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.Arrays;
import java.util.HashSet;
import java.util.Scanner;

public class Party {
    private static final int NO_SUPERIOR = -1;
    private static final int DELETED = -2;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int employees = sc.nextInt();
        int[] superior = new int[employees];
        Arrays.fill(superior, NO_SUPERIOR);
        for (int i = 0; i < employees; i++) {
            superior[i] = sc.nextInt();
            if(superior[i] != NO_SUPERIOR) {
                superior[i]--;
            }
        }
        int res = -1;
        while(true) {
            res++;
            boolean doBreak = true;
            HashSet<Integer> group = new HashSet<Integer>();
            for (int i = 0; i < superior.length; i++) {
                if(superior[i] != DELETED) {
                    doBreak = false;
                }
                
                if(superior[i] == NO_SUPERIOR) {
                    superior[i] = DELETED;
                    group.add(i);
                }
            }
            if(doBreak) {
                break;
            } else {
                for (int i = 0; i < superior.length; i++) {
                    if(group.contains(superior[i])) {
                        superior[i] = NO_SUPERIOR;
                    }
                }
            }
        }
        System.out.println(res);
    }
}