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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.FileNotFoundException;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author triveni
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskB solver = new TaskB();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskB {
		ArrayList<ArrayList<Integer>> graph = null;

		public void solve(int testNumber, InputReader in, PrintWriter out) {
			int n = in.nextInt();
			graph = new ArrayList<>(n + 1);
			for (int i = 0; i <= n; ++i) graph.add(new ArrayList<Integer>());
			for (int i = 2; i <= n; ++i) {
				int p = in.nextInt();
				graph.get(p).add(i);
			}
			boolean ans = dfs(1);
			out.println(ans ? "Yes" : "No");
		}

		boolean dfs(int u) {
			ArrayList<Integer> l = graph.get(u);
			if (l.size() == 0) return true;
			boolean ans = true;
			int c = 0;
			for (int child : l) {
				if (graph.get(child).size() == 0) c += 1;
				else ans &= dfs(child);
			}
			ans &= c > 2;
			return ans;
		}

	}

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

		public InputReader(InputStream inputStream) {
			reader = new BufferedReader(new InputStreamReader(inputStream));
			tokenizer = null;
		}

		public InputReader(String inputFile) throws FileNotFoundException {
			reader = new BufferedReader(new FileReader(inputFile));
			tokenizer = null;
		}

		public String nextLine() {
			String curr = "";
			try {
				curr = reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
			return curr;
		}

		public String nextString() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(nextLine());
				} catch (Exception e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

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

	}
}