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.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Main {
    public static void main(String[] args){
        Scanner input = new Scanner(System.in);
        int tc = input.nextInt();
        HashSet<Integer> set = new HashSet<Integer>();
        String answer = "Yes";
        int childrenarr[] = new int[tc+1];
        boolean isnotleaf[] = new boolean[tc+1];
        int parent[] = new int[tc+1];
        for (int i=0;i<tc-1;i++){
            int in = input.nextInt();
            set.add(in);
            childrenarr[in]++;
            parent[i+2] = in;
            if (isnotleaf[in]==false){
                isnotleaf[in] = true;
                if(in!=1) {
                        childrenarr[parent[in]]--;

                }



            }

        }
        for(Integer ele: set){
           if (childrenarr[ele]<=2)
               answer = "No";
        }
        System.out.println(answer);

    }
}