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 tres
{
	static int visited[]=new int[1001];
    static int arr[][]=new int[1001][1001];
    static int bac[]=new int[1001];
	static int n;
    static int temp=0;	
	static void dfs(int i)
	{ 
	    int flag=0;
	    for(int h=0;h<n;h++)
		{
		  if(arr[i][h]!=0)
		  {flag=1;
			  break;}			  
		}
		if(flag==0)
		{
			bac[temp]++;
			visited[i]++;
		}
	    visited[i]++;	
		int j;
		for(j=0;j<n;j++)
		{
			if(arr[i][j]==1&&visited[j]==0)
			{  
                temp=i;		
				dfs(j);
			}
		}
	}
	public static void main(String args[])
	{
		Scanner s=new Scanner(System.in);
		n=s.nextInt();
		int i;
		for(i=1;i<n;i++)
		{
			int a=s.nextInt();
			arr[a-1][i]=1;
		}
		dfs(0);
		int flag=0;
		for(i=0;i<n;i++)
		{
			if(visited[i]==1&&bac[i]<3)
			{
				flag=1;
				break;
			}
			
		}
		if(flag==1)
			System.out.println("No");
		else
			System.out.println("Yes");
	}
}