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)

n = gets.chomp.to_i
ary = gets.chomp.split.map(&:to_i)

ary1_hash = Hash.new(0)
0.step(n - 1, 2) do |i|
  ary1_hash[ary[i]] += 1
end
ary1 = ary1_hash.sort_by(&:last).reverse

ary2_hash = Hash.new(0)
1.step(n - 1, 2) do |i|
  ary2_hash[ary[i]] += 1
end
ary2 = ary2_hash.sort_by(&:last).reverse

ans = if ary1[0][0] != ary2[0][0]
  ary1[1..-1].inject(0){|sum, attr| sum + attr.last}.to_i +
    ary2[1..-1].inject(0){|sum, attr| sum + attr.last}.to_i
else
  ary1_sec = ary1[1][1] rescue 0
  ary2_sec = ary2[1][1] rescue 0
  if ary1_sec >= ary2_sec
    ary1[0..-1].inject(0){|sum, attr| sum + attr.last} - ary1_sec +
      ary2[1..-1].inject(0){|sum, attr| sum + attr.last}.to_i
  else
    ary1[1..-1].inject(0){|sum, attr| sum + attr.last}.to_i +
      ary2[0..-1].inject(0){|sum, attr| sum + attr.last} - ary2_sec
  end
end
puts ans