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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

/*
 public class _913B {

 }

 */
public class _913B {
  public void solve() throws FileNotFoundException {
    InputStream inputStream = System.in;

    InputHelper in = new InputHelper(inputStream);

    // actual solution
    int n = in.readInteger();

    List[] g = new List[n];

    for (int i = 0; i < n; i++) {
      g[i] = new ArrayList<Integer>();
    }

    for (int i = 0; i < n - 1; i++) {
      int p = in.readInteger();

      g[p - 1].add(i + 1);
    }

    dfs(0, -1, g);

    if (ans) {
      System.out.println("Yes");
    } else {
      System.out.println("No");
    }
    // end here
  }

  boolean ans = true;

  int dfs(int u, int p, List[] g) {
    if (g[u].size() == 0) {
      return 1;
    }

    int cans = 0;
    for (int i = 0; i < g[u].size(); i++) {
      int v = (int) g[u].get(i);

      cans += dfs(v, u, g);
    }

    if (cans < 3) {
      ans = false;
    }

    return 0;
  }

  public static void main(String[] args) throws FileNotFoundException {
    (new _913B()).solve();
  }

  class InputHelper {
    StringTokenizer tokenizer = null;
    private BufferedReader bufferedReader;

    public InputHelper(InputStream inputStream) {
      InputStreamReader inputStreamReader = new InputStreamReader(inputStream);
      bufferedReader = new BufferedReader(inputStreamReader, 16384);
    }

    public String read() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          String line = bufferedReader.readLine();
          if (line == null) {
            return null;
          }
          tokenizer = new StringTokenizer(line);
        } catch (IOException e) {
          e.printStackTrace();
        }
      }

      return tokenizer.nextToken();
    }

    public Integer readInteger() {
      return Integer.parseInt(read());
    }

    public Long readLong() {
      return Long.parseLong(read());
    }
  }
}