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)

class Counter < Hash
	def initialize(a=[])
		super
		self.default=0
		a.each{|e|self[e]+=1}
	end
  def most_common(n=nil)
    a=self.sort_by{|k,v|v}.reverse
    a=a[0,n] if n
    a
  end
	def self.[](*a)
		new(a)
	end
end
def Counter(a=[]) Counter.new(a) end
 
n,*v=`dd`.split.map &:to_i
v=v.each_slice(2).to_a
a,b=v.shift.zip(*v).map(&:compact).map{|e|Counter(e).most_common<<[0,0]}
if a[0][0] != b[0][0]
  p n - (a[0][1] + b[0][1])
else
  p [n-(a[1][1]+b[0][1]), n-(a[0][1]+b[1][1])].min
end