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.List;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		Vertex[] vertexs = new Vertex[n+1];
		vertexs[1] = new Vertex();

		for (int i = 2; i <= n; i++) {
			vertexs[i] = new Vertex();
			int parent = sc.nextInt();
			vertexs[parent].children.add(vertexs[i]);
		}
		
		System.out.println(vertexs[1].isSpruce() ? "Yes" : "No");

	}

}

class Vertex {
	public List<Vertex> children = new ArrayList<>();

	public boolean isSpruce() {
		int leafsNumber = 0;

		for (Vertex v : this.children) {
			if (!v.isSpruce()) {
				return false;
			}
			if (v.isLeaf()) {
				leafsNumber++;
			}
		}
		
		return this.isLeaf() || leafsNumber >= 3;
	}

	public boolean isLeaf() {
		return this.children.isEmpty();
	}
}