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.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

public class Codeforces913B {

    public static boolean check(int i) {
//        boolean result = false;
        int count = 0;
//        System.out.println(children.get(i));
        for (Integer integer : children.get(i)) {
            if (children.get(integer).size() == 0) {
                count++;
            }
            if (count == 3) {
                break;
            }
        }
        if (count == 3 || children.get(i).size()==0 ) {
            return true;
        }
        return false;
    }
    public static List<List<Integer>> children;

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = Integer.parseInt(scanner.nextLine());
        children = new ArrayList<>();
        for (int i = 1; i <= n + 1; i++) {
            children.add(new ArrayList<>());

        }
        for (int i = 2; i <= n; i++) {
            int parent = Integer.parseInt(scanner.nextLine());
            children.get(parent).add(i);
        }
        for (int i = 1; i <= n; i++) {
            if (!check(i)) {
                System.out.println("No");
                return;
            }
        }
        System.out.println("Yes");
    }
}