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.Arrays;
import java.util.Scanner;

public class P2 {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt();
		boolean[] valid = new boolean[n + 1];
		int[] child = new int[n + 1];
		int[] count = new int[n + 1];
		Arrays.fill(valid, true);
		
		for (int i = 2; i <= n; i++) {
			child[i] = sc.nextInt();
			valid[child[i]] = false;
		}
		
		for (int i = 2; i <= n; i++) {
			if (valid[i]) {
				count[child[i]]++;
			}
		}
		
		boolean flag = true;
		for (int i = 1; i <= n; i++) {
			if (valid[i]) {
				if (count[i] != 0) {
					flag = false;
					break;
				}
			} else {
				if (count[i] < 3) {
					flag = false;
					break;
				}
			}
		}
		
		if (flag) {
			System.out.println("Yes");
		} else {
			System.out.println("No");
		}
		
		sc.close();
	}
}