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.chomp.to_i
t = gets.chomp.split(' ').map {|i| i.to_i}
even = {}
odd = {}
t.length.times do |i|
  k = t[i]
  if (i + 1) % 2 == 0
    # even
    if even[k]
      even[k] += 1
    else
      even[k] = 1
    end
  else
    # odd
    if odd[k]
      odd[k] += 1
    else
      odd[k] = 1
    end
  end
end

m = 0
if even.length == 1 and even.keys == odd.keys
  m = t.length / 2
else
  even.keys.each do |ek|
    odd.keys.each do |ok|
      if ek != ok
        v = even[ek] + odd[ok]
        if m < v
          m = v
        end
      end
    end
  end
end

r = t.length - m
puts r