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.*;
import java.util.*;

public class Main {
    static boolean IS_DEBAG = false;

    int a[] = new int[2000+5];
    
    void solve() throws IOException {
        int n = nextInt();

        for( int i = 1; i <= n; ++i ){
            a[i] = nextInt();
        }

        int max = 1;
        for( int i = 1; i <= n; ++i ){
            int pos = i;
            int col = 1;
            if( pos == -1 ){
                continue;
            }
            while( a[pos] != -1 ){
                pos = a[pos];
                col++;
            }
            max = Math.max( max, col );
        }

        out.println(max);
    }

    private static final String INPUT_FILE = "inp.txt";

    public static void main(String[] args) throws IOException {
        long start_time = System.currentTimeMillis();
        if (new File(INPUT_FILE).exists())
            System.setIn(new FileInputStream(INPUT_FILE));
        new Main().solve();
	out.close();
        if( IS_DEBAG ){
            System.err.println("Time is: "+(System.currentTimeMillis()-start_time));
        }
    }

    private BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    private static PrintWriter out = new PrintWriter(System.out);;
    private StringTokenizer st = new StringTokenizer("");

    String nextToken() throws IOException {
        while (!st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }

    int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    String nextLine() throws IOException {
        st = new StringTokenizer("");
        return in.readLine();
    }

}