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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class C {

    static StringTokenizer st;
    static BufferedReader in;
    static ArrayList<Integer>[]ages;
    static int[]dis;
    
    public static void main(String[] args) throws IOException{
        in = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int n = nextInt();
        ages = new ArrayList[n+1];
        for (int i = 1; i <= n; i++) {
            ages[i] = new ArrayList<Integer>();
        }
        dis = new int[n+1];
        for (int i = 1; i <= n; i++) {
            int fath = nextInt();
            if (fath != -1)
                ages[fath].add(i);
        }
        for (int i = 1; i <= n; i++) {
            if (dis[i]==0) {
                dis[i] = 1;
                dfs(i);
            }
        }
        int max = 0;
        for (int i = 1; i <= n; i++) {
            max = Math.max(max, dis[i]);
        }
        System.out.println(max);
        pw.close();
    }

    private static void dfs(int v) {
        for (int to : ages[v]) {
            if (dis[v]+1 > dis[to]) {
                dis[to] = dis[v]+1;
                dfs(to);
            }
        }
    }

    private static int nextInt() throws IOException{
        return Integer.parseInt(next());
    }
    
    private static String next() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }
}
