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.*;
import java.util.*;

public class Mainn {

	public static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader() {
			reader = new BufferedReader(new InputStreamReader(System.in), 32768);
			tokenizer = null;
		}

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(System.in), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}
	}

	public static ArrayList<Integer>[] tree;
	public static int[] child;
	
	
	public static void main(String[] args) {

		// InputStream inputStream = System.in; // Useful when taking input other than
		// console eg file handling // check ctor of inputReader
		InputReader scn = new InputReader();

		int n = scn.nextInt();
		tree = new ArrayList[n + 1];
		child = new int[n + 1];
		for (int i = 0; i <= n; i++) {
			tree[i] = new ArrayList<>();
		}
		for (int i = 1; i < n; i++) {
			int x = scn.nextInt();
			tree[x].add(i + 1);
		}
		dfs(1);
		for(int i = 1; i < child.length; i++) {
			if(child[i] != -1 && child[i] < 3) {
				System.out.println("No");
				return;
			}
		}
		System.out.println("Yes");
	}
	
	public static int dfs(int node) {
		if(tree[node].size() == 0) {
			child[node] = -1;
			return 1;
		}
		
		for(int i = 0; i < tree[node].size(); i++) {
			int x = dfs(tree[node].get(i));
			child[node] += x;
		}
		
		return 0;
	}
}