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.InputStreamReader;
import java.util.ArrayList;
import java.util.LinkedList;
import java.util.Queue;

public class Party {

    class Node {
        int id, cnt;
        public Node(int x, int cnt) {
            this.id = x;
            this.cnt = cnt;
        }
    }

    void run() throws Exception {
        BufferedReader bfd = new BufferedReader(
                new InputStreamReader(System.in));
        int n = Integer.parseInt(bfd.readLine());
        ArrayList<Integer>[] adj = new ArrayList[n];
        ArrayList<Integer> roots = new ArrayList<Integer>();
        for (int i = 0; i < adj.length; ++i) adj[i] = new ArrayList<Integer>();
        boolean[] vis;
        for (int i = 0; i < n; ++i) {
            int p = Integer.parseInt(bfd.readLine());
            if (p == -1) {
                roots.add(i);
                continue;
            }
            adj[--p].add(i);
        }
        int mxLen = 0;
        for (int i = 0; i < roots.size(); ++i) {
            int x = roots.get(i);
            vis = new boolean[n];
            Queue<Node> q = new LinkedList<Node>();
            q.add(new Node(x, 1));
            vis[x] = true;
            while (!q.isEmpty()) {
                Node frnt = q.poll();
                mxLen = Math.max(mxLen, frnt.cnt);
                for (int k = 0; k < adj[frnt.id].size(); ++k) {
                    int nei = adj[frnt.id].get(k);
                    if (!vis[nei]) {
                        q.add(new Node(nei, frnt.cnt + 1));
                        vis[nei] = true;
                    }
                }
            }
        }
        System.out.println(mxLen);
    }

    public static void main(String[] args) throws Exception {
        new Party().run();
    }

}