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.InputStreamReader;
import java.io.IOException;
import java.util.Arrays;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Sunits789
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskA {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int n=in.nextInt();
        int manager[]=new int[n];
        int chamcha[][]=new int[n][n];
        int cl[]=new int[n];
        Arrays.fill(cl,0);
        for(int i=0;i<n;i++){
            int temp=in.nextInt()-1;
            manager[i]=temp;
            if(temp>=0){
                chamcha[temp][cl[temp]]=i;
                cl[temp]++;
            }
        }
        int ans=0;
        for(int i=0;i<n;i++){
            if(manager[i]<0){
                //System.out.println("Starting from "+i);
                int l=dfs(chamcha,cl,0,i);
                if(l>ans){
                    ans=l;
                }
            }
        }
        out.println(ans);
    }

    private int dfs(int chamcha[][],int cl[],int level,int k){
        //System.out.println("At "+k);
        int len=cl[k];
        int ret=0;
        level++;
        if(len==0){
            return level;
        }
        for(int i=0;i<len;i++){
            int temp=dfs(chamcha,cl,level,chamcha[k][i]);
            if(temp>ret){
                ret=temp;
            }
        }
        //System.out.println("Return for k "+(ret+level));
        return ret;
    }
}

class InputReader{
    private BufferedReader reader;
    private StringTokenizer tokenizer;

    public InputReader(InputStream stream){
        reader = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }
    public String next(){
        while (tokenizer == null||!tokenizer.hasMoreTokens()){
            try{
                tokenizer = new StringTokenizer(reader.readLine());
            }
            catch (IOException e){
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

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

    }

