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.Arrays;
import java.util.Scanner;

public class B {

	static ArrayList<Integer>[] g;
	static int[] p;
	static int[] c;

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		c = new int[n];
		g = new ArrayList[n];
		p = new int[n];
		Arrays.fill(p, -1);

		for (int i = 1; i < n; i++) {
			int ip = in.nextInt() - 1;
			if (g[ip] == null)
				g[ip] = new ArrayList<Integer>();
			g[ip].add(i);
			p[i] = ip;
		}
		if (n == 1) {
			System.out.println("Yes");
		} else {

			for (int i = 0; i < n; ++i) {
				if (g[i] == null)
					c[p[i]]++;
			}

			for (int i = 0; i < n; ++i) {
				if (g[i] == null) continue;
				if (c[i] < 3) {
					System.out.println("No");
					return;
				}
			}
		}
		System.out.println("Yes");
		in.close();
	}

}