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 tree1{

    public static void main(String args[]){

        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();

        int max = 0;
        int c;

        int pa[] = new int[n+1];
        int ca[] = new int[n+1];

        for (int i = 2 ; i <= n ; i++){
            c = sc.nextInt();

            if (c > max){
                max = c;
            }

            pa[i] = c;

            ca[c]++;

            //ca[pa[i]]--;
        }

        for (int i = 2 ; i<=max ; i++){
            if (ca[i] > 0)
                ca[pa[i]]--;
        }

        boolean flag = true;

        for (int i = 2 ; i<=n ; i++){
            //System.out.println(i + ": " + ca[i]);
            if (ca[pa[i]] < 3){
                System.out.println("No");
                return;
            }
        }

        System.out.println("Yes");
            
    }
}