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 (v5.18.2) (judge verdict: Time Limit Exceeded)

chomp($n = <>);
chomp($t = <>);
@s = ("", split(//, $t));

$max = int(length($t) / 2);

$flg = 0;
$r = 0;
while(1){
	last if(($max < 1) or ($flg == 1));
	for ($i = 1; $i + ($max - 1) + $max <= $n; $i++){
		$str = join("", @s[$i .. $i + $max - 1]);
		$a = ($t =~ s/$str/$str/g);
		if($a >= 2){
			$r = $max;
			$flg = 1;
			last;
		}
	}
	$max--;
}
print "$r\n";