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 qualified Data.ByteString.Char8 as BC
import Data.Maybe
import qualified Data.IntMap as IM
import Data.List
import Data.Ord

type Map = IM.IntMap Int

readIntsLine :: IO [Int]
readIntsLine = map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine

countUp :: Int -> Int -> Map -> Map
countUp = IM.insertWithKey f
  where f _ new old = old + new

count :: Int -> [Int] -> Map -> Map -> (Map, Map)
count c [] mo me = (mo, me)
count c (v:vs) mo me = count (c + 1) vs nextmo nextme
  where nextmo = if odd c then countUp v 1 mo else mo
        nextme = if even c then countUp v 1 me else me

main :: IO ()
main = do
  getLine
  vs <- readIntsLine
  let (mo, me) = count 1 vs IM.empty IM.empty
  let rsort = sortOn (Down . fst) . IM.toList
  let smo = rsort mo
  let sme = rsort me
  let o1 = head smo
  let e1 = head sme
  let o2 = if length smo > 1 then smo !! 1 else (fst o1, 0)
  let e2 = if length sme > 1 then sme !! 1 else (fst e1, 0)
  print $ if fst o1 /= fst e1
          then length vs - snd o1 - snd e1
          else length vs - max (snd o1 + snd e2) (snd o2 + snd e1)