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 s = new Scanner(System.in);
        int amount_vert = s.nextInt();
        ArrayList<ArrayList<Integer>> vertexs = new ArrayList<>();
        for (int i = 0; i <= amount_vert; i++)
            vertexs.add(new ArrayList<>());

        for (int i = 1; i < amount_vert; i++) {
            vertexs.get(s.nextInt()).add(i + 1);
        }
        int counter = 0;
        for (int i = 1; i < vertexs.size(); i++) {
            if (vertexs.get(i).size() == 0)
                continue;
            counter = 0;
            for (int j = 0; j < vertexs.get(i).size(); j++) {
                if (vertexs.get(vertexs.get(i).get(j)).size() == 0)
                    counter++;
            }
            if (counter < 3){
                System.out.println("No");
                return;
            }

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

    }
}