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)

n = gets.to_i
vs = gets.split.map(&:to_i)
even_table = Hash.new { 0 }
odd_table = Hash.new { 0 }
vs.each.with_index do |v, i|
  if i.even?
    even_table[v] += 1
  else
    odd_table[v] += 1
  end
end
ans = 1 << 60
sorted_even = even_table.sort_by { |_, v| -v }
sorted_odd = odd_table.sort_by { |_, v| -v }
[sorted_even.size, 2].min.times do |i|
  [sorted_odd.size, 2].min.times do |j|
    if sorted_even[i][0] == sorted_odd[j][0]
      count = n - [sorted_even[i][1], sorted_odd[j][1]].max
      ans = count if count < ans
    else
      count = n - (sorted_even[i][1] + sorted_odd[j][1])
      ans = count if count < ans
    end
  end
end
puts ans