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.StringTokenizer;
import java.util.TreeSet;

public class Main {
	
	static boolean[] visited;
	static ArrayList<Integer>[] adjList;
	static PrintWriter pw = new PrintWriter(System.out);
	public static void main(String[] args) throws  IOException, InterruptedException {
		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st ;
		StringBuilder sb = new StringBuilder();
		int n =Integer.parseInt(bf.readLine());
		adjList=new ArrayList[n];
		visited=new boolean[n];
		for(int i=0;i<n;i++) {
			adjList[i]=new ArrayList<>();
			
		}
	for(int i=0;i<n;i++) {
			int superior= Integer.parseInt(bf.readLine());
			if(superior!=-1) {
				adjList[superior-1].add(i);
			}
		}
	for(int i=0;i<n;i++) {
		if(!visited[i]) {
			dfs(i,1);
		}
		Arrays.fill(visited,false);
	}
	pw.println(maxCount);
		pw.flush();
		pw.close();
	}
	static int maxCount=0;
	public static void dfs(int u,int length) {
		if(adjList[u].size()==0&&length>maxCount) {
			maxCount=length;
		}
	
		if(visited[u]) {
			return;
		}
			visited[u]=true;
		for(int i=0;i<adjList[u].size();i++) {
			dfs(adjList[u].get(i),length+1);
		}
	}

}