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)

#!/usr/bin/env ruby

require 'set'

class Hash
  def push(key, value)
    self[key] = [] if self[key] == nil
    self[key].push(value)
  end
end

class Array
  def lower_bound(value)
    left = -1;
    right = self.length;
    while left + 1 < right
      mid = left + (right - left) / 2;
      if self[mid] >= value
        right = mid
      else
        left = mid
      end
    end
    right
  end

  def unique
    res = [self.first]
    each_cons(2) do |a, b|
      if a != b
        res.push(b)
      end
    end
    res
  end
end

def get_ints
  gets.chomp.split.map(&:to_i)
end

def get_ints_minus_one
  get_ints.map { |x| x - 1 }
end

def get_int
  gets.chomp.to_i
end

N = get_int
V = get_ints

odds = V.filter.with_index { |v, i| i % 2 == 1 }
evens = V.filter.with_index { |v, i| i % 2 == 0 }

ans = 0

odds_hash = Hash.new { |h, k| h[k] = 0 }

odds.each do |n|
  odds_hash[n] += 1
end

odds_sorted_hash = odds_hash.sort { |a, b| a[1] <=> b[1] }

events_hash = Hash.new { |h, k| h[k] = 0 }

evens.each do |n|
  events_hash[n] += 1
end

evens_sorted_hash = events_hash.sort { |a, b| a[1] <=> b[1] }

odd_ans = odds_sorted_hash.pop
even_ans = evens_sorted_hash.pop

if odd_ans[0] == even_ans[0]
  o = odds_sorted_hash.pop
  e = evens_sorted_hash.pop

  if o.nil?
    even_ans = [0, 0]
  elsif o[1] > e[1]
    odd_ans = o
  else
    even_ans = e
  end
end

puts odds.length - odd_ans[1] + evens.length - even_ans[1]