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.

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.

Constraints

• $2 \leq N \leq 5 \times 10^3$
• |S| = N
• S consists of lowercase English letters.

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

见题面 Input 部分

见题面 Output 部分