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.Scanner;

public class tree {

	public static void main(String[] args)
	{
		// TODO Auto-generated method stub
		Scanner input=new Scanner(System.in);
		int n=input.nextInt();
		int[] a=new int[n+1];
		
		int[] s=new int[n+1];
		a[0]=0;
		a[1]=0;
		for(int i=2;i<a.length;i++)
		{
			a[i]=input.nextInt();
		}
		
		
		for(int i=2;i<=n;i++)
		{
			if(temp(i,a)==1 && a[i]!=0)
				s[a[i]]++;
			
			
			
		}
		
		for(int i=2;i<s.length;i++)
		{
			if(s[a[i]]!=0 && s[a[i]]>=3 )
			{
				if(i==s.length-1)
					System.out.print("YES");
				else
					continue;
			}
			else
			{
				System.out.print("NO");
				break;
			}
		}
		
	}
	public static int temp(int i,int[] a)
	{
		int k=0;
		for(int j=0;j<a.length;j++)
		{
			if(i!=a[j])
			{
				if(j==a.length-1)
					return 1;
			}
			else
				return 0;
		}
		
		return 0;
			
	}
}