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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;
import java.util.*;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Party {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }
    static class TaskA {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            while(testNumber-->0){
                int n = in.nextInt();
                ArrayList<ArrayList<Integer>> a = new ArrayList<>();
                for(int i=0;i<=n;i++)
                    a.add(new ArrayList<Integer>());
                int minus = 0;
                int visited[] = new int[n+1];
                for(int i=1;i<=n;i++){
                    int b = in.nextInt();
                    if(b!=-1)
                        a.get(b).add(i);
                    else{
                        minus = 1;
                        visited[i] = 1;
                    }
                }
                int maxLength = 0;
                for(int i=1;i<=n;i++){
                    if(visited[i] == 1){
                        int b = dfs(a , visited , i , 1);
                        if(maxLength<b)
                            maxLength = b;
                    }
                }
                out.println(maxLength);
            }
        }
        public int dfs(ArrayList<ArrayList<Integer>> a, int visited[] , int index , int count){
            if(a.get(index).size() == 0)
                return count;
            visited[index] = 2;
            int c = 0;
            int l = a.get(index).size();
            for(int i=0;i<l;i++){
                int b = dfs(a , visited , a.get(index).get(i) , count+1);
                if(c<b){
                    c = b;
                }
            }
            return c;
        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

    }
}
