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 Data.Traversable
import Data.List

main = do
  t <- getLine
  ps <- map read . words <$> getLine
  putStrLn . show . solve $ ps


solve :: [Int] -> Int
solve [] = 0
solve (x:[]) = 0
solve (x:y:[]) = 0
solve ps =
  let l1 = sort $ everyOtherElem ps
      l2 = sort $ everyOtherElem (tail ps)
      (v1,mcnt1, scnt1) = countMax (head l1) 1 0 0 (tail l1)
      (v2,mcnt2, scnt2) = countMax (head l2) 1 0 0 (tail l2)
  in if v1 /= v2 then (length l1) - mcnt1 + (length l2) - mcnt2
    else if mcnt1 + scnt2 > mcnt2 + scnt1 then (length ps) - mcnt1 - scnt2 else (length ps) - mcnt2 - scnt1

countMax x cnt cntmax cnt2nd [] = (x, max cnt cntmax, cnt2nd)
countMax x cnt cntmax cnt2nd (s:sorted) =
  if x /= s then countMax s 1 (max cnt cntmax) (max cnt2nd (max cnt cntmax)) sorted else countMax x (cnt+1) cntmax cnt2nd sorted

everyOtherElem [] = []
everyOtherElem (x:[]) = [x]
everyOtherElem (x:y:xs) = x : everyOtherElem xs