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.LinkedList;
import java.util.Queue;
import java.util.Scanner;


public class main {
    static boolean []vis;
    static Queue<Nodee> s;
    public static void dfs(int []arr)
    {
        
        int level=0;
        while(s.peek()!=null){
            Nodee next= s.peek();
            s.poll();
            if(next.i>level)
                level=next.i;
            for(int i=0;i<arr.length;i++){
                if(!vis[i]){
                if(arr[i]==next.j){
                    s.add(new Nodee(next.i+1,i+1));
                    vis[i]=true;
                }
                }
            }
        }

     
System.out.println(level+1);


    }


    public static void main(String[] args) {
        Scanner scan =new Scanner(System.in);
        int n=scan.nextInt();
        vis=new boolean[n];
        int []arr=new int[n];
        s=new LinkedList<>();
        for(int i=0;i<n;i++){
            int v=scan.nextInt();
            arr[i]=v;
            if(arr[i]==-1){
                s.add(new Nodee(0, i+1));
            vis[i]=true;}
            
        }
        dfs(arr);
    }

}
class Nodee{
    int i,j;
    public Nodee(int a,int b) {
        i=a;
        j=b;
    }

}
