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.*;
import java.util.*;

public class Main {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        PrintStream out = System.out;

//        try {
//            inputStream = new FileInputStream("input.txt");
//        } catch (FileNotFoundException e) {
//            System.exit(13);
//        }

        Scanner in = new Scanner(inputStream);
        int n = in.nextInt();
        List<List<Integer>> g = new ArrayList<>();
        Set<Integer> roots = new HashSet<>();
        for (int i = 0; i < n; ++i) {
            g.add(new ArrayList<>());
            roots.add(i);
        }
        for (int i = 0; i < n; ++i) {
            int parent = in.nextInt();
            if (parent > 0) {
                --parent;
                g.get(parent).add(i);
                roots.remove(i);
            }
        }
        int answer = 0;
        for (Integer v : roots) {
            answer = Math.max(answer, dfs(g, v));
        }
        out.println(answer);
    }

    static int dfs(List<List<Integer>> g, int v) {
        if (g.get(v).size() == 0) return 1;
        int height = 0;
        for (Integer t : g.get(v)) {
            height = Math.max(height, dfs(g, t));
        }
        return height + 1;
    }
}
