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 ChristmasSpruce {
	static ArrayList<Integer>[] a;
	public static void main(String[] args) {
		Scanner scan=new Scanner(System.in);
		int n=scan.nextInt();
		a=new ArrayList[n];
		for(int i=0;i<n;i++) a[i]=new ArrayList<Integer>();
		for(int i=1;i<n;i++) {
			int x=scan.nextInt()-1;
			a[x].add(i);
		}
//		System.out.println(Arrays.toString(a));
		System.out.println(go(0)?"Yes":"No");
	}
	public static boolean go(int n) {
//		System.out.println(n);
		boolean res=true;
		int temp=0;
		for(int i:a[n]) {
			if(a[i].size()==0)temp++;
			else res&=go(i);
		}
//		System.out.println(temp);
		res&=temp>=3;
		return res;
	}
}