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
A = gets.split.map(&:to_i)

odd, even = 2.times.map{ Hash.new(0) }

A.each_with_index do |v,i|
  if i.odd?
    odd[v] += 1
  else
    even[v] += 1
  end
end

co = N / 2
ce = N - co

wo = odd.max_by(2){|k,v| v}
we = even.max_by(2){|k,v| v}

if we.size == 1 && wo.size == 1 && we.first[0] == wo.first[0]
  puts [we.first[1], wo.first[1]].min
else
  puts [ 
      we.first[0] == wo.first[0] ? N : ce - we.first[1] + co - wo.first[1], 
      we.first[0] == wo.last[0]  ? N : ce - we.first[1] + co - wo.last[1] ,
      we.last[0]  == wo.first[0] ? N : ce - we.last[1]  + co - wo.first[1],
      we.last[0]  == wo.last[0]  ? N : ce - we.last[1]  + co - wo.last[1] 
    ].min
end