CF913B.Christmas Spruce

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.

考虑一棵有根树。有根树中有一个特殊的顶点，称为根（root）。所有边的方向均从根出发。若存在一条从顶点 $v$ 指向顶点 $u$ 的有向边，则称顶点 $u$ 是顶点 $v$ 的子节点（child），顶点 $v$ 是顶点 $u$ 的父节点（parent）。若一个顶点没有子节点但有父节点，则称其为叶节点（leaf）。

我们称一棵有根树为“云杉树”（spruce），当且仅当它的每一个非叶节点至少有 3 个叶节点作为子节点。现给你一棵有根树，请判断它是否为云杉树。

有根树的定义可参见此处。

The first line contains one integer n — the number of vertices in the tree (3 ≤ n ≤ 1 000). 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.

第一行包含一个整数 $n$ —— 树中顶点的数量（$3 \leq n \leq 1\,000$）。接下来的 $n-1$ 行中，第 $i$ 行（$1 \leq i \leq n-1$）包含一个整数 $p_i$ —— 第 $i+1$ 个顶点的父节点编号（$1 \leq p_i \leq i$）。

顶点 1 是根节点。保证根节点至少有两个子节点。

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

如果该树是一棵云杉，则输出“Yes”，否则输出“No”。

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:

第一个例子：

第二个例子：

它不是云杉树，因为非叶顶点 1 仅有 2 个叶节点子节点。

第三个例子：