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.BufferedReader;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.util.Collections;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.Map;
import java.util.Map.Entry;
import java.util.concurrent.SynchronousQueue;

public class Main {

	public static void main(String[] args) throws Exception {

	 BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		int t = Integer.parseInt(br.readLine());
		t = t + 1;
		LinkedList<Integer>[] nodes = new LinkedList[t];
		for (int i = 1; i < t; i++) {
			nodes[i] = new LinkedList<>();
		}
		for (int i = 1; i < t - 1; i++) {
			int x = Integer.parseInt(br.readLine());
			nodes[x].add(i + 1);

		}
	
		boolean flag = true;
		for (int i = 1; i < t; i++) {
			int ct = 0;
			int size = nodes[i].size();
			if (size > 0 && size < 3) {
				flag = false;
				break;
			} else if (size != 0) {
				for (int j = 0; j < size; j++) {
					if (nodes[nodes[i].get(j)].size() != 0) {
						ct++;
					}
				}
			//	System.out.println(size + "  "  + ct);
				if (size - ct < 3) {
					flag = false;
					break;
				}
			}
		}
		System.out.println((flag ? "Yes" : "No"));
	}

}