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 B {
   public static void main(String[] args) {
      Scanner sc = new Scanner(System.in);
      
      int N = sc.nextInt();
      ArrayList<Integer>[] gr = new ArrayList[N + 1];
      for(int i = 0; i < N + 1; i++) {
         gr[i] = new ArrayList<Integer>();
      }
      
      for(int i = 2; i < N + 1; i++) {
         int p = sc.nextInt();
         gr[p].add(i);
      }
      
      for(int i = 1; i <= N; i++) {
         if(gr[i].size() == 0)
            continue;
         int count = 0;
         for(int j = 0; j < gr[i].size(); j++) {
            if(gr[gr[i].get(j)].size() == 0)
               count++;
         }
         if(count < 3) {
            System.out.println("No");
            System.exit(0);
         }
      }
      System.out.println("Yes");
   }
}