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-----
5
ababa

-----Sample Output-----
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 $l_1 + len \leq l_2$.

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