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 javafx.util.Pair;

import java.util.*;

public class Codeforces {
    public static void main(String[] args) {

        Scanner scan = new Scanner(System.in);

        int n = scan.nextInt();

        List<List<Integer>> children = new ArrayList<>(n);

        for (int i = 0; i < n; i++) {
            children.add(new ArrayList<>());
        }

        for (int i = 0; i < n-1; i++) {
            int parent = scan.nextInt();
            List<Integer> kids = children.get(parent-1);
            kids.add(i+1);
            children.set(parent - 1, kids);
        }

        boolean elka = true;

        int i = 0;

        while (elka && i < n) {
            List<Integer> kids = children.get(i);
            if (!kids.isEmpty()) {
                if (kids.size() < 3) {
                    elka = false;
                } else {
                    int leaves = 0;
                    for (Integer child:kids) {
                        if (children.get(child).isEmpty()) {
                            leaves++;
                        }
                    }
                    if (leaves < 3) {
                        elka = false;
                    }
                }
            }
            i++;
        }

        if (elka) {
            System.out.print("Yes");
        } else {
            System.out.print("No");
        }
    }


    /*public class Heap {
        public Heap() {

        }

        public void addElement(int x) {

        }
    }*/
}