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 (2.7.1) (judge verdict: Accepted)

n = gets.to_i
v = gets.chomp.split.map(&:to_i)
odd = Hash.new(0)
even = Hash.new(0)

(n / 2).times do |i|
  even[v[2 * i]] += 1
  odd[v[2 * i + 1]] += 1
end

ep = even.to_a.sort_by! {|_, v| v }
op = odd.to_a.sort_by! {|_, v| v }

ev1 = ep[-1][1]
ov1 = op[-1][1]
ek1 = ep[-1][0]
ok1 = op[-1][0]

if ek1 != ok1
  puts n - ov1 - ev1
else
  if ev1 + ov1 == n
    puts n / 2
  elsif ev1 == n / 2
    puts n / 2 - op[-2][1]
  elsif ov1 == n / 2
    puts n / 2 - ep[-2][1]
  else
    puts [n - ev1 - op[-2][1], n - ov1 - ep[-2][1]].min
  end
end