A company has n employees numbered from 1 to n. Each employee either has no immediate manager or exactly one immediate manager, who is another employee with a different number. An employee A is said to be the superior of another employee B if at least one of the following is true:

  * Employee A is the immediate manager of employee B
  * Employee B has an immediate manager employee C such that employee A is the superior of employee C. 



The company will not have a managerial cycle. That is, there will not exist an employee who is the superior of his/her own immediate manager.

Today the company is going to arrange a party. This involves dividing all n employees into several groups: every employee must belong to exactly one group. Furthermore, within any single group, there must not be two employees A and B such that A is the superior of B.

What is the minimum number of groups that must be formed?

Input

The first line contains integer n (1 ≤ n ≤ 2000) — the number of employees.

The next n lines contain the integers pi (1 ≤ pi ≤ n or pi = -1). Every pi denotes the immediate manager for the i-th employee. If pi is -1, that means that the i-th employee does not have an immediate manager. 

It is guaranteed, that no employee will be the immediate manager of him/herself (pi ≠ i). Also, there will be no managerial cycles.

Output

Print a single integer denoting the minimum number of groups that will be formed in the party.

Examples

Input

5
-1
1
2
1
-1


Output

3

Note

For the first example, three groups are sufficient, for example: 

  * Employee 1 
  * Employees 2 and 4 
  * Employees 3 and 5 
import java.util.*;
import java.io.*;

public class Main {
  
  static class Tree {
    private Node root;
    
    public void setRoot(Node root) {
      this.root = root;
    }
    
    public Node getRoot() {
      return root;
    }

    public int getLongestPath(Node node) {
      int max = 0;
      for(Node child: node.getChildren()) {
        max = Math.max(getLongestPath(child), max);
      }
      return 1 + max;
    }
  
    static class Node {
      private Node parent;
      private List<Node> children;
      
      public Node() {
        parent = null;

        children = new LinkedList<>();
      }
      
      public List<Node> getChildren() {
        return children;
      }
      
      public void setParent(Node parent) {
        this.parent = parent;
      }
    }
  }

  public static void main(String[] args) throws IOException {
    Reader r = new BufferedReader(new InputStreamReader(System.in));
    StreamTokenizer t = new StreamTokenizer(r);
    t.nextToken();
    
    int n = (int) t.nval;

    Map<Integer, Tree.Node> nodes = new HashMap<>(n);
    for(int i = 0; i < n; i++) {
      nodes.put(i, new Tree.Node());
    }
    
    List<Tree> trees = new ArrayList<>();
    for(int i = 0; i < n; i++) {
      t.nextToken();
      
      Integer parentId = (int) t.nval;
      
      if (parentId == -1) {
        Tree tree = new Tree();
        tree.setRoot(nodes.get(i));
        
        trees.add(tree);
      } else {
        Tree.Node parent = nodes.get(parentId - 1);
        Tree.Node child = nodes.get(i);

        child.setParent(parent);
        parent.getChildren().add(child);
      }
    }
    
    int max = 0;
    for(Tree tree: trees) {
      int currentMax = tree.getLongestPath(tree.getRoot());
      if (currentMax > max) {
        max = currentMax;
      }
    }
    
    System.out.println(max);
  }
}