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.Scanner;

/**
 * Created on 08/01/2018.
 *
 * @author ThanhKM thanhkhongminh@gmail.com
 */
public class PB {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] p = new int[n+1];
        boolean[] isLeaf = new boolean[n+1];
        for (int i = 1; i <= n; i++)
            isLeaf[i] = true;

        for (int i = 2; i <= n; i++) {
            p[i] = sc.nextInt();
            isLeaf[p[i]] = false;
        }

        int[] nChilds = new int[n+1];
        for (int i = 2; i <= n; i++) {
            if (isLeaf[i]) nChilds[p[i]]++;
        }

        boolean isSpruce = true;
        for (int i = 1; i <= n; i++) {
            if (!isLeaf[i] && nChilds[i] < 3) {
                isSpruce = false;
                break;
            }
        }

        System.out.println(isSpruce? "Yes": "No");
    }
}