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.util.stream.Collectors;
import java.util.stream.IntStream;

public class P115A {
    private static class Solver {
        private final PrintWriter out;

        public Solver(PrintWriter out) {
            this.out = out;
        }

        public void solve(InputReader in) {
            int n = in.nextInt();
            Map<Integer, Node> tree = IntStream.rangeClosed(1, n)
                                               .mapToObj(id -> new Node(id))
                                               .collect(Collectors.toMap(node -> node.id, node -> node));
            for (int i = 1; i <= n; i++) {
                int parentId = in.nextInt();
                Node node = tree.get(i);
                node.setParentId(parentId);
                if (parentId > 0) {
                    tree.get(parentId).addChild(node);
                }
                tree.put(i, node);
            }
            int maxDepth = tree.entrySet()
                               .stream()
                               .filter(e -> e.getValue().parentId == -1)
                               .map(e -> dfs(e.getValue()))
                               .max(Comparator.naturalOrder())
                               .orElse(0);
            out.println(maxDepth);
        }

        private int dfs(Node node) {
            return node.children.stream().map(c -> dfs(c)).max(Comparator.naturalOrder()).orElse(0) + 1;
        }

        private static class Node {
            private final int id;
            private final List<Node> children;

            private Integer parentId;

            private Node(int id) {
                this.id = id;
                this.children = new ArrayList<>();
            }

            void setParentId(int parentId) {
                if (this.parentId != null) {
                    throw new IllegalStateException("Parent id already set");
                }
                this.parentId = parentId;
            }

            Node addChild(Node child) {
                children.add(child);
                return this;
            }

            @Override
            public String toString() {
                return new StringJoiner(", ", Node.class.getSimpleName() + "[", "]")
                        .add("id=" + id)
                        .add("children=" + children)
                        .toString();
            }
        }
    }

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver(out);
        solver.solve(in);
        out.close();
    }

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