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)

gets
hs = Array.new(2) { Hash.new(0) }
gets.split.map(&:to_i).each_with_index do |v, i|
    hs[i % 2][v] += 1
end
target = hs.map{|h| h.max_by{|k, v| v }[0]}.uniq
if target.size == 1
    sorted = hs.map{|h| h.sort_by{|k, v| v}[0]}
    if (hs[0][sorted[0][0]] + hs[1][sorted[1][1]]) > (hs[0][sorted[0][1]] + hs[1][sorted[1][0]])
        begin
            target = [sorted[0][0], sorted[1][1]]
        rescue
            target = [sorted[0][0], -1]
        end
    else
        begin
            target = [sorted[0][1], sorted[1][0]]
        rescue
            target = [-1, sorted[1][0]]
        end
    end
end
puts hs.zip(target).map { |h, t|
    h.select{|k, v| k != t}.values.inject(0, :+)
}.inject(0, :+)