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.*;
import java.io.*;

public class ChristmasSpruce {
	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out);
		int N = Integer.parseInt(in.readLine());
		List<Integer>[] children = new List[N];
		for(int i = 0; i < N; ++i) children[i] = new ArrayList<Integer>();
		for(int i = 1; i < N; ++i)
			children[Integer.parseInt(in.readLine()) - 1].add(i);
		// 0 - LEAF
		// 1 - SPRUCE
		// 2 - NOT LEAF OR SPRUCE
		out.println(treeType(0, children) != 2 ? "Yes" : "No");
		in.close();
		out.close();
	}
	public static int treeType(int node, List<Integer>[] children) {
		if(children[node].isEmpty())
			return 0;
		int numLeaves = 0;
		for(int child : children[node]) {
			int treeType = treeType(child, children);
			if(treeType == 0)
				numLeaves++;
			else if(treeType == 2)
				return 2;
		}
		return numLeaves >= 3 ? 1 : 2;
	}
}