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.*;
import java.lang.*;
import java.net.*;


  
public class Main
{ 
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            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 cint() 
        { 
            return Integer.parseInt(next()); 
        } 
        
        long clong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double cdouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String cline() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }
    static class mycomp implements Comparator<Integer>{
        public int compare(Integer a, Integer b){
            return b-a;
        }
    }
    static boolean contains(int l,int r,int ans_l,int ans_r){
        if(r<ans_l||l>ans_r)return false;
        else return true;
    }

    
   public static void main(String[] args){
       FastReader f=new FastReader();
       int n=f.cint();boolean ok=true;
       HashMap<Integer,Integer>h=new HashMap<Integer,Integer>();
       HashMap<Integer,Integer>level=new HashMap<Integer,Integer>();
       int []arr=new int[n+1];
       arr[1]=-1;
       for(int i=2;i<n+1;i++){
           arr[i]=f.cint();
           if(h.containsKey(arr[i])){
               h.replace(arr[i],h.get(arr[i]+1));

           }
           else h.put(arr[i],1);
       }
       
       int []l_count=new int[n+1];
       for(int i=2;i<n+1;i++){
           if(!h.containsKey(i)){
               l_count[arr[i]]++;
           }
           

       }
       for(int i=1;i<n+1;i++){
           if(l_count[i]==0){
               if(h.containsKey(i)){
                   ok=false;
                   break;
               }
            }
               else if(l_count[i]>0&&l_count[i]<3){
                   ok=false;
                   break;
               }
           
       }
     
       if(ok)System.out.println("YES");
       else System.out.println("NO");
    }
}