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.Arrays;
import java.util.List;
import java.util.Scanner;

public class Main {

    public static void main(String[] Args) {
        int n = si(), p[] = sai_(n), o = 1;
        for (int i = 1; i <= n; i++) {
            int s = p[i];
            int d = 1;
            while (s != -1) {
                d++;
                s = p[s];
                o = Math.max(o, d);
            }
        }

        System.out.println(o);
    }

    static int toi(Object s) {
        return Integer.parseInt(s.toString());
    }

    // ----------------------- Library ------------------------
    static int[] dx_ = { 0, 0, 1, -1 };
    static int[] dy_ = { 1, -1, 0, 0 };
    
    static int[] dx = { 1, 0, -1, 1, -1, 1, 0, -1 }, dy = { 1, 1, 1, 0, 0, -1,
            -1, -1 };
    static Scanner scan = new Scanner(System.in);
    static int INF = 2147483647;

    // finds GCD of a and b using Euclidian algorithm
    public int GCD(int a, int b) {
        if (b == 0)
            return a;
        return GCD(b, a % b);
    }

    static List<String> toList(String[] a) {
        return Arrays.asList(a);
    }

    static String[] toArray(List<String> a) {
        String[] o = new String[a.size()];
        a.toArray(o);
        return o;
    }

    static int[] pair(int... a) {
        return a;
    }

    static int si() {
        return scan.nextInt();
    }

    static String ss() {
        return scan.nextLine();
    }

    static int[] sai(int n) {
        int[] a = new int[n];
        for (int i = 0; i < a.length; i++)
            a[i] = si();

        return a;
    }

    static int[] sai_(int n) {
        int[] a = new int[n + 1];
        for (int i = 1; i <= n; i++)
            a[i] = si();

        return a;
    }

    static String[] sas(int n) {
        String[] a = new String[n];
        for (int i = 0; i < a.length; i++)
            a[i] = ss();
        return a;
    }

    static Object[][] _sm1(int r, int c) {
        Object[][] a = new Object[r][c];
        for (int i = 0; i < r; i++)
            for (int j = 0; j < c; j++)
                a[i][j] = scan.next();
        return a;
    }

    static Object[][] _sm2(int r) {
        Object[][] a = new Object[r][3];
        for (int i = 0; i < r; i++)
            a[i] = new Object[] { ss(), ss(), ss() };
        return a;
    }
}
