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.text.ParseException;
import java.util.*;


public class Codeforces  {

    
    
    public static void main(String[] args) throws IOException, ParseException{
        Kattio sc = new Kattio(System.in,System.out);
        //Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        ArrayList<Integer>[] child = new ArrayList[n];
        for(int i=0 ; i<n ; i++){
            child[i] = new ArrayList<>();
        }
        for(int i=1 ; i<n ; i++){
            int p = sc.nextInt();
            child[p-1].add(i);
        }
        
        int s = 0;
        if(BFS(child,n,s)){
            System.out.println("Yes");
        }
        else{
            System.out.println("No");
        }
    }

    private static boolean BFS(ArrayList<Integer>[] child, int n, int s) {
        Queue<Integer> Q = new LinkedList<>();
        Q.add(s);
        while(!Q.isEmpty()){
            int x = Q.poll();
            if(child[x].size()!=0){
                if(child[x].size()>=3){
                    int a = 0;
                    for(int ch : child[x]){
                        if(child[ch].size()==0){
                            a++;
                        }
                        else{
                            Q.add(ch);
                        }
                    }
                    if(a<3){
                        return false;
                    }
                }
                else{
                    return false;
                }
            }
        }
        return true;
    }
   
    
    
    
    
    
    
    
    
    
    static class Kattio extends PrintWriter {
        public Kattio(InputStream i) {
            super(new BufferedOutputStream(System.out));
            r = new BufferedReader(new InputStreamReader(i));
        }
        public Kattio(InputStream i, OutputStream o) {
            super(new BufferedOutputStream(o));
            r = new BufferedReader(new InputStreamReader(i));
        }
        
        public Kattio(FileInputStream i) {
            super(new BufferedOutputStream(System.out));
            r = new BufferedReader(new InputStreamReader(i));
        }
        public Kattio(FileInputStream i, OutputStream o) {
            super(new BufferedOutputStream(o));
            r = new BufferedReader(new InputStreamReader(i));
        }
    public boolean hasMoreTokens() {
        return peekToken() != null;
    }

    public int nextInt() {
        return Integer.parseInt(nextToken());
    }

    public double nextDouble() {
        return Double.parseDouble(nextToken());
    }

    public long nextLong() {
        return Long.parseLong(nextToken());
    }

    public String next() {
        return nextToken();
    }



    private BufferedReader r;
    private String line;
    private StringTokenizer st;
    private String token;

    private String peekToken() {
        if (token == null)
            try {
                while (st == null || !st.hasMoreTokens()) {
                    line = r.readLine();
                    if (line == null) return null;
                    st = new StringTokenizer(line);
                }
                token = st.nextToken();
            } catch (IOException e) { }
        return token;
    }

    private String nextToken() {
        String ans = peekToken();
        token = null;
        return ans;
    }
}
    
}