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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Temp {
	// -------------------
	public static final int MOD = (int) (1e9 + 7);
	// ------------------

	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	StringTokenizer st;
	PrintWriter out = new PrintWriter(System.out);

	String next() {
		while (st == null || !st.hasMoreElements()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				e.printStackTrace();
			}
		}
		return st.nextToken();
	}

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

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

	// ------------------
	public static void main(String[] args) {
		Temp ob = new Temp();
		ob.run();
	}

	private void run() {
		int n = nextInt();
		int[] parent = new int[n+1];
		int[] cnt = new int[n+1];
		boolean[] isleaf = new boolean[n+1];
		Arrays.fill(isleaf, true);
		for(int i=2;i<=n;i++) {
			parent[i] = nextInt();
			isleaf[parent[i]]=false;
		}
		for(int i=2;i<=n;i++) {
			if(isleaf[i]) {
			 cnt[parent[i]] +=1;
			}
		}
		
		for(int i=1;i<=n;i++) {
			if(!isleaf[i] && cnt[i]<3) {
				out.println("No");
				out.close();
				return;
			}
		}
		out.println("Yes");
		out.close();
	}

}