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 main7 {
	static final int mxn = (int)1e5;
	public static void main(String[] args) throws IOException {
		Reader.init(System.in);
		int n = Reader.nextInt();
		// n vertices
		// a tree has n-1 edges
		int[] p = new int[mxn];
		int[] numchildren = new int[mxn];
		Arrays.fill(p, 0);
		Arrays.fill(numchildren, 0);

		for(int i = 1; i <= n-1; i++) {
			int indexofparent = Reader.nextInt();
			p[i + 1] = indexofparent;
			numchildren[indexofparent]++;

			//System.out.printf("%d - %d\n", i + 1, indexofparent);
		}

		// iterate over numchildren
		// if numchildren != 0, then iterate over vertices to see which vertex has parent this and numchildren == 0
		boolean found = true;
		for(int i = 1; i <= n; i++) {
			if(numchildren[i] != 0) {
				int count = 0;
				for(int j = i + 1; j <= n; j++) {
					if(numchildren[j] == 0 && p[j] == i) {
						count++;
					}
				}
				if(count < 3) {
					found = false;
					break;
				}
			}
		}
		String result = found ? "Yes" : "No";

		System.out.println(result);

	}

	static class Reader {
		static BufferedReader reader;
		static StringTokenizer tokenizer;
		
		static void init(InputStream input) {
			reader = new BufferedReader(new InputStreamReader(input));
			tokenizer = new StringTokenizer("");
		}
		
		static String next() throws IOException {
			while(!tokenizer.hasMoreTokens()) {
				tokenizer = new StringTokenizer(reader.readLine());
			}
			return tokenizer.nextToken();
		}
		
		static int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
		
		static long nextLong() throws IOException {
			return Long.parseLong(next());
		}
	}
}