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.Lazy.Char8 as B
import Data.Maybe
import qualified Data.IntMap as IM
import Data.List

solve n vs = n - (getUsable $ map feat $ divide vs)

divide [] = [[], []]
divide [e] = [[e], []]
divide (e:o:xs) = [e:es, o:os]
  where [es, os] = divide xs

feat xs = case sortOn (negate . snd) $ IM.toList $ count xs of
  [(k, n)]             -> (k, n, 0)
  (k, n) : (_, n') : _ -> (k, n, n')

count = foldr (flip (IM.insertWith (+)) 1) IM.empty

getUsable [(kA, fA, sA), (kB, fB, sB)]
  | kA /= kB  = fA + fB
  | otherwise = max (fA + sB) (fB + sA)

bsReadInts = map (fst . fromJust . B.readInt) . B.words

main = do
  n:vs <- bsReadInts <$> B.getContents
  putStrLn $ show $ solve n vs