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 class Virtual
{
	static Scanner in=new Scanner(System.in);
	public static void main(String[] args)
	{
		
		solveB();
	}
	
	
	
	private static void solveB()
	{
		// TODO Auto-generated method stub
		int n=in.nextInt();
		LinkedList<Integer>[] list=new LinkedList[n+1];
		for(int i=1;i<=n;i++)
		{
			list[i]=new LinkedList<Integer>();
		}
		for(int i=2;i<=n;i++)
		{
			int v=in.nextInt();
			list[v].add(i);
		}
		dfs(list,1);
		if(check)
		{
			System.out.println("YES");
		}
		else
		{
			System.out.println("NO");
		}
	}
	
	static boolean check=true;



	private static void dfs(LinkedList<Integer>[] list, int u)
	{
		// TODO Auto-generated method stub
		if(list[u].size()==0)return;
		int nl=0;
		for(int v:list[u])
		{
			dfs(list, v);
			if(list[v].size()==0)
			nl++;
		}
		if(nl<3)check=false;
	}

}