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.io.PrintWriter;
import java.util.Arrays;


public class Main {
    static boolean[][] graph;
    static boolean[] visited;
    static int maxDepth=0;
    static void dfs(int v, int d){
        if(d>maxDepth) maxDepth=d;
        visited[v]=true;
        for(int i=0; i<visited.length; i++){
            if (graph[v][i] && !visited[i])  
                dfs(i,d+1);
        }
    }

    public static void main(String[] args) throws NumberFormatException, IOException {
        // TODO Auto-generated method stub
        BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out=new PrintWriter(System.out);
        //BufferedReader in = new BufferedReader(new FileReader("input.txt"));
        //PrintWriter out = new PrintWriter(new FileWriter("output.txt"));
        int n=Integer.parseInt(in.readLine());
        graph=new boolean[n][n];
        visited=new boolean[n];
        int[] mas=new int[n];
        for(int i=0; i<n; i++){
            int cur=Integer.parseInt(in.readLine());
            if(cur>0){
                graph[cur-1][i]=true;
            }
            mas[i]=cur;
        }
        int res=1;
        for(int i=0; i<n; i++){
            if(mas[i]==-1){
                maxDepth=0;
                dfs(i,1);
                if(maxDepth>res) res=maxDepth;
            }
        }
        out.println(res);
        out.close();
    }
}

