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 com.sun.org.apache.xerces.internal.xs.LSInputList;

import java.io.*;
import java.lang.*;
import java.lang.reflect.Array;
import java.util.*;

public class Main {
    final static String fileName = "dominoes";
    final static boolean useFiles = false;

    public static void main(String[] args) throws FileNotFoundException {
        InputStream inputStream;
        OutputStream outputStream;
        if (useFiles) {
            inputStream = new FileInputStream(fileName + ".in");
            outputStream = new FileOutputStream(fileName + ".out");
        } else {
            inputStream = System.in;
            outputStream = System.out;
        }
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task(in, out);
        Debug.out = out;
        solver.solve();
        out.close();
    }
}

class Dsu{
    int n;
    int[] p, rank;
    Dsu(int n){
        this.n = n;
        p = new int[n];
        for (int i = 0; i < n; i++)
            p[i] = i;
        rank = new int[n];
    }
    void union(int a, int b) {
        a = findSet(a);
        b = findSet(b);
        if (a == b)
            return;
        if (rank[a] < rank[b]) {
            int t = a;
            a = b;
            b = t;
        }
        rank[a] = Math.max(rank[b] + 1, rank[a]);
        p[b] = a;
    }
    int findSet(int x){
        if (p[x] == x)
            return x;
        return p[x] = findSet(p[x]);
    }
}

class Task {
    int[] p, d;
    int rec(int x){
        if (x == -1)
            return 0;
        if (d[x] != -1)
            return d[x];
        return d[x] = rec(p[x]) + 1;
    }
    public void solve() {
        int n = in.nextInt();
        p = new int[n];
        d = new int[n];
        Arrays.fill(d, -1);
        for (int i = 0; i < n; i++){
            p[i] = in.nextInt();
            if (p[i] > 0)
                p[i]--;
        }
        int result = 0;
        for (int i = 0; i < n; i++){
            result = Math.max(result, rec(i));
        }
        out.println(result);
    }

    private InputReader in;
    private PrintWriter out;

    Task(InputReader in, PrintWriter out) {
        this.in = in;
        this.out = out;
    }
}

class Debug {
    public static PrintWriter out;

    public void printObjects(Objects... objects) {
        out.println(Arrays.deepToString(objects));
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

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

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

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