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.util.*;
public class A_GENERAL {

	private static boolean[] visited;
	public static void main(String[] args) {
		
		MyScanner sc = new MyScanner();
		
		int n = sc.nextInt();
		int[] deg = new int[n+1];
		ArrayList<Integer>[] childs = new ArrayList[n+1];
		for(int i = 2; i <= n; i++) {
			int v = sc.nextInt();
			deg[v]++;
			deg[i]++;
			if(childs[v] == null) childs[v] = new ArrayList();
			if(childs[i] == null) childs[i] = new ArrayList();
			childs[v].add(i);
		}
		ArrayDeque<Integer> q = new ArrayDeque<>();
		q.offer(1);
		while(!q.isEmpty()) {
			int u = q.poll();
			int cnt = 0;
//			System.out.println(u + " ");
			for(int i = 0; i < childs[u].size(); i++) {
				int v = childs[u].get(i);
//				System.out.println("v = " + v);
				if(deg[v] == 1) 
					cnt++;
				else	q.offer(v);
			}
			if(cnt < 3) {
				System.out.println("No");
				return;
			}
				
		}
		System.out.println("Yes");
		
	}

	static class MyScanner {
		BufferedReader br;
		StringTokenizer st;
		public MyScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		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());}
		double nextDouble() {return Double.parseDouble(next());}
		String nextLine(){String str = "";
		try {str = br.readLine();}
		catch (IOException e) {e.printStackTrace();}
		return str;}
	}
	
}