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.*;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Spruce {
    static ArrayList<Integer>[] list;

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        StringTokenizer st = new StringTokenizer(br.readLine());
        int n = Integer.parseInt(st.nextToken());
        list = new ArrayList[n];
        for(int i = 0; i < n; i++){
            list[i] = new ArrayList<>();
        }
        for(int i = 1; i < n; i++){
            st = new StringTokenizer(br.readLine());
            int A = Integer.parseInt(st.nextToken()) - 1;
            list[A].add(i);
            list[i].add(A);
        }
        for(int i = 0; i < n; i++){
            if(list[i].size() > 1){
                int leafCount = 0;
                for(int j = 0; j < list[i].size(); j++){
                    if(list[list[i].get(j)].size() == 1){
                        leafCount++;
                    }
                }
                if(leafCount < 3){
                    pw.println("No");
                    pw.close();
                    return;
                }
            }
        }
        pw.println("Yes");
        pw.close();
    }
}