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)

INF = 10 ** 6
n = gets.chomp.to_i
nums = gets.chomp.split(" ").map(&:to_i)
odds = Array.new(10 ** 5 + 1, 0)
evens = Array.new(10 ** 5 + 1, 0)
nums.each_with_index do |num, index|
  if index.even?
    odds[num] += 1
  else
    evens[num] += 1
  end
end

odds_candidates = []
evens_candidates = []

2.times do
  odds_max = odds.index(odds.max)
  if odds[odds_max] == -1
    break
  else
    odds_candidates << [odds_max, n / 2 - odds[odds_max]]
    odds[odds_max] = -1
  end

  evens_max = evens.index(evens.max)
  if evens[evens_max] == -1
    break
  else
    evens_candidates << [evens_max, n / 2 - evens[evens_max]]
    evens[evens_max] = -1
  end
end

odds_candidates << [INF, n / 2]
evens_candidates << [INF, n / 2]

mins = []

odds_candidates.each do |odds_candidate|
  evens_candidates.each do |evens_candidate|
    if odds_candidate[0] == evens_candidate[0]
      next
    else
      mins << odds_candidate[1] + evens_candidate[1]
    end
  end
end

puts mins.min