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.io.PrintWriter;
import java.util.ArrayList;
import java.util.Scanner;

public class Solution {
    
    static class Worker {
        private int master;
        private int id;

        public Worker(int master, int id) {
            this.master = (master >= 0 ? master : -1);
            this.id = id;
        }

        public int getId() {
            return id;
        }

        public int getMaster() {
            return master;
        }

        public void setMaster(int master) {
            this.master = master;
        }

        @Override
        public String toString() {
            return "id = " + id + " master = " + master;
        }
        
        
    }

    public static void main(String[] args) throws Exception {
        Scanner reader = new Scanner(System.in);
        PrintWriter writer = new PrintWriter(System.out);
        
        int n = reader.nextInt();
        
        ArrayList<Worker> list = new ArrayList<Worker>();
        
        for (int i = 0; i < n; i++) {
            int mas = reader.nextInt() - 1;
            
            list.add(new Worker(mas, i));
        }
        
        int room = 0;
        
        while (!list.isEmpty()) {
            ArrayList<Integer> except = new ArrayList<Integer>();
            
            for (int k = 0; k < list.size(); k++) {
                Worker w = list.get(k);
                
                if (w.master == -1 && !except.contains(w.id)) {
                    
                    for (int i = 0; i < list.size(); i++)
                        if (list.get(i).master == w.id) {
                            except.add(list.get(i).id);
                            list.get(i).master = -1;
                        }
                    
                    list.remove(k);
                    k--;
                }
            }
            
            room++;
        }
        
        writer.print(room);
        writer.close();
    }
}
