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.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class B {
	static ArrayList<Integer> G[];

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		G = new ArrayList[n+1];
		for (int i = 0 ; i < G.length;i++)
			G[i] = new ArrayList<Integer>();
		for (int i = 2; i < n+1; i++) {
			int num = scan.nextInt();
			G[num].add(i);
			
		}
		
		System.out.println(isSparse(1) ? "Yes" : "No");
	}

	public static boolean isSparse(int parent) {
		for (int k = parent; k < G.length; k++) {
			if (G[k].size() > 0 && G[k].size() < 3)
				return false;
			int count = 0;
			if (G[k].size() > 0){
				for (int i = 0; i < G[k].size(); ++i) {
					int tmp = G[k].get(i);
					if (G[tmp].size() == 0)
						count++;
				}
			if (count < 3)
				return false;}
		}
		return true;
	}
}