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 B913 {
	
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		Node root = new Node();
		
		root.data = 1;
		root.children = new ArrayList<Node>();

		for(int i = 2; i<=n; i++)
		{
			Node node = new Node();
			node.data = i;
			node.children = new ArrayList<Node>();
			insert_node(root, node, in.nextInt());
		}
		
		isSpruce(root);
		
		System.out.println("YES");

	}
	
	public static class Node<Integer> 
	{
		private int data;
		private List<Node> children;
	}
	
	public static void insert_node(Node root, Node node, int key)
	{
		if(root.data == key)
		{
			root.children.add(node);
			return;
		}

		for(Object n : root.children)
			insert_node((Node) n, node, key);
	}
	
	public static void isSpruce(Node root)
	{
		int leaves = 0;
		for(int i = 0; i < root.children.size(); i++)
		{
			if(isLeaf((Node) root.children.get(i)))
				leaves++;
			else
				isSpruce((Node) root.children.get(i));
		}

		if(leaves <= 2)
		{
			System.out.println("NO");
			System.exit(0);
		}
		
			
	}
	
	public static boolean isLeaf(Node root)
	{
		return root.children.size() == 0 ? true : false;
	}

}