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.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

public class Main {

    static class Node{
        List<Integer> children = new ArrayList<>();
    }

    public static boolean solution(List<Node> node){
        for(int i = 0; i < node.size(); i++){
            int sum = 0;
            if (node.get(i).children.size() == 0) continue;
            for (int j = 0; j < node.get(i).children.size(); j++){
                int k = node.get(i).children.get(j);
                if (node.get(k).children.size() == 0) sum++;
            }
            if(sum < 3) return false;

        }
        return true;
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int n = in.nextInt();
        List<Node> node = new ArrayList<>();
        for (int i = 0; i < n; i++) {
             node.add(new Node());
        }
        for(int i = 1; i < n; i++){
            int k = in.nextInt()-1;
            node.get(k).children.add(i);
        }
        if (solution(node)){
            System.out.println("Yes");
        }
        else System.out.println("No");
    }
}