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)

n = gets.to_i
vs = gets.chomp.split.map(&:to_i)
cnt = 0
even = Hash.new(0)
odd = Hash.new(0)
vs.each_with_index do |v,i|
	i += 1
	if i.even?
		even[v] += 1
	else
		odd[v] += 1
	end
end

even = even.sort_by(&:last)
odd = odd.sort_by(&:last)
if even[-1][0] == odd[-1][0]
	if odd.size == 1 && even.size == 1
		cnt += n/2
	elsif odd.size == 1
		cnt += n/2 - even[-2][1]
	elsif even.size == 1
		cnt += n/2 + n%2 - odd[-2][1]
	else
		if even[-1][1] > odd[-1][1]
			cnt += n - even[-1][1] - odd[-2][1]
		else
			cnt += n - even[-2][1] - odd[-1][1]
		end
	end
else
	cnt += n - even[-1][1] - odd[-1][1]
end

puts cnt