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 Perl (5.26.1) (judge verdict: Time Limit Exceeded)

use strict;
use warnings;
package ZAlgorithm;
sub z_algorithm(@){
	my$n=@_;
	return()if$n==0;
	my@z=(0);
	my$j=0;
	for my$i(1..$n-1){
		$z[$i]=$j+$z[$j]<=$i?0:$j+$z[$j]-$i<$z[$i-$j]?$j+$z[$j]-$i:$z[$i-$j];
		$z[$i]++while$i+$z[$i]<$n&&$_[$z[$i]]eq$_[$i+$z[$i]];
		$j=$i if$j+$z[$j]<$i+$z[$i];
	}
	$z[0]=$n;
	return@z;
}
package main;
my$N=<>;
my$s=<>;
chomp$s;
my@s=split"",$s;
my$ans=0;
for(0..$N-1){
	my@z=ZAlgorithm::z_algorithm(@s);
	for(0..$#z){
		my$l=$z[$_];
		$ans=$l if$l<=$_&&$ans<$l;
	}
	shift@s;
}
print$ans,$/;