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.math.BigInteger;
import java.nio.IntBuffer;
import java.util.*;

public class Main {

    public static void main(String[]args)throws IOException{
        //MyScanner sc = new MyScanner(new FileReader("input.txt"));
        //PrintWriter out = new PrintWriter("output.txt");
        PrintWriter out = new PrintWriter(System.out);
        MyScanner sc = new MyScanner(System.in);
        Vector<Integer> arr[] = new Vector[1100];
        int t =sc.nextInt();
        for(int i = 1 ; i<= t ; i ++)
        {
            arr[i] = new Vector<>();
        }
        for(int i = 1 ; i< t ; i ++)
        {
            int v = sc.nextInt();
            arr[v].add(i+1);
        }
        boolean ch = true;
        for(int i = 1 ; i<= t ; i ++)
        {
            int cnt = arr[i].size() ;

            for(int j = 0 ; j < arr[i].size() ; j ++)
            {

                if(arr[arr[i].elementAt(j)].size() >= 1)cnt--;
               
            }
            if(cnt< 3 && arr[i].size()!=0)ch = false;
        }
        if(ch == true)out.println("Yes");
        else out.println("No");

        out.flush();
        out.close();

    }

    static class MyScanner
    {
        StringTokenizer st;
        BufferedReader br;

        public MyScanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

        public MyScanner(FileReader s) throws FileNotFoundException {	br = new BufferedReader(s);}

        public String next() throws IOException
        {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {return Integer.parseInt(next());}

        public long nextLong() throws IOException {return Long.parseLong(next());}

        public String nextLine() throws IOException {return br.readLine();}

        public double nextDouble() throws IOException { return Double.parseDouble(next()); }

        public boolean ready() throws IOException {return br.ready();}
    }
}