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.util.Map.Entry;
import java.io.*;

public class Contest {

	static ArrayList<Integer>[] adjList;
	static boolean[] vis;
	static int max;

	public static void dfs(int x, int l) {
		vis[x] = true;
		for (int u : adjList[x]) {
			if (!vis[u]) {
				vis[u] = true;
				dfs(u, l + 1);
			}
		}
		max = Math.max(max, l);
	}

	public static void main(String args[]) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		adjList = new ArrayList[n];
		for (int i = 0; i < n; i++) {
			adjList[i] = new ArrayList<>();
		}
		for (int i = 0; i < n; i++) {
			int temp = Integer.parseInt(br.readLine());
			if (temp != -1) {
				adjList[temp - 1].add(i);
			}
		}
		int ans = Integer.MIN_VALUE;
		for (int i = 0; i < n; i++) {
			vis = new boolean[n];
			dfs(i, 0);
			ans = Math.max(ans, max);
		}
		System.out.println(ans + 1);
	}
}
