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.io.InputStream;
import java.io.PrintStream;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

/**
 */
public class Main913B {
	public static void main(String[] args) {
		run(System.in, System.out);
	}

	public static void run(InputStream in, PrintStream out) {

		try (Scanner sc = new Scanner(in)) {
			int n = sc.nextInt();
			Map<Integer, List<Integer>> graph = new HashMap<>();

			for (int i = 1; i <= n + 1; i++) {
				graph.put(i, new ArrayList<>());
			}

			for (int i = 1; i < n; i++) {
				int parent = sc.nextInt();
				graph.get(parent).add(i + 1);
			}

			for (Integer node : graph.keySet()) {
				List<Integer> children = graph.get(node);
				int cnt = 0;
				for (Integer child : children) {
					if (graph.get(child).size() == 0) cnt++;
				}
				if (children.size() > 0 && cnt < 3) {
					out.print("No");
					return;
				}

			}

			out.print("Yes");
		}
	}

}