Problem:
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

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

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

{-# LANGUAGE BangPatterns, MultiWayIf #-}

import Control.Applicative ((<$>))
import qualified Data.Vector.Unboxed as VU
import qualified Data.ByteString.Char8 as BS


main :: IO ()
main = do
  n <- read <$> getLine
  s <- VU.unfoldrN n BS.uncons <$> BS.getLine
  print $ VU.maximum
    $ VU.map (\ !gap -> max gap $ test s $ VU.drop gap s)
    $ VU.tail $ VU.generate n id

test :: VU.Vector Char -> VU.Vector Char -> Int
test v1 v2
 = VU.maximum
   $ VU.scanl' (\ !l !b -> if b then l+1 else 0) (0::Int)
   $ VU.zipWith (==) v1 v2