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: Wrong Answer)

import Data.List

main = do
    n <- readLn :: IO Int
    v <- map read . words <$> getLine :: IO [Int]
    let odds  = indexFilter odd v
        evens = indexFilter even v
    print $ if evens == odds
               then length evens
               else diff evens + diff odds

indexFilter :: (Int -> Bool) -> [a] -> [a]
indexFilter f = indexFilter' f 1
    where
        indexFilter' _ _ [] = []
        indexFilter' f index (x:xs)
          | f index   = x : indexFilter' f (index+1) xs
          | otherwise = indexFilter' f (index+1) xs

diff :: (Eq a, Ord a) => [a] -> Int
diff = sum . init . sort . map length . group . sort