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.strip.to_i
even = Hash.new(0)
odd = Hash.new(0)
all = Hash.new(0)

A = gets.strip.split.map(&:to_i)

A.unshift 0

(1..N).each_with_index do |i|
  if i.even?
    even[A[i]] += 1
  else
    odd[A[i]] += 1
  end
  all[A[i]] += 1
end


if all.size > 1
  if even.size.eql?(2) && odd.size.eql?(1)
    o1 = odd.keys.first
    puts even.select { |k, v| k != o1 }.values.first
  elsif even.size.eql?(1) && odd.size.eql?(2)
    e1 = even.keys.first
    puts odd.select { |k, v| k != e1 }.values.first
  elsif even.size.eql?(2) && odd.size.eql?(2)
    e1, e2 = even.sort.keys
    o1, o2 = odd.sort.keys    
    puts (e1 + o2) < (e2 + o1) ? e1 + o2 : e2 + o1
  else
    puts 0
  end 
else
  puts all.values.first / 2
end