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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public 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();
    }

    static class TaskA {
        ArrayList<Integer>[] g;
        int maxDepth = Integer.MAX_VALUE;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int[] p = new int[n];
            g = new ArrayList[n];
            for (int i = 0; i < n; i++) {
                g[i] = new ArrayList<>();
            }
            for (int i = 0; i < n; i++) {
                int v = in.nextInt();
                p[i] = v;
                if (v == -1)
                    continue;
                v--;
                g[v].add(i);
                g[i].add(v);
            }

            int best = Integer.MIN_VALUE;
            for (int i = 0; i < n; i++)
                if (p[i] == -1) {
                    maxDepth = Integer.MIN_VALUE;
                    dfs(i, -1, 1);
                    best = Math.max(best, maxDepth);
                }

            out.println(best);
        }

        void dfs(int from, int prev, int depth) {
            boolean anySeen = false;
            for (Integer v : g[from]) {
                if (v == prev)
                    continue;
                anySeen = true;
                dfs(v, from, depth + 1);
            }

            if (!anySeen)
                maxDepth = Math.max(maxDepth, depth);
        }

    }

    static class InputReader {
        StringTokenizer st;
        BufferedReader br;

        public InputReader(InputStream is) {
            BufferedReader br = new BufferedReader(new InputStreamReader(is));
            this.br = br;
        }

        public String next() {
            if (st == null || !st.hasMoreTokens()) {
                String nextLine = null;
                try {
                    nextLine = br.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (nextLine == null)
                    return null;
                st = new StringTokenizer(nextLine);
            }
            return st.nextToken();
        }

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

    }
}

