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)

#!/usr/bin/perl
my ($n) = map { $_ - 0 } split(/\s+/,<STDIN>);
my $s = <STDIN>;

my @tails = ();

for(my $i=0;$i<$n;$i++){
  $tails[$i] = substr($s,$i,length($s)-$i);
}

my @s = sort { $a cmp $b } @tails;

my @ss = ();
$#ss = $#s;

for(my $i=0;$i<=$#s-1;$i++){
  my $l = length($s[$i]);
  $l = length($s[$i+1]) if length($s[$i+1])<$l;
  my $cnt = 0;
  my $j = 0;
  while( $j<$l and substr($s[$i],$j,1) eq substr($s[$i+1],$j,1) ){
    $cnt++;
    $j++;
  }
  my $st1 = $n - length($s[$i]);
  my $st2 = $n - length($s[$i+1]);
  if( $cnt > abs($st1 - $st2) ){
    $cnt = abs($st1 - $st2);
  }
  $ss[$j] = $cnt;
}

my @sss = sort { $b <=> $a } @ss;
print "$sss[0]\n";