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)

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

evens = vs.each_with_index.to_a.select { |_v, i| i.even? }.map(&:first)
odds = vs.each_with_index.to_a.select { |_v, i| i.odd? }.map(&:first)
e_freq = evens.group_by(&:itself).map { |k, v| [v.length, k] }.sort.reverse
o_freq = odds.group_by(&:itself).map { |k, v| [v.length, k] }.sort.reverse
e_freq.push([0, 0])
o_freq.push([0, 0])
x = [[e_freq[0], o_freq[0]], [e_freq[1], o_freq[0]], [e_freq[0], o_freq[1]]].compact.map do |e, o|
  [e[0] + o[0], e[1] != o[1]]
end.select { |x| x[1] }.sort.reverse.first.first

puts vs.count - x