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.BufferedWriter;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class CodeForces115A {

	static ArrayList<Integer> visitedList = new ArrayList();
	
	public static void ArrayPrint(int[] arr){
	    for(int i=0;i<arr.length;i++){
	    	System.out.println(arr[i]);
	    }
	}
	
	public static void mPrint(int[][] myMatrix, int n){
	      for(int i=0;i<n;i++){
	            for(int j=0;j<n;j++){
	            System.out.print(myMatrix[i][j] + " ");
	            }
	           System.out.println();
	      }
	}
	
	public static int dfs(int[][] adjM,int start, int depth, int maxDepth) {
		for(int j=1;j<adjM.length;j++) {
			if(adjM[start][j] == 1 && !visitedList.contains(j)) {
				visitedList.add(start);
				maxDepth = dfs(adjM,j,depth+1,maxDepth);
			}
		}
		if(maxDepth < depth) {
			maxDepth = depth;
		}
		depth = depth -1;
		//System.out.println("max depth for node "+start+" is: "+maxDepth);
		return maxDepth;
	}
	
	public static void main(String[] args) throws IOException {
		
	FastReader file = new FastReader();
	int n = file.nextInt();
	int[] inputArr = new int[n];
	ArrayList<Integer> bossList = new ArrayList();
	for(int i=0;i<n;i++) {
		inputArr[i] = file.nextInt();
		if(inputArr[i] == -1) {
			bossList.add(i+1);
		}
	}
	//+1 to ignore 0
	int[][] adjM = new int[n+1][n+1];
	//population of adj matrix and ctr is a variable for input array to vary:
	int ctr = 0;
	for(int i=1;i<=n;i++) {
		for(int j=1;j<=n+1;j++) {
			if(ctr+1 == i && inputArr[ctr] == j && j != -1) {
				adjM[i][j] = 1;
				adjM[j][i] = 1;
				//System.out.println("went in");
				break;
			}
		}
		ctr++;
	}
	//mPrint(adjM,n+1);
	//dfs and main code of counting levels
	int answer = 0;
	for(int i=0;i<bossList.size();i++) {
		//System.out.println("bossNode: "+bossList.get(i));
		int temp = dfs(adjM,bossList.get(i),1,0);
		if(temp > answer) {
			answer = temp;
		}
	}
	System.out.println(answer);
	}

}

class FastReader
{
   BufferedReader br;
   StringTokenizer st;
   
   public FastReader() throws FileNotFoundException
   {
      br = new BufferedReader(new InputStreamReader(System.in));
   }
   
   public FastReader(String file) throws FileNotFoundException
   {
      br = new BufferedReader(new FileReader(file));
   }
 
   String next()
   {
      while (st == null || !st.hasMoreElements())
      {
         try
         {
            st = new StringTokenizer(br.readLine());
         }
         catch (IOException  e)
         {
            e.printStackTrace();
         }
      }
      return st.nextToken();
   }
 
   int nextInt()
   {
      return Integer.parseInt(next());
   }
 
   long nextLong()
   {
      return Long.parseLong(next());
   }
 
   double nextDouble()
   {
      return Double.parseDouble(next());
   }
 
   String nextLine()
   {
      String str = "";
      try
      {
         str = br.readLine();
      }
      catch (IOException e)
      {
         e.printStackTrace();
      }
      return str;
   }
}

