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:
/******************************************************************************

                            Online Java Compiler.
                Code, Compile, Run and Debug java program online.
Write your code in this editor and press "Run" button to execute it.

*******************************************************************************/
import java.util.*;
public class Main
{
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
	    int[] arr=new int[1002];
	    int[][] adj=new int[1002][1002];
	    int n=sc.nextInt();
	    for(int i=2;i<n+1;i++)
	    {
	        int x=sc.nextInt();
	        adj[x][i]=1;
	        arr[x]++;
	    }
	    String ans="Yes";
	    for(int i=1;i<1001;i++)
	    {
	        if(arr[i]>0)
	        {
	            int temp=0;
	        for(int j=1;j<1001;j++)
	        {
	            if(adj[i][j]==1)
	            {
	                if(arr[j]==0)
	                temp++;
	            }
	        }
	        if(temp<3)
	        {
	            System.out.println("No");
	            return;
	        }
	        }
	    }
	    System.out.println("Yes");
	}
}