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


public class R87qAParty {

	static ArrayList<Integer> g[];
	
	@SuppressWarnings("unchecked")
	public static void main(String args[] ) throws Exception {
		   
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	    PrintWriter w = new PrintWriter(System.out);
	    
	    StringTokenizer st1 = new StringTokenizer(br.readLine());
	    int n = ip(st1.nextToken());
	        
	    g = new ArrayList[n];
	    for(int i=0;i<n;i++)
	    	g[i] = new ArrayList<Integer>();
	    
	    ArrayList<Integer> roots = new ArrayList<Integer>();
	    
	    for(int i=0;i<n;i++){
	    	int p = ip(br.readLine());
	    	if(p != -1)
	    		g[p - 1].add(i);
	    	else
	    		roots.add(i);
	    }
	    
	    int ans = 0;
	    for(int root : roots)
	    	ans = Math.max(ans, dfs(root));
	    
	    w.println(ans);
	    w.close(); 
	}
	
	public static int dfs(int curr){
		int s = g[curr].size();
		int ans = 0;
		for(int i=0;i<s;i++)
			ans = Math.max(ans,dfs(g[curr].get(i)));
		ans++;
		return ans;
	}
	
	public static int ip(String s){
		return Integer.parseInt(s);
	}
}
