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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class ar {

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (final IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (final IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    static boolean[] seen;
    static Map<Integer, Integer> map;
    static Map<Long, Long> lmap;
    static Set<Character> charset;
    static Set<Integer> set;
    static int[] arr;
    static int[][] dp;
    static int rem = (int) 1e9 + 7;
    static List<List<Integer>> graph;
    static int[][] kmv = { { 2, 1 }, { 1, 2 }, { 2, -1 }, { -1, 2 }, { -2, 1 }, { 1, -2 }, { -1, -2 }, { -2, -1 } };
    static char[] car;
    static boolean[] primes;
    static int MAX = (int) 1e4 + 1;
    static double[] dar;
    static long[] lar;
    static long[][] dlar;

    static void Sieve() {
        primes = new boolean[MAX];
        primes[0] = true;
        primes[1] = true;
        for (int i = 2; i * i < MAX; i++) {
            if (!primes[i]) {
                for (int j = i * i; j < MAX; j += i) {
                    primes[j] = true;
                }
            }
        }
    }

    public static void main(String[] args) throws java.lang.Exception {
        FastReader scn = new FastReader();
        int n=scn.nextInt();
        graph=new ArrayList<>();
        for(int i=1;i<=n+1;i++)graph.add(new ArrayList<>());

        for(int i=2;i<=n;i++){
            int num=scn.nextInt();
            graph.get(num).add(i);
        }
        // System.out.println(graph);
        if(func(1)){
            System.out.print("Yes");
            return;
        }else{
            System.out.print("No");
        }
    }

    static boolean func(int cur){
        int cnt=0;
        boolean ans=true;
        for(int i=0;i<graph.get(cur).size();i++){
            if(graph.get(graph.get(cur).get(i)).size()==0){
                // System.out.println("NO HAI");
                // System.out.println(graph.get(cur).get(i));
                cnt++;
            }
            if(graph.get(graph.get(cur).get(i)).size()>0){
              ans&=func(graph.get(cur).get(i));
            }
        }
        return ans&&cnt>=3;
    }
}