，这个顶点叫做叶结点。 如果一颗有根树的每个非叶结点至少有三个是叶结点的孩子，这棵树是一棵云杉。 给你一颗有根树，检查它是否是一棵云杉。 输入格式： 第一行包含一个整数 n（3<=n<=1000），树中的顶点数。 接下来的n-1行每行包含一个整数 p_{i}（1<=i<=n-1，1<=p_{i}<=i），表示第i+1个顶点的父亲。 顶点1为根，保证根最少有两个孩子。 输出格式： 如果它是云杉，输出"Yes"，否则，输出 "No"。 Translated by Fowany

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](https://goo.gl/1dqvzz).

输入输出格式

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

输入样例 #1

4
1
1
1

输出样例 #1

Yes

输入样例 #2

7
1
1
1
2
2
2

输出样例 #2

No

输入样例 #3

8
1
1
1
1
3
3
3

输出样例 #3

Yes

说明

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: