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 Control.Monad
import Data.List
import Data.Ord
import qualified Data.ByteString.Char8 as B
import qualified Data.IntMap as M

mf n Nothing = Just n
mf n (Just a) = Just (n+a)

main = do
    n<-readLn::IO Int
    vs<-unfoldr (B.readInt.B.dropWhile(==' '))<$>B.getLine::IO[Int]
    print $ sol vs
---
sol vs = minimum $ map (\n-> on n + enn n ) $ M.keys mo
    where
        os = map fst $ filter (odd.snd) $ zip vs [1..]
        es = map fst $ filter (even.snd) $ zip vs [1..]
        mo = foldl' (flip (M.alter (mf 1))) M.empty os
        me = foldl' (flip (M.alter (mf 1))) M.empty es
        se = sortBy (flip $ comparing snd) $ M.toList me
        on n = (length os) - (mo M.! n)
        enn n = case dropWhile ((==n).fst) se of
            [] -> length es
            ((_,x):_) -> length es - x