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.*;
import java.io.*;

public class B {
    public static void main(String[] args) throws IOException{
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        int n = Integer.parseInt(f.readLine());
        ArrayList<Integer>[] children = new ArrayList[n+1];
        for(int i = 0; i < n+1; i++){
            children[i] = new ArrayList<Integer>();
        }
        for(int i = 0; i < n-1; i++){
            int a = Integer.parseInt(f.readLine());
            children[a].add(i+2);
        }
        boolean[] leaves = new boolean[n+1];

        boolean valid = true;
        for(int i = 1; i < n+1; i++){
            if(children[i].size() != 0){
                int count = 0;
                for(int e: children[i]){
                    if(children[e].size() == 0) count++;
                }
                if(count < 3){
                    valid = false;
                    break;
                }
            }
        }

        if(valid){
            out.println("Yes");
        }else{
            out.println("No");
        }
        out.close();

    }
}