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 
/**
 * Created by IntelliJ IDEA.
 * User: shakhov
 * Date: 15.06.2011
 * Time: 15:22:46
 * To change this template use File | Settings | File Templates.
 */

//6
//86 402 133 524 405 610   6 4 1

import java.io.*;
import java.util.*;

public class CodeForces {
	double eps = 0.00001;

	public void solve() throws IOException {	
		int n=nextInt();
		int[] arr=new int[n];
		for(int i=0;i<n;i++){
			arr[i]=nextInt()-1;
		}
		int c=1;
		for(int i=0;i<n;i++){
			int h=1;
			int t=i;
			while(arr[t]!=-2){
				h++;
				t=arr[t];
			}
			c=Math.max(c, h);
		}
		out.print(c);
		/*List<Set<Integer>> ls=new ArrayList<Set<Integer>>();
		ls.add(new HashSet<Integer>());
		for(int i=0;i<n;i++){
			if(arr[i]==-2){
				ls.get(0).add(i);
			} else {
				
			}
		}*/
		
	}

	
	private BufferedReader reader;
	private StringTokenizer tokenizer;
	private String separator;
	public PrintWriter out;

	public static void main(String[] args) throws IOException {
		// new CodeForces().run(new FileReader("input.txt"), new
		// FileWriter("output.txt"));
		new CodeForces().run(new InputStreamReader(System.in), new OutputStreamWriter(System.out));
	}

	public void run(Reader reader, Writer writer) {
		try {
			this.reader = new BufferedReader(reader);
			out = new PrintWriter(writer);
			tokenizer = new StringTokenizer("");
			separator = System.getProperty("line.separator");
			separator = Character.toString(separator.charAt(separator.length() - 1));
			long t1 = System.currentTimeMillis();
			solve();
			out.flush();
			reader.close();
			writer.close();
			long t2 = System.currentTimeMillis();
			System.err.println("Time = " + (t2 - t1));
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}

	String nextToken() throws IOException {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			tokenizer = new StringTokenizer(reader.readLine());
		}
		return tokenizer.nextToken();
	}

}
