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.BufferedReader;
import java.io.InputStreamReader;
import java.io.Reader;
import java.io.StringReader;
import java.util.*;
import java.lang.*;

public class Spruce {
    public static void main(String[] args) {
        try {
            boolean spruceFlag = true;
            int numVertices;
            HashMap<Integer, List<Integer>> relMap = new HashMap<Integer, List<Integer>>();
            int temp;
            BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));
            numVertices = Integer.valueOf(bufferedReader.readLine());
            for (int i = 0; i < numVertices - 1; i++) {
                temp = Integer.valueOf(bufferedReader.readLine());
                if(relMap.get(temp) == null){
                    relMap.put(temp, new ArrayList<Integer>());
                    relMap.get(temp).add(i+2);
                } else{
                    relMap.get(temp).add(i+2);
                }
            }
            for(int vertex : relMap.keySet()){
                temp = relMap.get(vertex).size();
                if(temp > 0 && temp < 3){
                    spruceFlag = false;
                    System.out.println("No");
                    break;
                } else if(temp >= 3){
                    for(int childVertex : relMap.get(vertex)){
                        if(relMap.get(childVertex) != null){
                            temp--;
                            if(temp < 3){
                                System.out.println("No");
                                spruceFlag = false;
                                break;
                            }
                        }
                    }
                    if(spruceFlag == false){
                        break;
                    }
                }
            }
            if(spruceFlag){
                System.out.println("Yes");
            }
        } catch (Exception e) {
            System.out.println("Exception " + e);
        }
    }
}