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: Time Limit Exceeded)

num = gets

line = gets.split(' ')

g_kisuu_arr = Array.new
g_gusuu_arr = Array.new

line.each_with_index do |value, index|
	if index.odd? then
		g_gusuu_arr.push(value)
	else
		g_kisuu_arr.push(value)
	end
end

g_kisuu_uniq = g_kisuu_arr.uniq
kisuu_hash = Hash.new()
g_kisuu_uniq.each do |ref_atai| 
 cnt = 0
 g_kisuu_arr.each do |ch_atai|
 	cnt = cnt + 1 if ref_atai == ch_atai
 end
 kisuu_hash[ref_atai] = cnt
end
sort_kisuu_hash = kisuu_hash.sort_by { |key, value| value }.reverse

g_gusuu_uniq = g_gusuu_arr.uniq
gusuu_hash = Hash.new()
g_gusuu_uniq.each do |ref_atai| 
 cnt = 0
 g_gusuu_arr.each do |ch_atai|
  cnt = cnt + 1 if ref_atai == ch_atai
 end
  gusuu_hash[ref_atai] = cnt
end

sort_gusuu_hash = gusuu_hash.sort_by { |key, value| value }.reverse

change_count = 0

if sort_gusuu_hash[0].first != sort_kisuu_hash[0].first then
	chanage_count = num.to_i - (sort_gusuu_hash[0].last.to_i + sort_kisuu_hash[0].last.to_i)
else
	if sort_gusuu_hash.length > 1 and sort_kisuu_hash.length > 1 then
		if sort_gusuu_hash[1].last > sort_kisuu_hash[1].last then
			chanage_count = num.to_i - (sort_gusuu_hash[1].last.to_i + sort_kisuu_hash[1].last.to_i)
		else
			chanage_count = num.to_i - (sort_gusuu_hash[0].last.to_i + sort_kisuu_hash[1].last.to_i)
		end

	elsif sort_gusuu_hash.length > 1 and sort_kisuu_hash.length == 1 then
		chanage_count = num.to_i - (sort_gusuu_hash[1].last.to_i + sort_kisuu_hash[0].last.to_i)
	elsif sort_gusuu_hash.length == 1 and sort_kisuu_hash.length > 1 then
		chanage_count = num.to_i - (sort_kisuu_hash[1].last.to_i + sort_gusuu_hash[0].last.to_i)
	else
		chanage_count = num.to_i / 2
	end	  	  
end

puts chanage_count