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 
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;

/**
 *
 * @author sataev_mb
 */
public class A {

    static boolean a[][];

    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(in.readLine());
        a = new boolean[n][n];
        int root[] = new int[n];
        Arrays.fill(root, -1);
        int j = 0;
        for (int i = 0; i < a.length; i++) {
            int val = Integer.parseInt(in.readLine());
            if (val != -1) {
                a[val-1][i] = true;
            } else {
                root[j++] = i;
            }
        }
               
        int maxDepth = Integer.MIN_VALUE;
        j = 0;
        while (j<root.length && root[j] != -1) {
            int m = calc(root[j]);
            if (m > maxDepth) {
                maxDepth = m;
            }
            j++;
        }
        System.out.println(maxDepth);
    }

    static int calc(int k) {
        int maxDepth = Integer.MIN_VALUE;
        int j = 0;
        for (int i = 0; i < a[k].length; i++) {
            if (a[k][i]) {
                int c = calc(i)+1;
                if (maxDepth < c) {
                    maxDepth = c;
                }
                j++;
            }
        }
        if (j == 0) {
            return 1;
        } else {
            return maxDepth;

        }
    }

}
