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 ti{
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		HashMap<Integer,ArrayList<Integer>> map = new HashMap<>();
		for(int i=1;i<n;i++){
			int a = sc.nextInt();
			if(map.containsKey(a)){
				ArrayList<Integer> arr = map.get(a);
				arr.add(i+1);
			}
			else{
				ArrayList<Integer> arr = new ArrayList<>();
				arr.add(i+1);
				map.put(a,arr);
			}
			for(Map.Entry<Integer,ArrayList<Integer>> entry : map.entrySet()){
				ArrayList<Integer> q = entry.getValue();
				if(q.contains(a)){
					q.remove((Integer)a);
				}
			}
		}
		int flag=0;
		for(Map.Entry<Integer,ArrayList<Integer>> entry : map.entrySet()){
			ArrayList<Integer> q = entry.getValue();
			if(q.size()<3){
				flag=1;
				break;
			}
		}
		if(flag==1){
			System.out.println("No");
		}
		else{
			System.out.println("Yes");
		}
	}
}