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.chomp.to_i

v = gets.chomp.split(" ").map(&:to_i)

v1 = Hash.new(0)
v2 = Hash.new(0)

n.times do |i|
  if i.odd?
    v1[v[i]] += 1
  else
    v2[v[i]] += 1
  end
end

k1 = v1.sort{|a, b| a[1] <=> b[1]}.reverse
k2 = v2.sort{|a, b| a[1] <=> b[1]}.reverse

if k1[0][0] == k2[0][0]
  if k1.length == 1 && k2.length == 1
    puts n/2
  elsif k1.length == 1
    puts [n - k1[0][1] - k2[1][1], n - n/2 - k2[0][1]].min
  elsif k2.length == 1
    puts [n - k1[0][1] - n/2, n - k1[1][1] - k2[0][1]].min
  else
    puts [n - k1[0][1] - k2[1][1], n - k1[1][1] - k2[0][1]].min
  end
else
  puts n - k1[0][1] - k2[0][1]
end