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.*;

public class Main {
    
    LinkedList<Integer> graph[];
    int V;
    public Main(int v){
        this.V = v;
        graph = new LinkedList[v+1];
        for(int i=1; i<v+1; i++){
            graph[i] = new LinkedList<>();
        }
    }
    
    public void addEdge(int src, int des){
        graph[src].add(des);
    }
    
    
    public boolean getsome(Set<Integer> set){
        for (int i : set) {
            int count = 0;
            for(int y:graph[i]){
                Iterator<Integer> itr1 = graph[y].listIterator();
                if(!itr1.hasNext()){
                    count++;
                }
            }
            if(count<3){
                return false;
            }
        }
        return true;
    }
    
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        Main grp = new Main(n);
        Set<Integer> set = new HashSet<Integer>();
        
        for(int i=0; i<n-1; i++){
            int s = Integer.parseInt(br.readLine());
            set.add(s);
            grp.addEdge(s, i+2);
        }
        
        if(grp.getsome(set)){
            System.out.println("Yes");
        }else{
            System.out.println("No");
        }
                
    }
}