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)

def checkall(even, odd)
  input_ary = even + odd
  input_ary.uniq.length == 1
end
def ok?(ary)
  ary.uniq.length == 1
end
def getmode(ary, item)
  data = {}
  sorted = ary.sort()
  sorted.each do |val|
    unless data.include? val
      data[val] = 1
    else
      data[val] += 1
    end
  end
  max_count_value, max_count = data.sort {|(cur_key, cur_val), (nxt_key, nxt_val)|
    cur_val <=> nxt_val
  }.reverse[item-1]
  return [max_count_value, max_count]
end
def modify(ary, count, max_count)
  count += (ary.length - max_count)
  return count
end
n = gets.chomp!.to_i
ary = gets.chomp!.split(' ').map(&:to_i)
count = 0
even = ary.select.with_index{ |_, idx| idx % 2 == 0 }
odd = ary.select.with_index{ |_, idx| idx % 2 != 0 }
if checkall(even, odd)
  count = [even.length, odd.length].min
  puts count
else
  even_mode, even_mode_max_count = getmode(even, 1)
  odd_mode, odd_mode_max_count = getmode(odd, 1)
  # 最頻値が一致していれば書き換えると一致してしまうのでそれぞれの二番目の数を選ぶ。それぞれの二番目の頻度の値両方を取得し、値の大きい方の頻度値を更新する
  if even_mode == odd_mode
    second_even_mode, second_even_mode_max_count = getmode(even, 2)
    second_odd_mode, second_even_mode_max_count = getmode(odd, 2)
    if second_even_mode >= second_odd_mode
      even_mode = second_even_mode
      even_mode_max_count = second_even_mode_max_count
    else
      odd_mode = second_odd_mode
      even_mode_max_count = second_even_mode_max_count
    end
  end
  if ok?(even) && ok?(odd)
    puts count
  elsif ok?(even)
    count = modify(odd, count, odd_mode_max_count)
    puts count
  elsif ok?(odd)
    count = modify(even, count, even_mode_max_count)
    puts count
  else
    count += modify(odd, count, odd_mode_max_count)
    count = modify(even, count, even_mode_max_count)
    puts count
  end
end