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: Accepted)

def solve(arr)
  return 0 if arr.uniq.size == 1

  mode = arr.group_by{|e| e}.max_by{|_,v| v.size}.first
  return arr.count{|x| x != mode}
end

n = gets.to_i
v = gets.chomp.split(" ").map(&:to_i)
ve = v.select.with_index {|e,i| i%2==0}
vo = v.select.with_index {|e,i| i%2==1}

if v.uniq.size == 1
  puts n/2
  exit
end

ve_group = ve.group_by{|e| e}.sort_by{|_,v| v.size}
ve_mode = ve_group[-1].first

vo_group = vo.group_by{|e| e}.sort_by{|_,v| v.size}
vo_mode = vo_group[-1].first

if ve_mode == vo_mode
  if ve.uniq.size == 1
    count = vo.size - vo_group[-2][1].size + ve.size - ve_group[-1][1].size
  elsif vo.uniq.size == 1
    count = ve.size - ve_group[-2][1].size + vo.size - vo_group[-1][1].size
  else
    count = [vo.size - vo_group[-2][1].size + ve.size - ve_group[-1][1].size,
             ve.size - ve_group[-2][1].size + vo.size - vo_group[-1][1].size].min
  end
else
  count = ve.size - ve_group[-1][1].size + vo.size - vo_group[-1][1].size
end

puts count