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 =
    List.sort (fun (_, x) (_, y) -> compare y x) @@
    IntMap.bindings @@
    Array.fold_left (fun m v ->
      IntMap.add v (1 + try IntMap.find v m with Not_found -> 0) m) IntMap.empty @@
    Array.init (n / 2) @@ fun i -> vs.(2 * i + 1) in
  let evens =
    List.sort (fun (_, x) (_, y) -> compare y x) @@
    IntMap.bindings @@
    Array.fold_left (fun m v ->
      IntMap.add v (1 + try IntMap.find v m with Not_found -> 0) m) IntMap.empty @@
    Array.init (n / 2) @@ fun i -> vs.(2 * i) in
  let v, m, m' =
    match odds with
    | [(v, n)] -> v, n, 0
    | (v, n) :: (_, n') :: _ -> v, n, n' in
  let v_, m_, m_' =
    match evens with
    | [(v, n)] -> v, n, 0
    | (v, n) :: (_, n') :: _ -> v, n, n' in
  Printf.printf "%d\n" @@ n - (if v = v_ then max (m + m_') (m' + m_) else m + m_)