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)

{-# LANGUAGE BangPatterns #-}

import Data.Bits
import Data.List
import Data.IntMap.Strict (IntMap)
import qualified Data.IntMap.Strict as IntMap
import qualified Data.ByteString.Char8 as B

freqMapWithParity :: [Int] -> (IntMap Int, IntMap Int)
freqMapWithParity
  = foldl' (\(!now,!prev) k -> (prev, IntMap.insertWith (+) k 1 now))
    $ (IntMap.empty, IntMap.empty)

obtainFreq :: IntMap Int -> (Int, Int, Int, Int)
obtainFreq = IntMap.foldlWithKey' loop (minBound, 0, minBound, 0)
  where
    loop (!v1, !n1, !v2, !n2) !v !n
      | n >= n1   = (v,  n,  v1, n1)
      | n >= n2   = (v1, n1, v,  n)
      | otherwise = (v1, n1, v2, n2)

chooseBest ::
  (Int, Int, Int, Int) -> (Int, Int, Int, Int) -> ((Int, Int), (Int, Int))
chooseBest (!lv1, !ln1, !lv2, !ln2) (!rv1, !rn1, !rv2, !rn2)
  | lv1 /= rv1 = ((lv1, ln1), (rv1, rn1))
  | ln1 >= rn1 = ((lv1, ln1), (rv2, rn2))
  | otherwise  = ((lv2, ln2), (rv1, rn1))

query :: Int -> [Int] -> Int
query n vs = n - ln - rn
  where
    (l,r) = freqMapWithParity vs
    lf = obtainFreq l
    rf = obtainFreq r
    ((_, ln), (_, rn)) = chooseBest lf rf

main :: IO ()
main = do
  n <- read <$> getLine
  vs <- unfoldr (B.readInt . B.dropWhile (== ' ')) <$> B.getLine
  putStrLn $ show $ query n vs