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 qualified Data.ByteString.Char8 as BS
import Data.Maybe (fromJust)
import Data.List
import Data.Function

alternateSplit :: [a] -> ([a],[a])
alternateSplit = foldr (\x (l,r)-> (x:r,l)) ([],[])

solve :: [Int] -> Int
solve v
  | allSame v = length v `div` 2 
  | otherwise =
    let (l,r) = alternateSplit v
        ml1 = mode l
        ml2 = mode . filter (/=ml1) $ l
        mr1 = mode r
        mr2 = mode . filter (/=mr1) $ r
     in if ml1 /= mr1
           then cnt ml1 l + cnt mr1 r
           else min (cnt ml1 l + cnt mr2 r) (cnt ml2 l + cnt mr1 r)
  where
    allSame v = all (== head v) v
    mode = head . maximumBy (compare `on` length) . group . sort
    cnt c = length . filter (/=c)

main :: IO ()
main = do
    n <- readLn :: IO Int
    v <- map (fst . fromJust . BS.readInt)
        . BS.words <$> BS.getLine :: IO [Int]
    print $ solve v