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.util.*;
import java.io.*;
import java.math.BigInteger;
public class Main {
    public Main() {}
    public static void main(String[]args) throws Exception
    {
        Main main = new Main();
        main.gimmiepoints();
        
    }
    Person[] ppl;
    public void gimmiepoints() throws Exception
    {
        Parser in = new Parser(System.in);
        int people = in.nextInt();
        ppl = new Person[people];
        for(int i = 0 ; i < people; i++)
        {
            ppl[i] = new Person(in.nextInt());
        }
        int max = 0;
        for(int i = 0; i < people;i++)
        {
            if(ppl[i].manager == -1) ppl[i].level = 1;
            else if(ppl[i].level == -1)
            {
                ppl[i].level = getLevel(i,0);
            }
            max = Math.max(ppl[i].level,max);
        }
        System.out.println(max);
            
    }
    
    public int getLevel(int i, int a)
    {
        while(ppl[i].level == -1)
        {
            a++;
            i = ppl[i].manager-1;
            if(i == -2) return a;
        }
        return a + ppl[i].level;
    }
    
}

class Person
{
    int manager;
    int level = -1;
    public Person(int a){manager = a;}
}

class Parser
{
   final private int BUFFER_SIZE = 1 << 16;

   private DataInputStream din;
   private byte[] buffer;
   private int bufferPointer, bytesRead;

   public Parser(InputStream in)
   {
      din = new DataInputStream(in);
      buffer = new byte[BUFFER_SIZE];
      bufferPointer = bytesRead = 0;
   }

   public long nextLong() throws Exception
   {
      long ret = 0;
      byte c = read();
      while (c <= ' ') c = read();
      boolean neg = c == '-';
      if (neg) c = read();
      do
      {
         ret = ret * 10 + c - '0';
         c = read();
      } while (c > ' ');
      if (neg) return -ret;
      return ret;
   }
   
   public String next() throws Exception
   {
      StringBuilder ret =  new StringBuilder();
      byte c = read();
      while (c <= ' ') c = read();
      do
      {
         ret = ret.append((char)c);
         c = read();
      } while (c > ' ');
      //System.out.println(ret + "!!!!!!");
      return ret.toString();
   }

   public int nextInt() throws Exception
   {
      int ret = 0;
      byte c = read();
      while (c <= ' ') c = read();
      boolean neg = c == '-';
      if (neg) c = read();
      do
      {
         ret = ret * 10 + c - '0';
         c = read();
      } while (c > ' ');
      if (neg) return -ret;
      return ret;
   }
   
   private void fillBuffer() throws Exception
   {
      bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
      if (bytesRead == -1) buffer[0] = -1;
   }

   private byte read() throws Exception
   {
      if (bufferPointer == bytesRead) fillBuffer();
      return buffer[bufferPointer++];
   }
}
