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
v = gets.chomp.split(" ")
a_map = {}
b_map = {}
v.each_slice(2) do |pair|
  a_map[pair[0]] ||= 0
  b_map[pair[1]] ||= 0
  a_map[pair[0]] += 1 
  b_map[pair[1]] += 1 
end

a_max = a_map.max{|a,b| a[1] <=> b[1]}
b_max = b_map.max{|a,b| a[1] <=> b[1]}
if a_max[0] == b_max[0]
  b_map.delete b_max[0]
  b_second = b_map.max{|a,b| a[1] <=> b[1]} || [nil, 0]
  a_map.delete a_max[0]
  a_second = a_map.max{|a,b| a[1] <=> b[1]} || [nil, 0]

  if a_max[1] + b_second[1] >= b_max[1] + a_second[1]
    puts n - a_max[1] - b_second[1]
  else
    puts n - b_max[1] - a_second[1]
  end
else
  puts n - a_max[1] - b_max[1]
end