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: Runtime Error)

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

even_h = {}
odd_h = {}
v.each_with_index do |e, i|
  if i % 2 == 0
    odd_h[e] ||= 0
    odd_h[e] += 1
  else
    even_h[e] ||= 0
    even_h[e] += 1
  end
end
even = even_h.sort_by { |(k, v)| -v }
odd  = odd_h.sort_by { |(k, v)| -v }

## For Debug
# p even  # [[1, 3], [3, 1], ...]
# p odd   # [[1, 3], [2, 2], ...]

if even[0][0] != odd[0][0]  # number
  total_cnt = even[0][1] + odd[0][1]
  p (n - total_cnt)
else  # number is equal
  # Use the next largest value of odd
  cnt1 = even[0][1] + odd[1][1]
  # Use the next largest value of even
  cnt2 = even[1][1] + odd[0][1]
  total_cnt = [cnt1, cnt2].max
  p (n - total_cnt)
end