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.*;

public class Main {

    static boolean atleast3LeafChild(Map<Integer, List<Integer>> map, int parent) {

        List<Integer> children = map.get(parent);
        if (children.size() == 0)
            return true;
        if (children.size() < 3)
            return false;
        int leafCount = 0;
        for (int x : children) {
            if (map.get(x).size() == 0)
                leafCount++;
        }

        return leafCount >= 3;
    }

    static boolean isSpuce(Map<Integer, List<Integer>> map) {
        boolean isSpruce = true;
        for (Map.Entry<Integer, List<Integer>> e : map.entrySet()) {
            if (!atleast3LeafChild(map, e.getKey())) {
                isSpruce = false;
                break;
            }
        }
        return isSpruce;
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        Map<Integer, List<Integer>> map = new HashMap<>();
        int n = in.nextInt();
        map.put(1, new ArrayList<>());
        for (int i = 1; i < n; i++) {
            int parent = in.nextInt();
            map.put(i + 1, new ArrayList<>());
            if (map.get(parent) != null) {
                List<Integer> children = map.get(parent);
                children.add(i + 1);
                map.put(parent, children);
            }
        }

        if (isSpuce(map))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}