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.math.BigInteger;
import java.util.Locale;
import java.util.StringTokenizer;

/**
 * @author kgs
 */
public class C {

    private void solve() throws IOException {
        int res = 0;
        int n = nextInt();
        int[] p = new int[n + 1];
        p[0] = -1;
        for (int i = 1; i <= n; i++) {
            p[i] = nextInt();
        }
        for (int i = 1; i <= n; i++) {
            int curr = 1;
            int pos = i;
            while (p[pos] != -1) {
                curr++;
                pos = p[pos];
            }
            res = Math.max(res, curr);
        }
        out.println(res);
    }

    // ----------------- HELPER ROUTINES ------------------

    private BufferedReader in;
    private PrintWriter out;
    private StringTokenizer strTok;

    private String nextLine() throws IOException {
        return in.readLine();
    }

    private String nextToken() throws IOException {
        while (strTok == null || !strTok.hasMoreTokens()) {
            String line = nextLine();
            if (line != null) {
                strTok = new StringTokenizer(line);
            } else {
                return null;
            }
        }
        return strTok.nextToken();
    }

    private int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    private long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    private double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    private BigInteger nextBig() throws IOException {
        return new BigInteger(nextToken());
    }

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

    private long getMemory() {
        return (Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory()) / 1024 / 1024;
    }

    private void run() {
        Locale.setDefault(Locale.US);
        try {
            boolean onlineJudge = System.getProperty("ONLINE_JUDGE") != null;
            if (!onlineJudge) {
                in = new BufferedReader(new FileReader("src/input.txt"));
                out = new PrintWriter("src/output.txt");
            } else {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            }
            long startMem = getMemory();
            long startTime = System.currentTimeMillis();
            solve();
            long endTime = System.currentTimeMillis();
            long endMem = getMemory();
            if (!onlineJudge) {
                System.out.println("Running time = " + (endTime - startTime) + "ms");
                System.out.println("Memory used = " + (endMem - startMem) + "MB");
                System.out.println("Total memory = " + getMemory() + "MB");
            }
            in.close();
            out.close();
        } catch (Throwable t) {
            t.printStackTrace();
            System.exit(1);
        }
    }

}
