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.*;
import java.text.DecimalFormat;
import java.util.*;

/**
 * Created by hieptk on 2/17/2017.
 */
public class Main {

    class IOManager {
        BufferedReader reader;
        PrintWriter writer;
        StringTokenizer tokenizer;

        IOManager() {
            reader = new BufferedReader(new InputStreamReader(System.in));
            writer = new PrintWriter(new BufferedOutputStream(System.out));
        }

        IOManager(String file) throws FileNotFoundException {
            reader = new BufferedReader(new FileReader(file));
            writer = new PrintWriter(new BufferedOutputStream(System.out));
        }

        String next() throws IOException {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                String line = reader.readLine();
                if (line == null)
                    throw new IOException("No lines left.");
                tokenizer = new StringTokenizer(line);
            }
            return tokenizer.nextToken();
        }

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

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

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

        public void writeSpace(Object obj) {
            writer.print(obj.toString() + " ");
        }

        public void writeLine(Object obj) {
            writer.println(obj.toString());
        }

        public void writeDouble(Double x, int n) {
            String format = "%." + n + "f";
            writer.printf(format, x);
        }

        public void close() {
            writer.close();
        }
    }

    class Pair {
        public int u, v;

        Pair(int u, int v) {
            this.u = u;
            this.v = v;
        }
    }

    class Graph {
        public int n, m;
        public List<Integer>[] adj;

        public Graph(int n, int m) {
            this.n = n;
            this.m = m;
            adj = new List[n + 1];
            for (int i = 0; i <= n; ++i) {
                adj[i] = new ArrayList<>();
            }
        }

        public void add(int u, int v) {
            adj[u].add(v);
        }

        public void add2Ways(int u, int v) {
            add(u, v);
            add(v, u);
        }
    }

    // Actually forest
    class Tree extends Graph {

        public Tree(int n, int m) {
            super(n, m);
        }

        public int getHeight(int i) {
            int res = 0;
            for (Integer j: adj[i]) {
                res = Math.max(res, getHeight(j) + 1);
            }
            return res;
        }
    }

    IOManager ioManager;

    Main() {
        ioManager = new IOManager();
    }

    Main(String file) throws FileNotFoundException {
        ioManager = new IOManager(file);
    }


    void solve() throws IOException {
        int n = ioManager.nextInt();
        Tree g = new Tree(n, n - 1);
        List<Integer> roots = new ArrayList<>();
        for (int i = 1; i <= n; ++i) {
            int p = ioManager.nextInt();
            if (p != -1) {
                g.add(p, i);
            } else {
                roots.add(i);
            }
        }
        int res = 0;
        for (Integer root: roots) {
            res = Math.max(res, g.getHeight(root) + 1);
        }
        ioManager.writeLine(res);
    }

    void close() {
        ioManager.close();
    }

    public static void main(String args[]) throws IOException {
//		Main solver = new Main("input.txt");
        Main solver = new Main();
        solver.solve();
        solver.close();
    }
}
