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