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.*;

public class Party {

	public static void main(String[] args) {
		Scanner keyboard = new Scanner(System.in);
		LinkedHashMap<String, String> bossesMap = new LinkedHashMap<String, String>();
		int n = keyboard.nextInt();
		for (int i = 1; i <= n; i++) {
			String parentLabel = keyboard.next();
			if (!parentLabel.equals("-1") && parentLabel.length() > 0) {
				bossesMap.put(Integer.toString(i), parentLabel);
			} else {
				bossesMap.put(Integer.toString(i), null);
			}
		}
		System.out.println(retrieveMinimumPartyGroups(bossesMap));
		keyboard.close();
	}

	private static int retrieveMinimumPartyGroups(LinkedHashMap<String, String> bossesMap) {
		TreeSet<String> depths = new TreeSet<String>();
		bossesMap.keySet().forEach(key -> depths.add(calcDepth(key, bossesMap)));
		return depths.size();
	}

	private static String calcDepth(String key, LinkedHashMap<String, String> bossesMap) {
		int depth = 1;
		for (String cursor = bossesMap.get(key); cursor != null; cursor = bossesMap.get(cursor)) {
			depth++;
		}
		return Integer.toString(depth);
	}

}
