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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.UnsupportedEncodingException;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Queue;
import java.util.StringTokenizer;

public class Main {
    
    public static void main(String[] args) throws UnsupportedEncodingException, IOException {
        Reader.init(System.in);
        StringBuilder s = new StringBuilder();
        int n = Reader.nextInt(), i, cur;
        Graph g = new Graph();
        for(i = 1; i <= n; i++) {
            cur = Reader.nextInt();
            if(cur != -1)
                g.addEdge(cur, i);
            else g.getVertex(i).isParent = true;
        }
        int max = 0;
        Queue<Vertex> q;
        Vertex V;
        for(Vertex v : g.vertexMap.values())
            if(v.isParent) {
                q = new LinkedList<Vertex>();
                q.add(v);
                while(!q.isEmpty()) {
                    V = q.poll();
                    for(Vertex vv : V.args) {
                        vv.level = V.level + 1;
                        max = Math.max(max, vv.level);
                        q.add(vv);
                    }
                }
            }
        s.append(max + 1).append('\n');
        System.out.print(s);
    }
    
}

class Vertex {
    int name, level;
    boolean isParent;
    List<Vertex> args;
    public Vertex(int name) {
        this.name = name;
        args = new LinkedList<Vertex>();
    }
}

class Graph {
    
    Map<Integer, Vertex> vertexMap = new HashMap<Integer, Vertex>();
    
    public Vertex getVertex(int name) {
        Vertex v = vertexMap.get(name);
        if(v == null) {
            v = new Vertex(name);
            vertexMap.put(name, v);
        }
        return v;
    }
    
    public void addEdge(int n1, int n2) {
        Vertex v = getVertex(n1);
        Vertex w = getVertex(n2);
        v.args.add(w);
    }
    
}

class Reader {

    static BufferedReader reader;
    static StringTokenizer tokenizer;

    static void init(InputStream input) throws UnsupportedEncodingException {
        reader = new BufferedReader(
                new InputStreamReader(input, "UTF-8"));
        tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static String nextLine() throws IOException {
        return reader.readLine();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
}



