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.ArrayList;
import java.util.HashSet;

/**
 * Created by Tejas on 26-06-2018.
 */
public class Main {
    static int superior[];
    static int MAXLEVEL=0;
    static ArrayList<Integer>[] adjList;
   /* public static void main(String[] args) throws IOException {
        BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));
        int N = Integer.parseInt(bufferedReader.readLine());

        superior=new int[N+1];

        for(int i=1;i<=N;i++)
            hashSetOfLeaves.add(i);
        for(int i=1;i<=N;i++){
            int x=Integer.parseInt(bufferedReader.readLine());
            superior[i]=x;
            hashSetOfLeaves.remove(x);
        }

        for(int i:hashSetOfLeaves)
            dfs(i,1);

        System.out.println(MAXLEVEL);
    }*/

    public static void main(String[] args) throws IOException {
        BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));
        int N = Integer.parseInt(bufferedReader.readLine());

        adjList=new ArrayList[N+1];
        superior=new int[N+1];
        for (int i = 0; i < N+1; i++)
            adjList[i]=new ArrayList();

        ArrayList<Integer> roots=new ArrayList<>();
        for(int i=1;i<=N;i++){
            int x=Integer.parseInt(bufferedReader.readLine());
            superior[i]=x;
            if(x==-1) roots.add(i);
            else adjList[x].add(i);
        }
        for(int x: roots)
            dfs(x,1);
        System.out.println(MAXLEVEL);
    }

    private static void dfs(int source,int level) {
        MAXLEVEL=Math.max(MAXLEVEL,level);
        for(int x:adjList[source])
            dfs(x,level+1);
    }
}
