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)

def counts(nums)
  nums.each_with_object(Hash.new(0)) { |i, h| h[i] += 1 }.sort_by { |num, count| [count, num] }.reverse
end

N = gets.to_i
evens, odds = gets.split(" ").map(&:to_i).partition.with_index { |n, i| i % 2 == 0 }

even_counts = counts(evens)
odd_counts = counts(odds)

even_num, even_no_op_count = even_counts[0]
odd_num,  odd_no_op_count  = odd_counts[0]

ans = if even_num == odd_num
  candidates = [
    even_counts.fetch(1, [0]).last + odd_no_op_count,
    even_no_op_count  + odd_counts.fetch(1, [0]).last
  ]
  N - candidates.max
else
  N - (even_no_op_count + odd_no_op_count)
end

puts ans