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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;


public class CF_115A {
	static FastScanner sc = new FastScanner(System.in);
	static PrintWriter out = new PrintWriter(System.out);
	
	public static void main(String[] args) {
		new CF_115A().run();
		out.close();
	}
	
	public void run(){
		int n = sc.nextInt();
		int[] a = new int[n+1];
		int[] dp = new int[n+1];
		for(int i = 1;i<=n;i++){
			a[i]= sc.nextInt();
		}
		for(int i = 1;i<=n;i++){
			if(a[i]==-1){
				dp[i] = 1;
			}
			else{
				if(dp[a[i]]!=0)
					dp[i] = dp[a[i]]+1;
				else{
					int cnt = 0;
					int index = i;
					while(index!=-1){
						index = a[index];
						cnt++;
					}
					dp[i] = cnt;
				}
			}
		}
		int max = -1;
		for(int i = 1;i<=n;i++){
			max = Math.max(max, dp[i]);
		}
		out.println(max);
	}

	static class FastScanner {
		private final InputStream stream;
	    private final byte[] buf = new byte[8192];
	    private int curChar, snumChars;

	    public FastScanner(InputStream st) {
	      this.stream = st;
	    }

	    //读一个字节
	    public int read() {
	      if (snumChars == -1)
	        throw new InputMismatchException();
	      if (curChar >= snumChars) {
	        curChar = 0;
	        try {
	          snumChars = stream.read(buf);
	        } catch (IOException e) {
	          throw new InputMismatchException();
	        }
	        if (snumChars <= 0)
	          return -1;
	      }
	      return buf[curChar++];
	    }

	    public int nextInt() {
	      int c = read();
	      while (isSpaceChar(c)) {
	        c = read();
	      }
	      int sgn = 1;
	      if (c == '-') {
	        sgn = -1;
	        c = read();
	      }
	      int res = 0;
	      do {
	        res *= 10;
	        res += c - '0';
	        c = read();
	      } while (!isSpaceChar(c));
	      return res * sgn;
	    }
	    public boolean isSpaceChar(int c) {
	      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	    }
	}
}
