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: Wrong Answer)

def hahs_sort_desc(hash)
  hash.sort {|a,b| a[1]<=>b[1]}.reverse
end

def max_key(hash)
  hash = hahs_sort_desc(hash)
  hash[0][0]
end

def func(hash, exclude_key = nil)
  res = 0
  if exclude_key
    # 2つ目の計算
    keys = hash.keys
    max_key = max_key(hash)

    if max_key == exclude_key
      if keys.size == 1
        res = hash.first[1]
      else
        hash = hahs_sort_desc(hash)
        target_key = hash[1][0]
        hash.each{|k,v| res += v if k != target_key}
      end
    else
      if keys.size != 1
        hash = hahs_sort_desc(hash)
        hash[1..-1].each{|k,v| res += v}
      end
    end
  else
    if hash.keys.size != 1
      hash = hahs_sort_desc(hash)
      hash[1..-1].each{|k,v| res += v}
    end
  end
  res
end

_ = gets.to_i
a = []
b = []
x = Hash.new(0)
y = Hash.new(0)
gets.chomp.split.each_with_index do |s, i|
  s = s.to_i
  if i.even?
    a << s
    x[s] += 1
  else
    b << s
    y[s] += 1
  end
end

puts func(x) + func(y, max_key(x))