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.ArrayList;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;
public class ChristmasSpruse {
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        ArrayList<Integer> ar[]=new ArrayList[n+1];
        for(int i=1;i<=n;i++)
        {
            ar[i]=new ArrayList<>();
        }
        
        for(int i=2;i<=n;i++)
        {
            int x=sc.nextInt();
            ar[x].add(i);
        }
        int c=0;
        Queue<Integer> q=new LinkedList<>();
        q.add(1);
        while(q.size()!=0)
        {
            int r=q.remove();
            
            if(ar[r].size()==0)
                continue;
            
            c=0;
            for(int j=0;j<ar[r].size();j++)
            {
                if(ar[ar[r].get(j)].size()==0)
                {
                    c+=1;
                }
                q.add(ar[r].get(j));
            }
            if(c<3)
            {
                System.out.println("NO");
                return;
            }
            
        }
        System.out.println("YES");
    }
}