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)

counts = Array.new(2) { Hash.new(0) }
V.each_with_index do |v, idx|
  counts[idx % 2][v] += 1
end

sorted1 = counts[0].sort_by { |k, v| -v }
sorted2 = counts[1].sort_by { |k, v| -v }

# p N
# p counts
# p sorted1
# p sorted2

ans = Float::INFINITY
0.upto(1) do |i|
  0.upto(1) do |j|
    next if sorted1[i] && sorted2[j] && sorted1[i][0] == sorted2[j][0]
    next if sorted1[i].nil? && sorted2[j].nil?
    # puts "i:#{i}, j:#{j}, #{sorted1[i]} #{sorted2[j]}"

    a = (N / 2 - (sorted1[i] ? sorted1[i][1] : 0)) + (N / 2 - (sorted2[j] ? sorted2[j][1] : 0))
    ans = a if ans > a
  end
end

puts ans