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.ArrayList;
import java.util.Scanner;



/**
 *
 * @author Yan
 */
public class Test {
    /**
     * @param args the command line arguments
     */
    static ArrayList<Integer>[] mas;
    static boolean prov(int x){
        int k=0;
        for (int i:mas[x]){
            if (mas[i].size()==0) k++; 
        }
        if (k>=3) return true; else return false;
    }
    public static void main(String[] args) {
        Scanner in=new Scanner(System.in);
        int n=in.nextInt();
        mas=new ArrayList[n+1];
        for (int i=1; i<=n; i++) mas[i]=new ArrayList<Integer>();
        for (int i=2; i<=n; i++){
            mas[in.nextInt()].add(i);
        }
        int z=0;
        for (int i=1; i<=n; i++){
            if (mas[i].size()>0&&!prov(i)){
                System.out.print("No");
                z=1; break;       
            }
        }
        if (z==0) System.out.print("Yes");
    }
}