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 cp {

    public static void main(String args[]) {

    	Scanner sc = new Scanner();

    		int n = sc.nextInt();

    		ArrayList<ArrayList<Integer>> al = new ArrayList<>();


    		for(int i=0;i<=n;i++)
    		{
    			al.add(new ArrayList<>());
    		}

    		boolean poss = true;

    		for(int i=0;i<n-1;i++)
    		{
    			al.get(sc.nextInt()).add(i+2);
    		}

    		for(int i=0;i<=n;i++)
    		{
    		//	out.println(al.get(i));
    			if(al.get(i).size()>0)
    			{
    				int count = 0;
    				for(int x:al.get(i))
    				{
    					if(al.get(x).size()==0)
    						count++;
    				}
    				if(count<3)
    					{poss=false;break;}
    			}
    			// if(!poss)
    			// 	break;
    		}

    		if(poss)
    			out.println("Yes");
    		else out.println("No");
    		
    	out.close();
    }

    static	PrintWriter out=new PrintWriter(System.out);
	static class Scanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String nextLine() {
			while (!st.hasMoreTokens())
				try { 
                                        st=new StringTokenizer(br.readLine());				               
                                } catch (IOException e) {}
			return st.nextToken();
		}
		char nextChar() {
			char c = '$';
				try { 
                                        c = (char)br.read();			               
                                } catch (IOException e) {}
			return c;
		}		
		int nextInt() {
			return Integer.parseInt(nextLine());
		}
		float nextFloat() {
			return Float.parseFloat(nextLine());
		}
		double nextDouble() {
			return Double.parseDouble(nextLine());
		}
		long nextLong() {
			return Long.parseLong(nextLine());
		}
	}
}