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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace FreeWorks
{
    class Program
    {

        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            string s = Console.ReadLine();
            int len = s.Length;

            int[,] dp = new int[len, len];
            
            for (int j = 0; j < len - 1; j++)
            {
                if (s[len - 1] ==s[j])
                {
                    dp[len - 1, j] = 1;
                }
            }

            for (int i = len - 2; i >= 0; i--)
            {
                for (int j = 0; j < i; j++)
                {
                    if (s[i] == s[j]) dp[i, j] = dp[i + 1, j + 1] + 1;
                }
            }

            int max = 0;
            for (int i = 0; i < len; i++)
            {
                for (int j = 0; j < i; j++)
                {
                    max = Math.Max(max, Math.Min(dp[i, j], i - j));
                }
            }

            Console.WriteLine(max);
    
        }   
    }
}