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;
import java.util.Arrays;
import java.util.Comparator;
import java.util.StringTokenizer;

/**
 * Author -
 * User: kansal
 * Date: 9/15/11
 * Time: 9:00 PM
 */
public class CF87C {
    public static void main(String[] args) {
        reader = new BufferedReader(new InputStreamReader(System.in));
        int n = nextInt();
        int[] out = new int[n];
        int[] mgr = new int[n];
        for(int i = 0; i < n; ++i) {
            int e = nextInt() - 1;
            if (e >= 0) ++out[e];
            mgr[i] = e;
        }

        Integer[] o = new Integer[n];
        for(int i = 0; i < n; ++i) o[i] = i;
        sort(o, out);

        int res = 0;
        int[] dec = new int[n];
        while (true) {
            ++res;
            int k = 0;
            boolean go = false;
            for(int i = 0; i < n; ++i) {
                if (out[o[i]] > 0) break;
                else if (mgr[o[i]] >= 0) {
                    out[o[i]] = n + 1;
                    dec[k++] = mgr[o[i]];
                    go = true;
                }
            }
            for(int i = 0;i < k; ++i) --out[dec[i]];
            if (!go) break;
            sort(o, out);
        }

        System.out.println(res);
    }

    private static void sort(Integer[] o, final int[] out) {
        Arrays.sort(o, new Comparator<Integer>() {
            public int compare(Integer o1, Integer o2) {
                return out[o1] - out[o2];
            }
        });
    }

    public static BufferedReader reader;

    public static StringTokenizer tokenizer = null;

    static String nextToken() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    static public int nextInt() {
        return Integer.parseInt(nextToken());
    }

    static public long nextLong() {
        return Long.parseLong(nextToken());
    }

    static public String next() {
        return nextToken();
    }

    static public String nextLine() {
        try {
            return reader.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return null;
    }

}
