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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n = gets.chomp.to_i
v = gets.chomp.split.map(&:to_i)
max_cnt_num = v.uniq.map { |i| [i, v.count(i)] }.sort_by { |e| e[1] }.last.first
odds = []
evens = []
v.each_with_index do |e, i|
  if i.odd?
    odds << e
  else
    evens << e
  end
end
o = odds.count(max_cnt_num)
e = evens.count(max_cnt_num)
e_max_cnt_num = (evens - [max_cnt_num]).uniq.map { |i| [i, v.count(i)] }.sort_by { |e| e[1] }.last&.first
if o <= e
  o_max_cnt_num = (odds - [max_cnt_num]).uniq.map { |i| [i, v.count(i)] }.sort_by { |e| e[1] }.last&.first
  if o_max_cnt_num.nil?
    puts (odds.count + (evens.count - e))
  else
    puts (odds.count - odds.count(o_max_cnt_num)) + (evens.count - e)
  end
else
  if e_max_cnt_num.nil?
    puts (evens.count + (odds.count - e))
  else
    puts (evens.count - evens.count(e_max_cnt_num)) + (odds.count - o)
  end
end