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 Data.List

getter::IO ([Int],[Int])
getter = do
   dat<-(return.(map read).words)=<<getLine
   return (eat ([],[]) dat)
      where eat (x,y) []        = (x,y)
            eat (x,y) (z:w:rest)= eat (z:x,w:y) rest

solver::Int->[Int]->[Int]->Int
solver n xs ys = let (x_head:x_rest) = ((sortBy (\ x-> \ y ->compare (length y) (length x))).group.sort) xs in
                 let (y_head:y_rest) = ((sortBy (\ x-> \ y ->compare (length y) (length x))).group.sort) ys in
                 if head x_head /= head y_head
                   then n - ((length x_head)+(length y_head))
                   else let x_loss = (length x_head) - ((length.head) x_rest) in
                        let y_loss = (length y_head) - ((length.head) y_rest) in
                        case (x_rest,y_rest) of
                         ([],[])    -> div n 2
                         ([],_:_)   -> n - ((length x_head)+(length y_head)-y_loss)
                         (_:_,[])   -> n - ((length x_head)+(length y_head)-x_loss)
                         otherwise  -> n - ((length x_head)+(length y_head)-(min x_loss y_loss))

main::IO()
main=do
  n<-(return.read)=<<getLine
  (x,y)<-getter
  print (solver n x y)