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.io.FileInputStream;
import java.util.ArrayList;
import java.util.Scanner;
import java.util.Vector;


public class Test { 
	
	
	static Vector[] tree = new Vector[1005];
	static int[] pre = new int[1005];
	
	public static void main(String args[]){
		Scanner cin = null;
		cin = new Scanner(System.in);
		for(int i = 1; i < 1005; i++)
			tree[i] = new Vector<Integer>();
		
		int n, m;
		n = cin.nextInt();
		for(int i = 2; i <= n; i++) {
			m = cin.nextInt();
			tree[m].add(i);
		}
		if(dfs(1))
			System.out.println("Yes");
		else 
			System.out.println("No");
	}
	static boolean dfs(int j) {
		if(tree[j].size() == 0)
			return true;
		for(int i = 0; i < tree[j].size(); i++) {
			if(dfs((Integer)tree[j].get(i)) == false)
				return false;
			if(pre[(Integer)tree[j].get(i)] == 0) {
				pre[j]++;
			}
		}
		if(pre[j] >= 3)
			return true;
	    return false;
	}
}