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 Abd El-Rahman Saeed
 */
public class CodeForces {

    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int n = s.nextInt();
        Node[] list = new Node[n];
        list[0] = new Node(0, 1);
        for (int i = 1; i < list.length; i++) {
            list[i] = new Node(s.nextInt(), i + 1);
        }
        for (Node list1 : list) {
            for (int j = 1; j < list.length; j++) {
                if (list[j].parent == list1.nodeNumber) {
                    list1.child.add(list[j].nodeNumber);
                }
                list1.LeafsChilds = list1.child.size();
            }
        }

        for (Node list1 : list) {
            list1.child.stream().forEach((child) -> {
                if (list[child - 1].child.size() > 0) {
                    list1.LeafsChilds--;
                }
            });
        }

        for (Node list1 : list) {
            if (list1.LeafsChilds < 3 && list1.child.size() > 0) {
                System.out.println("No");
                return;
            }
        }
        System.out.println("Yes");
    }
}

class Node {

    int nodeNumber;
    int parent;
    ArrayList<Integer> child = new ArrayList<>();
    int LeafsChilds;

    public Node(int parent, int nodeNumber) {
        this.parent = parent;
        this.nodeNumber = nodeNumber;
    }
}