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 Main {

    public static void main(String[] args){

        Scanner sc = new Scanner(System.in);
        int n=sc.nextInt();

        List<List<Integer>> ls = new ArrayList<>();

        for(int i=0;i<n;i++){
            ls.add(new ArrayList<>());
        }

        for(int i=0;i<n-1;i++){
            int x=sc.nextInt()-1;
            ls.get(x).add(i+1);
        }

        int c=0;
        boolean flag=true;

        for(int i=0;i<n;i++){
            if(!(ls.get(i).isEmpty())){
                c=0;
                for(int ch:ls.get(i)){
                    if(ls.get(ch).isEmpty()){
                        c++;
                    }
                }

                if(c<3){
                    System.out.print("NO");
                    flag=false;
                    break;
                }

            }
        }

        if(flag==true){
            System.out.print("YES");
        }




    }

}