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.IOException;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;


public class Codeforces_115A_Party {
	static final int VISITED = 2, EXPLORED = 1, UNVISITED = 0;
	static ArrayList<Integer>[] adjList;
	static int[] visited;
	static int V;
	static int dfs(int u)				//O(V + E) adjList, O(V^2) adjMat	
	{
		
	
		if(visited[u]==-1){
			
		
		for(int v: adjList[u])
				visited[u]=  Math.max(dfs(v),visited[u]);
		
		return ++visited[u];
		}
		return visited[u];

	}
	public static void main(String[] args) throws NumberFormatException, IOException {
		
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		visited= new int[n];
		Arrays.fill(visited, -1);
		adjList = new ArrayList[n];
		for(int i = 0; i < n; ++i)
			adjList[i] = new ArrayList<Integer>();
		
	
		for(int i = 0; i < n; ++i)
		{
			int u = sc.nextInt();
			if(u!=-1){
			adjList[u-1].add(i);
			}
			
		}
		int res=0;
			for (int i = 0; i < n; i++) {
				res=Math.max(res, dfs(i));
			}
		
		System.out.println(res+1);
	}
	
	

}
