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: Wrong Answer)

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

b = Hash.new(0)
c = Hash.new(0)

n.times{|i|
  b[a[i]]+=1 if i%2==0
  c[a[i]]+=1 if i%2==1
}

if a.uniq.size == 1
  p n/2
else
  b = b.sort{|a,b|a[1]<=>b[1]}
  c = c.sort{|a,b|a[1]<=>b[1]}
  if b[-1][0] == c[-1][0]
    if b[-2]
      p n/2 - c[-2][1]
    elsif c[-2]
      p n/2 - b[-2][1]
    else
      p n/2 - [b[-2][1],c[-2][1]].max
    end
  else
    p (n/2 - b[-1][1]) + (n/2 - c[-1][1])
  end
end