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 PHP (7.4.4) (judge verdict: Accepted)

<?php
list($n) = ints();
list($s) = strs();
$max = 0;
for ($i = 0; $i < $n; ++$i) {
    $t = substr($s, $i);
    $lcp = zAlgo($t);
    for ($j = 0; $j < $n - $i; ++$j)
        $max = max($max, min($j, $lcp[$j]));
}
echo $max;
// sとs[i:]が、先頭から最大で何文字まで一致しているか格納した配列を返す
// O(N)
function zAlgo(string $s): array
{
    $n = strlen($s);
    $res = array_fill(0, $n, 0);
    $res[0] = $n;
    $i = 1;
    $len = 0;
    while ($i < $n) {
        while ($i + $len < $n && $s[$len] === $s[$i + $len]) ++$len;
        $res[$i] = $len;
        if ($len === 0) {
            ++$i;
            continue;
        }
        $k = 1;
        while ($i + $k < $n && $k + $res[$k] < $len) {
            $res[$i + $k] = $res[$k];
            ++$k;
        }
        $i += $k;
        $len -= $k;
    }
    return $res;
}
function strs()
{
    return explode(' ', trim(fgets(STDIN)));
}
function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}