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;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int num = sc.nextInt();
        ArrayList<Integer> arr = new ArrayList<Integer>(1001);
        int[] data = new int[num+1];
        int[] leaf = new int[num+1];
        leaf[1] = -1;
        arr.add(0);
        arr.add(0);
        for(int i=0;i<num-1;++i){
            arr.add(sc.nextInt());
            sc.nextLine();
        }
//        System.out.println(arr.toString());
        for(int i=2;i<=num;++i){
            if(!arr.contains(i)){
                data[arr.get(i)]++;
            }else{
                leaf[i] = -1;
            }
        }
//        for(int j:leaf){
//            System.out.print(j+" ");
//        }
//        System.out.println();
        for(int i=1;i<num+1;++i){
            if(leaf[i]==-1 && data[i]<3){
                System.out.print("No");
                return;
            }
        }
        System.out.print("Yes");
    }
}