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.to_i
v = gets.split.map(&:to_i)

l = v.length

x = Hash.new(0)
y = Hash.new(0)
v.each_with_index do |a, i|
  if i.even?
    x[a] += 1
  else
    y[a] += 1
  end
end

if x.length == 1 && y.length == 1
  if x == y
    puts x.values[0]
  else
    puts 0
  end
  exit
end

x_sort = x.sort{ |a, b| a[1] <=> b[1] }
y_sort = y.sort{ |a, b| a[1] <=> b[1] }

if x_sort.length == 1
  if x_sort[0][0] == y_sort[-1][0]
    puts l / 2 - y_sort[-2][1]
  else
    puts l / 2 - y_sort[-1][1]
  end
elsif y_sort.length == 1
  if y_sort[0][0] == x_sort[-1][0]
    puts l / 2 - x_sort[-2][1]
  else
    puts l / 2 - x_sort[-1][1]
  end
else
  if x_sort[-1][0] == y_sort[-1][0]
    puts [l - x_sort[-1][1] - y_sort[-2][1],  l - y_sort[-1][1] - x_sort[-2][1]].min
  else
    puts l - x_sort[-1][1] - y_sort[-1][1]
  end
end