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.*;
import java.io.*;
public class probB {
	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		int n  = sc.nextInt();
		Node[] roots = new Node[n];
		for(int i = 0; i < n; i++)
			roots[i] = new Node();
		for(int i = 1; i < n; i++) {
			roots[sc.nextInt()-1].sub.add(i);
		//	System.out.println(5641);
		}
		//System.out.println(Arrays.toString(roots));
		boolean ans = true;
		for(int i = 0; i < n; i++) {
			int child =0;
		//	System.out.println(roots[i].sub);
			for(int k = 0; k < roots[i].sub.size(); k++) {
				//System.out.println(roots[i].sub.get(k));
				//System.out.println(roots[k].sub);
				if(roots[roots[i].sub.get(k)].sub.size()==0)
					child++;
			}
			//System.out.println( i +  " " + child);
			if(roots[i].sub.size() != 0 && child < 3) {
				ans = false;
				break;
			}
			//System.out.println(child);
					
		}
		if(ans)
			System.out.println("Yes");
		else
			System.out.println("No");
		sc.close();
	}
	static class Node {
		ArrayList<Integer> sub = new ArrayList<Integer>();
		public Node() {
			
		}
		public String toString() {
			return sub.toString();
		}
	}
}