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: Time Limit Exceeded)

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

a = v.uniq

count_p1 = 0
count_p2 = 0
min_count = v.length

if a.length == 1
  min_count = v.length / 2
end

a.each do |a1|
  a.each do |a2|
    break if a1 == a2
    n.times do |i|
      count_p1 += 1 if (i%2 == 0 && v[i] != a1) || (i%2 == 1 && v[i] != a2)
      count_p2 += 1 if (i%2 == 0 && v[i] != a2) || (i%2 == 1 && v[i] != a1)
    end
    min_count = [count_p1, count_p2, min_count].min
    count_p1 = 0
    count_p2 = 0
  end
end

puts min_count