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.ArrayList;
import java.util.Arrays;
import java.util.List;

public class C {
	public static BufferedReader in;
	public static PrintWriter out;

	public static void main(String[] args) throws IOException {
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);

		boolean showLineError = true;
		if (showLineError) {
			solve();
			out.close();
		} else {
			try {
				solve();
			} catch (Exception e) {
			} finally {
				out.close();
			}
		}

	}

	static void debug(Object... os) {
		out.println(Arrays.deepToString(os));
	}

	private static void solve() throws IOException {
		int n = Integer.parseInt(in.readLine());
		List<Integer>[] g = (List<Integer>[]) new List[n];
		for(int i =0;i<n;i++)
			g[i]= new ArrayList<Integer>();
		List<Integer> list = new ArrayList<Integer>();
		int[] height = new int[n];
		Arrays.fill(height, -1);
		for(int i =0;i<n;i++){
			int prev = Integer.parseInt(in.readLine())-1;
			if(prev==-2){
				list.add(i);
			}else{
				g[prev].add(i);
			}
		}
		for(int u : list){
			height[u]=go(g,u,height);
		}
		int max =0;
		for(int a : height)
			max = Math.max(max, a);
		out.println(max+1);
	}

	private static int go(List<Integer>[] g, int u, int[] height) {
		if(height[u]!=-1)
			return height[u];
		if(g[u].size()==0)
			return height[u]=0;
		
		for(int v : g[u])
			height[u]=Math.max(height[u], 1+go(g,v,height));
		
		return height[u];
	}

}