Problem: 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).

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 pi (1 ≤ i ≤ n - 1) — the index of the parent of the i + 1-th vertex (1 ≤ pi ≤ 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.

Examples

Input

4
1
1
1


Output

Yes


Input

7
1
1
1
2
2
2


Output

No


Input

8
1
1
1
1
3
3
3


Output

Yes

Note

The first example:

<image>

The second example:

<image>

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

The third example:

<image>

Solution (in JAVA):

Solution:
import java.util.*;
public final class codechef
{
    public static void main(String args[])
    {
        Scanner sc=new Scanner(System.in);
        
        int n=sc.nextInt();
        boolean adj[][]=new boolean[n+1][n+1];
        for(int i=2;i<=n;i++)
        {
            int x=sc.nextInt();
            adj[x][i]=true;
        }
        boolean leaf[]=new boolean[n+1];
        for(int i=2;i<=n;i++)
        {
            leaf[i]=true;
            for(int j=2;j<=n;j++)
            {
                if(adj[i][j]==true)
                leaf[i]=false;
            }
        }
        boolean flag=true;
        for(int i=1;i<=n;i++)
        {
            if(!leaf[i])
            {
                int c=0;
                for(int j=1;j<=n;j++)
                {
                    if(adj[i][j]&&leaf[j])
                    c++;
                }
                if(c<3)
                flag=false;
            }
            
        }
        System.out.println(flag?"Yes":"No");
    }
}