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.math.*;
import java.io.*;
import java.lang.*;
import java.util.*;

public class Solution{
    public static ArrayList<Integer>[] adj;
    public static boolean[] visited;
    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        adj = new ArrayList[n+1];
        visited = new boolean[n];
        
        for(int i=1;i<=n;i++)
            adj[i] = new ArrayList<>();
            
        for(int i=2;i<=n;i++){
            int par = scan.nextInt();
            adj[par].add(i); 
        }
        
        if(dfs(1)) System.out.println("Yes");
        else System.out.println("No");
        
    }
    
    static boolean dfs(int vertex){
        int count = 0;
        for(int x: adj[vertex]){
            if(adj[x].isEmpty()) count++;
        }
        if(!adj[vertex].isEmpty() && count<3) return false;
        
        for(int x: adj[vertex]){
            if(!dfs(x)) return false;
        }
        return true;
    }
}