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.IOException;
import java.util.ArrayList;
import java.util.Scanner;

public class ProblemC {
	static Scanner sc = new Scanner(System.in);
	static int n , manager[] ;
	static ArrayList<Integer>[]  child ;
	
	static int getDepth(int idx ){
		int depth = 0 ;
		for(int i = 0 ; i < child[idx].size() ; i ++){
			depth = Math.max(depth, getDepth(child[idx].get(i))) ;
			}
		return depth+1 ;
	}
	public static void main(String[] args) throws IOException {
		n = sc.nextInt() ;
		manager = new int[n] ;
		child = new ArrayList[n] ;
		for(int i = 0 ; i < n ; i ++)child[i] = new ArrayList<>() ;
		
		for(int i = 0 ; i < n ; i ++){
			int x = sc.nextInt()-1 ;
			manager[i] = x;
			if(x!=-2)child[x].add(i);
		}
		
//		for(int i = 0 ; i < n ; i ++){
//			System.out.println("manager "+ (i+1));
//			for(int j = 0 ; j < child[i].size() ; j ++)
//				System.out.println(child[i].get(j)+1);
//		}
		
		int ans = 0 ;
		for(int i = 0 ; i < n ; i ++)
			if(manager[i]==-2)
				ans = Math.max(ans, getDepth(i)) ;
		
		System.out.println(ans);
	}

}