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 A115 
{

	static int gen=1;
	static ArrayList<Integer>[]adjList;
	public static void t(int x,int g)
	{
		gen=Math.max(gen, g);
		for(int y:adjList[x])
		{
			t(y,g+1);
		}
	}
	public static void main(String[] args) 
	{
		Scanner sc = new Scanner (System.in);
		int n=sc.nextInt();
		int arr[]=new int[n];
		adjList=new ArrayList[n];
		
		for(int i=0;i<n;i++)
		{
			arr[i]=sc.nextInt();
			adjList[i]=new ArrayList<Integer>();
		}
		for(int i=0;i<n;i++)
		{
			if(arr[i]!=-1)
				adjList[arr[i]-1].add(i);
		}
		for(int i=0;i<n;i++)
		{
			if(arr[i]==-1)t(i,1);
		}
		System.out.println(gen);
		

	}

}
