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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

/**
 *
 * @author evgeny11
 */
public class C {
    
    public static int boss[];

    public static void main(String[] args) throws IOException{
        
        String res="";
        /**
         * Input parameters
         */
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int n=Integer.parseInt(in.readLine());
        boss=new int[n];
        for(int i=0;i<n;i++){
            int p=Integer.parseInt(in.readLine());
            if(p<0){
                boss[i]=-1;
            } else {
                boss[i]=p-1;
            }
        }
        /**
         * Close stream
         */
        in.close();
        
        /**
         * Main part
         */
        
        
        int maxL=0;
        for(int i=0;i<n;i++){
           int l=trav(i,1);
           if(l>maxL) maxL=l;
        }
        
        System.out.println(Integer.toString(maxL));
        
        

        
     
        /**
         * Output result
         */
//        System.out.println(res);
        
    }

    private static int trav(int i, int l) {
        if(boss[i]<0){
            return l;
        } else {
            return trav(boss[i],l+1);
        }
    }
    
}   