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: Time Limit Exceeded)

{-# LANGUAGE FlexibleContexts #-}
import Control.Monad
import Control.Monad.State
import Control.Monad.Reader
import Control.Arrow
-- import Control.Comonad
import Data.Maybe
import Data.List
import Data.Bool
import Data.Fixed
import Data.Tuple
import Data.Ratio
import qualified Data.Map.Strict as M
import qualified Data.Array.IO as IA
import qualified Data.Vector as V
 
getI = read <$> getLine :: IO Int
getIs = map read . words <$> getLine :: IO [Int]
getD = read <$> getLine :: IO Double
getDs = map read . words <$> getLine :: IO [Double]
getInt = read <$> getLine :: IO Integer
getInts = map read . words <$> getLine :: IO [Integer]
 
type Row = Integer
type Col = Integer
type PointI = (Integer, Integer)
type Point = (Int, Int)
 
mmm = 1000000007
fact n
    | n < 1 = 1
    | True = foldr1 (*) [1..n]
fi = fromInteger
fig = fromIntegral
rf = realToFrac
 
(.<.) f g -- combination
    | f < g = 0 
    | g < 1 || f < 1 = 1
    | True = foldr1 (*) (take g [f,f-1..]) `div` fact g
(.>.) f g --combination with repetition
    | g < 1 || f < 1 = 1
    | True = fact (f + g - 1) `div` (fact (f - 1) * fact g)
comb = (.<.)
combWp = (.>.)
 
unique a = unique_ (reverse . sort $ a) [] Nothing
    where
        unique_ [] arr _ = arr
        unique_ (x:xs) arr n
            | n == Just x = unique_ xs arr n
            | otherwise = unique_ xs (x:arr) $ Just x
 
zeroume keta num
    | (length . show $ num) > keta = show num
    | otherwise = do 
        let zeros = take keta $ repeat '0'
        reverse . take keta $ (reverse . show $ num) ++ zeros
 
i2b num
    | num < 2 = show num
    | otherwise = i2b_ num []
        where
            i2b_ num str
                | num == 0 = str
                | num == 1 = '1':str
                | otherwise = do
                    let next = num `div` 2
                    let this = if odd num then '1' else '0'
                    i2b_ next (this:str)
 
mapIncr = mapPlus 1
mapPlus n Nothing = Just n
mapPlus n a = (+) n <$> a
 
countIf f = length . filter f
 
-- 
--
--

getMin [] _ = Nothing
getMin _ [] = Nothing
getMin ee@(e:es) oo@(o:os) 
  | e == o = do
    let a = getMin ee os
    let b = getMin es oo
    if all isNothing [a, b] then Nothing 
    else if all isJust [a,b] then minimum <$> sequence [a, b]
    else head $ filter isJust [a, b]
  | True = Just . foldr1 (+) $ map snd [e, o]
main = do
  l <- getI
  inps <- getIs
  let len = div l 2
  let [evens, odds] = map (map (\y -> inps !! y)) [[0,2..l-2], [1,3..l - 1]]
  let em = sortOn snd . M.toList $ foldr (\x -> M.alter (mapInit len) x) M.empty evens
  let om = sortOn snd . M.toList $ foldr (\x -> M.alter (mapInit len) x) M.empty odds
  putStrLn . show . maybe len id $ getMin em om
  where
    mapInit len Nothing = Just $ len - 1 
    mapInit len (Just a) = Just $ a - 1