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.*;

import java.util.*;
import java.math.*;






public class Main{
    public static void main(String[] args) throws IOException {
  
         BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
    int n=Integer.parseInt(bf.readLine());
    visited=new boolean[n+1];
     a=new int[n+1];
    ar=new ArrayList[n+1];
    boolean check[]=new boolean[n+1];
    for(int i=1;i<=n;i++){ar[i]=new ArrayList<>();}
    int inc=2;
  for(int i=1;i<n;i++){
      int x=Integer.parseInt(bf.readLine());
  ar[x].add(inc);
  ar[inc].add(x);
  inc++;
  if(!check[x]) {check[x]=true;}
     }

  dfs(1);
  boolean key=true;
        
 for(int i=0;i<a.length;i++){if(check[i]&&a[i]<3){key=false;break;}}
  if(key){System.out.println("YES");}else{System.out.println("NO");}
    }
    static boolean visited[];
    static int count=0;
  static ArrayList<Integer> ar[];
  static void dfs(int z){
  visited[z]=true;
  int count=0;
  for(int i=0;i<ar[z].size();i++){
  if(!visited[ar[z].get(i)]){
      dfs(ar[z].get(i));
    
  }
  if(ar[ar[z].get(i)].size()==1){count++;}
  }
  a[z]=count;
  }
  static int a[];
   
  
}