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.ArrayList;
import java.util.Scanner;

public class MainClass {
    static int n;
    static ArrayList<Integer> son[];    
    public static void main(String[] args){
        inputData();
        System.out.println(isSpruce() ? "Yes" : "No");
    }    
    public static void inputData(){
       Scanner in = new Scanner(System.in);
       n = in.nextInt();
       son = new ArrayList[n];
       for(int i = 0; i < n; i++)
           son[i] = new ArrayList<>();
       for(int i = 1; i < n; i++){
           int x = in.nextInt() - 1;           
           son[x].add(i);
       }
    }
    public static boolean isSpruce(){
        for(int i = 0; i < n; i++){
            if (!son[i].isEmpty()){
                int leafCnt = 0;
                for(Integer u: son[i]){
                    if (son[u].isEmpty())
                        leafCnt++;
                } 
                //System.out.println(leafCnt);
                if (leafCnt < 3)
                    return false;
            }
        }                   
        return true;
    }
}