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: Wrong Answer)

n = gets.to_i
vs = gets.split.map(&:to_i)
odds = vs.select.with_index { |v, i| i.odd? }.group_by(&:itself)
evens = vs.select.with_index { |v, i| i.even? }.group_by(&:itself)

ob = [0, 0]
osb = [0, 0]
odds.each do |v, arr|
  if arr.count > ob[1]
    osb = ob
    ob = [v, arr.count]
  end
end

eb = [0, 0]
esb = [0, 0]
evens.each do |v, arr|
  if arr.count > eb[1]
    esb = eb
    eb = [v, arr.count]
  end
end

if ob[0] != eb[0]
  puts n - ob[1] - eb[1]
elsif osb[0] != 0 && esb[0] != 0
  if ob[1] - osb[1] > eb[1] - esb[1]
    puts n - ob[1] - esb[1]
  else
    puts n - osb[1] - eb[1]
  end
else
  puts 10001
  if osb[0] == 0 && esb[0] == 0
    puts n/2
  else
    puts n/2 - (osb[0] == 0 ? esb[1] : osb[1])
  end
end