Problem:
Score : 500 points

Problem Statement

Given is a string S of length N.

Find the maximum length of a non-empty string that occurs twice or more in S as contiguous substrings without overlapping.

More formally, find the maximum positive integer len such that there exist integers l_1 and l_2 ( 1 \leq l_1, l_2 \leq N - len + 1 ) that satisfy the following:

l_1 + len \leq l_2

S[l_1+i] = S[l_2+i] (i = 0, 1, ..., len - 1)

If there is no such integer len, print 0.

Constraints

2 \leq N \leq 5 \times 10^3

|S| = N

S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

N
S

Output

Print the maximum length of a non-empty string that occurs twice or more in S as contiguous substrings without overlapping. If there is no such non-empty string, print 0 instead.

Sample Input 1

5
ababa

Sample Output 1

2

The strings satisfying the conditions are: a, b, ab, and ba. The maximum length among them is 2, which is the answer.
Note that aba occurs twice in S as contiguous substrings, but there is no pair of integers l_1 and l_2 mentioned in the statement such that l_1 + len \leq l_2.

Sample Input 2

2
xy

Sample Output 2

0

No non-empty string satisfies the conditions.

Sample Input 3

13
strangeorange

Sample Output 3

5

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using static AtCoderProject.Utility;
using BigInteger = System.Numerics.BigInteger;
using BitArray = System.Collections.BitArray;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using TextReader = System.IO.TextReader;

namespace AtCoderProject
{
    public class Program
    {
        public object Calc()
        {
            var N = consoleReader.Int;
            s = consoleReader.String;
            var subs = Enumerable.Range(0, N + 1).Select(i => s.Substring(i)).ToArray();
            var max = 0;
            for (int i = 0; i < s.Length; i++)
                for (int j = i; j < s.Length; j++)
                {
                    var len = j - i + 1;
                    //if (subs[j + 1].Length < len) break;
                    var target = s.Substring(i, len);
                    if (subs[j + 1].Contains(target))
                    {
                        max = Math.Max(max, len);
                    }
                }

            return max;
        }
        string s;

        #region いつもの
        private readonly ConsoleReader consoleReader;
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc()); static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
    }

    public class ConsoleReader
    {
        private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries);
        private string[] line = Array.Empty<string>();
        private int linePosition;
        private TextReader textReader;
        public ConsoleReader(TextReader tr) { textReader = tr; }
        public int Int => int.Parse(String);
        public long Long => long.Parse(String);
        public double Double => double.Parse(String);
        public string String
        {
            get
            {
                if (linePosition >= line.Length)
                {
                    linePosition = 0;
                    line = ReadLineSplit();
                }
                return line[linePosition++];
            }
        }
        public class SplitLine
        {
            public SplitLine(ConsoleReader cr) { String = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); }
            public int[] Int => String.Select(x => int.Parse(x)).ToArray();
            public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray();
            public long[] Long => String.Select(x => long.Parse(x)).ToArray();
            public double[] Double => String.Select(x => double.Parse(x)).ToArray();
            public string[] String { get; }
        }
        public SplitLine Split => new SplitLine(this);
        public class RepeatReader : IEnumerable<ConsoleReader>
        {
            ConsoleReader cr; int count;
            public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; }
            public IEnumerator<ConsoleReader> GetEnumerator() => Enumerable.Repeat(cr, count).GetEnumerator();
            System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => GetEnumerator();

            public IEnumerable<string> String => this.Select(cr => cr.String);
            public IEnumerable<int> Int => this.Select(cr => cr.Int);
            public IEnumerable<int> Int0 => this.Select(cr => cr.Int - 1);
            public IEnumerable<long> Long => this.Select(cr => cr.Long);
            public IEnumerable<double> Double => this.Select(cr => cr.Double);
        }
        public RepeatReader Repeat(int count) => new RepeatReader(this, count);
    }
    public static class Utility
    {
        public static IComparer<T> ReverseComparer<T>() where T : IComparable<T>
            => Comparer<T>.Create((x, y) => y.CompareTo(x));
    }
    #endregion
}