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.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class two {
	static ArrayList<ArrayList<Integer>> Graph;
	static int Discovered[];
	static int levels=0;

	public static void main(String[] args) throws IOException {
		Reader.init(System.in);
		int j=1;
		int N=Reader.nextInt();
		Discovered=new int[N];
		Graph=new ArrayList<ArrayList<Integer>>();
		for(int i=0;i<N;i++) {
			Graph.add(new ArrayList<Integer>());
		}
		
		while(j<=N) {
			
			int Superior=Reader.nextInt();
			if(Superior==-1) {
				//nosupcount++;
				j++;
				continue;
			}else {
				//System.out.println(Superior-1+"  "+(j-1));
				Graph.get(Superior-1).add(j-1);
				j++;
			}
		}
		
		
		j=0;
		int max=0;
		for(j=0;j<N;j++) {
			int x=DFS(j);
			//System.out.println(x);
			if(max<x) {
				max=x;
			}
			//System.out.println("!");
			//System.out.println(x);
			//System.out.println(levels-1+" LEVEL");
			//levels=0;
		}
		
		System.out.println(max);;
		
	
		
	}
	
	public static int DFS(int v) {
		if(Discovered[v]==1) {
			System.out.println("HERE!!");
			return 0;
		}
		else {
			
			//Discovered[v]=1;
			int max=1;
			//System.out.println(Graph.get(v).size()+" SIZE");
			for(int i=0;i<Graph.get(v).size();i++) {
				if(Discovered[Graph.get(v).get(i)]==0) {
					//System.out.println("xxx");
					int d=1+DFS(Graph.get(v).get(i));
					if(max<d) {
						max=d;
					}
					
				}
			}
			
			return max;
		}
	}

}
class Reader
{
	static BufferedReader reader;
	static StringTokenizer tokenizer;
	
	/** call this method to initialise reader for InputStream */
	static void init(InputStream input)
	{
		reader = new BufferedReader(new InputStreamReader(input));
		tokenizer = new StringTokenizer("");
	}
	
	/** get next word */
	static String next() throws IOException
	{
		while (!tokenizer.hasMoreTokens())
		{
			// TODO add check for eof if necessary
			tokenizer = new StringTokenizer(reader.readLine());
		}
		return tokenizer.nextToken();
	}
	
	static int nextInt() throws IOException
	{
		return Integer.parseInt(next());
	}
	
	
	static long nextLong() throws IOException{
		return Long.parseLong(next());
	}
	
	static double nextDouble() throws IOException
	{ return Double.parseDouble(next());
	}
}
