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.InputStreamReader;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
import java.util.ArrayList;
import java.util.Arrays;

public class C {
    
    /////////////////////////////////////////////////////////////////
    // IO
    /////////////////////////////////////////////////////////////////
    private static StreamTokenizer in;
    private static PrintWriter out;
    private static BufferedReader inB;
    
    private static int nextInt() throws Exception{
        in.nextToken();
        return (int)in.nval;
    }
    
    private static String nextString() throws Exception{
        in.nextToken();
        return in.sval;
    }
    
    static{
        out = new PrintWriter(System.out);
        inB = new BufferedReader(new InputStreamReader(System.in));
        in = new StreamTokenizer(inB);
    }
    /////////////////////////////////////////////////////////////////
    
    private static int[][] mas;
    private static int n;
    private static int calc(int i) {
        if(mas[i][1] != -1)return mas[i][1];
        if(mas[i][0] == -1)return 0;
        return mas[i][1] = calc(mas[i][0]-1) + 1;
    }
    public static void main(String[] args)throws Exception {
        n = nextInt();
        mas = new int[n][2];
        
        for(int i = 0; i<n; i++) {
            mas[i][0] = nextInt();
            mas[i][1] = -1;
        }
        
        for(int i = 0; i<n; i++) {
            if(mas[i][1] != -1)continue;
            mas[i][1] = calc(i);
        }
        
        int max= 0 ;
        for(int i = 0; i<n; i++) {
            if(mas[i][1] > max)max = mas[i][1];
        }
        
        println(max+1);
        
    }
    
    
    /////////////////////////////////////////////////////////////////
    // pre - written
    /////////////////////////////////////////////////////////////////
    private static void println(Object o) throws Exception {
        out.println(o);
        out.flush();
    }
    private static void exit(Object o) throws Exception {
        println(o);
        exit();
    }
    private static void exit() {
        System.exit(0);
    }
    private static final int  INF = Integer.MAX_VALUE;
    private static final int MINF = Integer.MIN_VALUE;
    //////////////////////////////////////////////////////////////////
}
