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.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;

public class Main {

	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n =Integer.parseInt(br.readLine());
		int[] points = new int[n+1];
		int[] leaf = new int[n+1];
		ArrayList<ArrayList<Integer>> children = new ArrayList<>();
		children.add(null);
		children.add(new ArrayList<>());
		for (int z = 2; z <= n; z++) {
			int edge = Integer.parseInt(br.readLine());
			points[z] = edge;
			children.add(new ArrayList<>());
			children.get(edge).add(z);
			
		}
		boolean spruce = true;
		for (int i = 1; i <= n; i++) {
			if (children.get(i).size() == 0) {
				leaf[i] = 1;
			}
		}
//		for (int i = 1; i < children.size();i++) {
//			System.out.print("{");
//			for (int j = 0; j < children.get(i).size();j++) {
//				System.out.print(children.get(i).get(j)+",");
//			}
//			System.out.print("}");
//			System.out.println();
//		}
//		for (int i = 0; i < leaf.length;i++) {
//			System.out.print(leaf[i] + " ");
//		}
		for (int i = 1; i <= n; i++) {
			if (leaf[i] == 0) {
				// points[i]
				if (children.get(i).size() >= 3) {
					int count = 0;
					for (int a : children.get(i)) {
						if (leaf[a] == 1) {
							count++;
						}
					}
					if (count >= 3) {
						continue;
					} else {
						spruce = false;
						break;
					}
				} else {
					spruce = false;
					break;
				}
			}
		}
		if (spruce == true) {
			System.out.println("Yes");
		} else {
			System.out.println("No");
		}
		
	}

}