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 B {
	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		boolean[] check = new boolean[n];
		HashSet<Integer>[] point = new HashSet[n];
		int[] parent = new int[n];
		for(int i=0; i<n; i++) {
			check[i] = true;
			point[i] = new HashSet<Integer>();
			parent[i] = -1;
		}
		for(int i=1; i<=n-1; i++) {
			int e = sc.nextInt();
			parent[i] = e; //i+1 has parent e
			point[e-1].add(i+1); //e has child i+1
			if(point[e-1].size()>=3) {
				check[e-1] = true;
			} else {
				check[e-1] = false;
			}
			if(parent[e-1]>=0) {
				point[parent[e-1]-1].remove(e); // e now has child so not a leaf
				if(point[parent[e-1]-1].size() <3) {
					check[parent[e-1]-1] = false;
				}
			}
		}
		boolean flag = false;
		for(boolean b: check) {
			if(!b) {
				System.out.println("NO");
				flag = true;
				break;
			}
		}
		if(!flag) {
			System.out.println("YES");
		}
	}
}