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.