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Contest: Task: Related: TaskD TaskF

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

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

No non-empty string satisfies the conditions.

Sample Input 3

13
strangeorange