Problem:
Score : 300 points

Problem Statement

A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:

For each i = 1,2,..., n-2, a_i = a_{i+2}.

Exactly two different numbers appear in the sequence.

You are given a sequence v_1,v_2,...,v_n whose length is even.
We would like to make this sequence /\/\/\/ by replacing some of its elements.
Find the minimum number of elements that needs to be replaced.

Constraints

2 \leq n \leq 10^5

n is even.

1 \leq v_i \leq 10^5

v_i is an integer.

Input

Input is given from Standard Input in the following format:

n
v_1 v_2 ... v_n

Output

Print the minimum number of elements that needs to be replaced.

Sample Input 1

4
3 1 3 2

Sample Output 1

1

The sequence 3,1,3,2 is not /\/\/\/, but we can make it /\/\/\/ by replacing one of its elements: for example, replace the fourth element to make it 3,1,3,1.

Sample Input 2

6
105 119 105 119 105 119

Sample Output 2

0

The sequence 105,119,105,119,105,119 is /\/\/\/.

Sample Input 3

4
1 1 1 1

Sample Output 3

2

The elements of the sequence 1,1,1,1 are all the same, so it is not /\/\/\/.

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Applicative
import Control.Arrow ((&&&))
import Data.ByteString.Char8 (ByteString)
import qualified Data.ByteString.Char8 as B
import Data.List
import Data.Char (isSpace)

main :: IO ()
main = solve <$> (flip div 2 <$> readLn) <*> f >>= print
  where
    f = readil B.readInt <$> B.getLine

solve :: Int -> [Int] -> Int
solve n vs = min (h ds us) (h us ds)
  where
    f (as, bs) [] = (as, bs)
    f (as, bs) (x:y:ys) = f (x:as, y:bs) ys
    (as, bs) = f ([], []) vs
    g = sortBy (flip compare) . map (length &&& head) . group . sort
    (ds, us) = (g as, g bs)
    h xs ys = n - (fst . head) xs + case filter (\(_,s) -> s /= ((snd . head) xs)) ys of
                                     [] -> n
                                     ((m,_):_) -> n - m

readil :: Integral a =>  (ByteString -> Maybe (a, ByteString)) -> ByteString -> [a]
readil f = unfoldr g
  where
    g s = do
      (n, s') <- f s
      return (n, B.dropWhile isSpace s')