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 C{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		Map<Integer,List<Integer>> m = new HashMap<>();
		m.put(1,new ArrayList<Integer>());
		for (int i=2;i<n+1;i++){
			int encours = sc.nextInt();
			List<Integer> l = new ArrayList<>();
			m.put(i,l);
			m.get(encours).add(i);
		}
		if (estSpruce(m,1)){
			System.out.println("Yes");
		} else{
			System.out.println("No");
		}
	}

	public static boolean estSpruce(Map<Integer,List<Integer>> m,int root){
		if (m.get(root).size()==0){
			return true;
		}
		List<Integer> fils = m.get(root);
		int nbFils = 0;
		boolean res = true;
		for (int p : fils){
			if (m.get(p).size()==0){
				nbFils++;
			} else {
				res = res && estSpruce(m,p);
			}
		}
		return (res && (nbFils>=3));
	}
}