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)

nu = gets.to_i
array = gets.chomp.split(' ').map(&:to_i)
count1 = []
count2 = []
(0..nu - 1).each do |i|
  if i.even?
    count1.push(array[i])
  else
    count2.push(array[i])
  end
end
count3 = Array.new(10**5 + 1, 0)
count4 = Array.new(10**5 + 1, 0)

(0..count1.length - 1).each do |i|
  count3[count1[i]] += 1
end
(0..count1.length - 1).each do |i|
  count4[count2[i]] += 1
end

check1 = [0, 0]
check2 = [0, 0]
check3 = [0, 0]
check4 = [0, 0]
(1..10**5).each do |i|
  if check1[1] < count3[i]
    check1[1] = count3[i]
    check1[0] = i
  end
  if check2[1] < count4[i]
    check2[1] = count4[i]
    check2[0] = i
  end
end
(1..10**5).each do |i|
  if check3[1] < count3[i] && i != check1[0]
    check3[1] = count3[i]
    check3[0] = i
  end
  if check4[1] < count4[i] && i != check2[0]
    check4[1] = count4[i]
    check4[0] = i
  end
end

if check1[0] != check2[0]
  puts (count1.length - check1[1]) + (count2.length - check2[1])
  exit
end

if (check1[1] + check4[1]) > (check2[1] + check3[1])
  puts (count1.length - check1[1]) + (count2.length - check4[1])
else
  puts (count1.length - check3[1]) + (count2.length - check2[1])
end