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.

Input

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.

Output

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

Note

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: