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.Map as Map -- Heap?

main = do
    n  <- read <$> getLine
    vs <- ((fmap read . words) <$> getLine) :: IO [Int]
    let lMap = Prelude.foldl createMap empty (oddLs vs)
    let rMap = Prelude.foldl createMap empty (evenLs vs)

    let lAns = Map.foldr max 0 lMap
    let rAns = Map.foldr max 0 rMap

    let lfMap = Map.filter (==lAns) lMap
    let rfMap = Map.filter (==rAns) rMap

    if keys lfMap == keys rfMap then do
        let lAns' = Map.foldr max 0 (Map.filter (/=lAns) lMap)
        let rAns' = Map.foldr max 0 (Map.filter (/=rAns) rMap)
        print $ min (n - lAns' - rAns) (n - lAns - rAns')
    else print (n - lAns - rAns)

createMap :: Map Int Int -> Int -> Map Int Int
createMap old n
    | member n old = insert n (old!n + 1) old
    | otherwise    = insert n 1 old

maxWithKey :: Int -> Int -> (Int,Int) -> (Int,Int)
maxWithKey k a (j,b) = (if a>b then k else j, max a b)

oddLs :: [a] -> [a]
oddLs []       = []
oddLs (x:[])   = [x]
oddLs (x:_:xs) = x:oddLs xs

evenLs :: [a] -> [a]
evenLs []      = []
evenLs (x:[])  = []
evenLs (_:y:ys)= y:evenLs ys