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.Scanner;
import java.util.Stack;

public class C {
	static int mod = 1000000007;
	static ArrayList<Integer>[] g;

	public static void main(String[] args) {

		Scanner nik = new Scanner(System.in);
		int n = nik.nextInt();

		ArrayList<Integer>[] a = new ArrayList[n];
		for (int i = 0; i < n; i++) {
			a[i] = new ArrayList<>();
		}

		for (int i = 1; i < n; i++) {
			int temp = nik.nextInt() - 1;
			a[temp].add(i);
		}
		boolean b = true;
		for (int i = 0; i < n; i++) {
			if (a[i].size() > 0) {
				int c = 0;
				for (int j = 0; j < a[i].size(); j++) {

					if (a[a[i].get(j)].size() == 0) {
						c++;
					}
				}
				if (c < 3) {
					b = false;
				}

			}
		}
		if (b) {
			System.out.println("Yes");
		} else {
			System.out.println("No");
		}
	}

}