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.chomp.split(' ').map(&:to_i)[0]
v = gets.chomp.split(' ').map(&:to_i)

count_odd = Hash.new(0)
count_even = Hash.new(0)
v.each_with_index do |x, i|
  count_odd[x] += 1 if i.even?
  count_even[x] += 1 if i.odd?
end

odd_max = count_odd.max{ |x, y| x[1] <=> y[1] } 
even_max = count_even.max{ |x, y| x[1] <=> y[1] } 

if odd_max[1] >= even_max[1]
  count_even.delete(odd_max[0])
  even_max = count_even.empty? ? [0, 0] : count_even.max{ |x, y| x[1] <=> y[1] } 
else
  count_odd.delete(even_max[0])
  odd_max = count_odd.empty? ? [0, 0] : count_odd.max{ |x, y| x[1] <=> y[1] } 
end
puts n - odd_max[1] - even_max[1]