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.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.util.*;

public final class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }
}



class Graph {
    private ArrayList<ArrayList<Integer>> neighbors;
    public Graph(int n) {
        this.neighbors = new ArrayList<ArrayList<Integer>>();
        for (int i = 0; i < n; i++) {
            neighbors.add(new ArrayList<>());
        }
    }
    public void addEdge(int from, int to) {
        if (neighbors.size() <= from) {
            // System.out.println(neighbors.size() + " " + from + " " + to);
            throw new RuntimeException("out of index");
        }
        neighbors.get(from).add(to);
    }

    public ArrayList<Integer> getNeighbors(int from) {
        if (neighbors.size() <= from) {
            throw new RuntimeException("out of index");
        }
        return neighbors.get(from);
    }
}



class TaskA {

    private void maxLevel(Graph graph, int node, HashMap<Integer, Integer> result) {
        if (result.containsKey(node)) {
            return;
        }
        int max = 0;
        for (Integer neighbor: graph.getNeighbors(node)) {
            if (!result.containsKey(neighbor)) {
                maxLevel(graph, neighbor, result);
            }
            max = Math.max(max, result.get(neighbor));
        }
        result.put(node, max + 1);
    }

    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int n = in.nextInt();
        Graph graph = new Graph(n);
        for (int i = 0; i < n; i++) {
            int parent = in.nextInt();
            parent--;
            if (parent != -2) {
                graph.addEdge(parent, i);
            }
        }
        // out.println("added all edges");
        HashMap<Integer, Integer> memory = new HashMap<>();
        // out.println("starting");
        int result = 0;
        for (int i = 0; i < n; i++) {
            if (!memory.containsKey(i)) {
                maxLevel(graph, i, memory);
                result = Math.max(result, memory.get(i));
            }
        }
        out.println(result);
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }
}

