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.IOException;
import java.util.*;


public class Main {

    public static boolean checkSpruce(int p[],int n) {
        boolean result = true;
        Set<Integer> parents = new TreeSet<Integer>();
        List<Vertex> vertexList = new ArrayList<Vertex>(n);
        for (int i = 1; i < n; i++)
            vertexList.add(new Vertex(i));

        for(int i = 0; i < n-1; i++) {
            vertexList.get(p[i]).children.add(i+2);
            parents.add(p[i]);
        }
        parents.add(1);              //For tree root
        for (Vertex vertex : vertexList) {
            if(vertex.children.size() != 0) {
                int count = 0;
                for (Integer child : vertex.children) {
                    if (!parents.contains(child))
                        count++;
                }
                if (count < 3) {
                    result = false;
                    break;
                }
            }
        }
        return result;
    }
    public static void main(String args[]) throws IOException {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int p[] = new int[n-1];
        for(int i = 0; i < n-1; i++)
            p[i] = sc.nextInt();
        if(checkSpruce(p,n))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}

class Vertex {
    int number;
    List<Integer> children;
    Vertex(int number) {
        this.number = number;
        children = new ArrayList<>();
    }
}