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.util.*;

public class A {

    int[] p, d;

    void solve() throws IOException {
        in("__std"); out("__std");

        int n = readInt();
        p = new int[n];
        for (int i = 0; i < n; ++i) {
            p[i] = readInt() - 1;
        }
        d = new int[n];
        int max = 0;
        for (int i = 0; i < n; ++i) {
            max = Math.max(max, dfs(i));
        }
        println(max);

        exit();
    }

    int dfs(int i) {
        if (d[i] == 0) {
            d[i] = 1;
            if (p[i] >= 0) {
                d[i] += dfs(p[i]);
            }
        }
        return d[i];
    }

    void in(String name) throws IOException {
        if (name.equals("__std")) {
            in = new BufferedReader(new InputStreamReader(System.in));
        } else {
            in = new BufferedReader(new FileReader(name));
        }
    }

    void out(String name) throws IOException {
        if (name.equals("__std")) {
            out = new PrintWriter(System.out);
        } else {
            out = new PrintWriter(name);
        }
    }

    void exit() {
        out.close();
        System.exit(0);
    }

    int readInt() throws IOException {
        return Integer.parseInt(readToken());
    }

    long readLong() throws IOException {
        return Long.parseLong(readToken());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readToken());
    }

    String readLine() throws IOException {
        st = null;
        return in.readLine();
    }

    String readToken() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }

    boolean eof() throws IOException {
        return !in.ready();
    }

    void print(String format, Object ... args) {
        out.println(new Formatter(Locale.US).format(format, args));
    }

    void println(String format, Object ... args) {
        out.println(new Formatter(Locale.US).format(format, args));
    }

    void print(Object value) {
        out.print(value);
    }

    void println(Object value) {
        out.println(value);
    }

    void println() {
        out.println();
    }

    StringTokenizer st;

    BufferedReader in;
    PrintWriter out;

    public static void main(String[] args) throws IOException {
        new A().solve();
    }
}
