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.*;
import java.util.*;

public class Party implements Runnable {
        int n; 
        int []a;
		int dfs(int i)
		{
			if(i>=n || i<0 || a[i]<0)
				return 1;
			return 1+dfs(a[i]);
		}
		void solve() throws IOException {
			n = nextInt();
			a = new int[n];
			for(int i=0;i<n;i++)
				a[i] = nextInt()-1;
			
			int ret = 0;
			for(int i=0;i<n;i++)
				ret = Math.max(ret,dfs(i));
			writer.println(ret);
         }
       
        BufferedReader reader;
        StringTokenizer tokenizer;
        PrintWriter writer;

        public void run() {
            try {
                reader = new BufferedReader(new InputStreamReader(System.in));
                writer = new PrintWriter(System.out);
                //reader = new BufferedReader(new FileReader("input.txt"));
                //writer = new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));
                tokenizer = null;
                solve();
                reader.close();
                writer.close();
            } catch (Exception e) {
                e.printStackTrace();
                System.exit(1);
            }
        }

        int nextInt() throws IOException {
            return Integer.parseInt(nextToken());
        }

        long nextLong() throws IOException {
            return Long.parseLong(nextToken());
        }

        double nextDouble() throws IOException {
            return Double.parseDouble(nextToken());
        }

        String nextToken() throws IOException {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }
            return tokenizer.nextToken();
        }

        public static void main(String[] args) {
                new Party().run();
        }

}