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 OCaml (4.02.3) (judge verdict: Accepted)

module IntMap = Map.Make (struct
  type t = int
  let compare = compare
end)

let () = Scanf.scanf "%d\n" @@ fun n ->
  let vs = Array.init n @@ fun _ -> Scanf.scanf "%d " @@ fun v -> v in
  let (odds, evens) =
    Array.fold_left (fun (odds, evens) v ->
      (evens, IntMap.add v (1 + try IntMap.find v odds with Not_found -> 0) odds))
    (IntMap.empty, IntMap.empty) vs in
  Printf.printf "%d\n" @@ ( - ) n @@
  match
    List.sort (fun (_, x) (_, y) -> compare y x) @@
    IntMap.bindings odds,
    List.sort (fun (_, x) (_, y) -> compare y x) @@
    IntMap.bindings evens
  with
  | [(u, l)], [(v, m)] ->
      if u = v then max l m else l + m
  | (u, l) :: (_, m) :: _, [(v, n)] -> 
      if u = v then max l (m + n) else l + n
  | [(u, l)], (v, m) :: (_, n) :: _ -> 
      if u = v then max (l + n) m else l + m
  | (u, l) :: (_, m) :: _, (v, n) :: (_, o) :: _ ->
      if u = v then max (l + o) (m + n) else l + n