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.*;
import java.util.*;

public class Main
{ 
    static BufferedReader br;
    static StringTokenizer st;
    
    public static class AL<T> extends ArrayList<T> {};
    
    public static void main(String[] args) throws IOException 
	{
		br = new BufferedReader(new InputStreamReader(System.in));
		st = new StringTokenizer(br.readLine());
		int n = nxtInt() + 1;
		
		int[] tr = new int[n], cnt = new int[n];
		//boolean[] isLf = new int[n];

		for(int i=2; i<n; i++) 
		{
		    tr[i] = Integer.parseInt(br.readLine());
		    cnt[tr[i]]++;
		}
		
		for(int i=n-1; i>=0; i--)
		{
		    if(cnt[i] >= 3) 
		    {
		        cnt[tr[i]]--;
		        if(cnt[tr[i]] == 0) cnt[tr[i]] = -1;
		    }
		}
		
		boolean flg = true;
		for(int i=1; i<n; i++)
		{
		    if(cnt[i] == -1 || !(cnt[i] == 0 || cnt[i] >= 3)) 
		    {
		        flg = false;
		        break;
		    }
		}
		System.out.print(flg? "Yes": "No");
	}
	
	static int nxtInt(){
            return Integer.parseInt(st.nextToken());
      }
      
      static long nxtLong(){
            return Long.parseLong(st.nextToken());
      }
      
      static double nxtDoub(){
            return Double.parseDouble(st.nextToken());
      }
}