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.*;
import java.math.BigInteger;

public class Main{
    final boolean isFileIO =  false;
    BufferedReader in;
    PrintWriter out;
    StringTokenizer st = new StringTokenizer("");
    String delim = " ";

    public static void main(String[] args) throws IOException {
        Main m = new Main();
        m.initIO();
        m.solve();
        m.in.close();
        m.out.close();
    }

    public void initIO() throws IOException {
        if(!isFileIO) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt"); 
        }
    }
  
    String nt() throws IOException {
        if(!st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken(delim);
    }

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

    int ni() throws IOException {
        return Integer.parseInt(nt());
    }

    long nl() throws IOException {
        return Long.parseLong(nt());
    }

    double nd() throws IOException {
        return Double.parseDouble(nt());
    }

    ArrayList<ArrayList<Integer>> g = new ArrayList<ArrayList<Integer>>();

    int cnt = 0;
    boolean[] used;
    public void solve() throws IOException {
        int n = ni();
        for(int i = 0; i < n; i++) {
            g.add(new ArrayList<Integer>());
        }
        for(int i = 0; i < n; i++) {
            int p = ni();
            if(p != -1) {
                g.get(i).add(p - 1);
            }
        }
        used = new boolean[n];
        int max = 0;
        for(int i = 0; i < n; i++) {
            cnt = 0;
            Arrays.fill(used, false);
            dfs(i);
            max = Math.max(cnt, max);
        }
        out.println(max);
    }

    public void dfs(int u) {
        cnt++;
        used[u] = true;
        for(int i = 0; i < g.get(u).size(); i++) {
            if(!used[g.get(u).get(i)]) {
                dfs(g.get(u).get(i));
            }
        }
    }
}

class Utils {

    public static long binpow(long a, long exp, long mod) {
        if(exp == 0) {
            return 1;
        }
        if(exp % 2 == 0) {
            long temp = binpow(a, exp / 2, mod);
            return (temp * temp) % mod;
        } else {
            return (binpow(a, exp - 1, mod) * a) % mod;
        }
    }

    public static long inv(long a, long mod) {
        return binpow(a, mod - 2, mod);
    }

    public static long addmod(long a, long b, long mod) {
        return ((a + b) % mod + mod) % mod;
    }

    public static long gcd(long a, long b) {
        if(b == 0)
            return a;
        return gcd(b, a % b);
    }

    //mul must be < 10^18
    public static long mulmod(long a, long b, long mod) {
        return (a * b + (((a * b) / mod) + 1) * mod) % mod;
    }
}