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: Wrong Answer)

namespace ABC141.E
{
    using System;
    using System.Collections.Generic;
    using System.Linq;
    using System.Text;
    using System.Text.RegularExpressions;
    using static System.Console;



    public class Program
    {

        public static void Main(string[] args)
        {
            ReadLine();
            WriteLine(ReadLine());

        }

        public static int Solve(string s)
        {
            for (int len = s.Length / 2; len > 0; len--)
            {
                for (int i = 0; i < s.Length - 2 * len; i++)
                {
                    if (Regex.IsMatch(s.Substring(i + len), s.Substring(i, len)))
                        return len;
                }
            }
            return 0;
        }
    }
}