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.util.*;


public class B {

  void solve() throws IOException {
    int n = nextInt();
    int[] p = new int[n];
    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 x=nextInt() - 1;
      child[x].add(i);
    }
    boolean[] l = new boolean[n];
    for(int i =0;i<n;i++){
      l[i] = child[i].isEmpty();
    }
    boolean good = true;
    for(int i=0;i<n;i++) {
      if (!l[i]) {
        long count = child[i].stream()
            .filter(x -> l[x])
            .count();
        if (count<3) {
          good = false;
          break;
        }
      }
    }
    if (good){
      out.print("Yes");
    } else {
      out.println("No");
    }
  }

  public static void main(String[] args) throws IOException {
    new B().run();
  }

  void run() throws IOException {
    reader = new BufferedReader(new InputStreamReader(System.in));
//		reader = new BufferedReader(new FileReader("input.txt"));
    tokenizer = null;
    out = new PrintWriter(new OutputStreamWriter(System.out));
//		out = new PrintWriter(new FileWriter("output.txt"));
    solve();
    reader.close();
    out.flush();

  }

  BufferedReader reader;
  StringTokenizer tokenizer;
  PrintWriter out;

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

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

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

  String nextToken() throws IOException {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      tokenizer = new StringTokenizer(reader.readLine());
    }
    return tokenizer.nextToken();
  }
}