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.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Spruce {
    public static void main(String[] args){
        Scanner s = new Scanner(new InputStreamReader(System.in));
        int n = s.nextInt();
        Node[] nodes = new Node[n];
        for(int i = 0; i < n; i++){
            nodes[i] = new Node();
        }
        for(int i = 0; i < n - 1; i++){
            int parent = s.nextInt();
            nodes[i + 1].setParent(nodes[parent - 1]);
            nodes[parent - 1].addChild(nodes[i + 1]);
        }
        System.out.println(validate(nodes) ? "Yes" : "No");
    }

    public static boolean validate(Node[] nodes){
        for(Node node : nodes){
            if(!node.isLeaf()){
                int count = (int) node.children.stream().filter(Node::isLeaf).count();
                if(count < 3){
                    return false;
                }
            }
        }
        return true;
    }

    public static class Node {
        Node parent;
        List<Node> children;
        public Node(){
            children = new ArrayList<>();
        }
        public void setParent(Node parent){
            this.parent = parent;
        }
        public void addChild(Node child){
            children.add(child);
        }
        public boolean isLeaf(){
            return children.isEmpty();
        }
    }
}