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 (2.7.1) (judge verdict: Wrong Answer)

n=gets.to_i

v=gets.chomp.split(" ").map { | x | x.to_i}

a = {}
b = {}
v.each_with_index { | item, idx |
  if (idx % 2 == 0) then
    a[item] = (a[item] || 0) + 1
  else
    b[item] = (b[item] || 0) + 1
  end
}
as = a.keys.to_a
as.sort! { | x,y | a[y] <=> a[x] }

bs = b.keys.to_a
bs.sort! { | x,y | b[y] <=> b[x] }

if as[0] == bs[0] && a[as[0]] + b[bs[0]] == n then
  puts a[as[0]]
elsif a[as[0]] == b[bs[0]] then
  d = n - a[as[0]] - b[bs[0]]
  puts d
elsif a[as[0]] > b[bs[0]] then
  d = n - a[as[0]] - b[bs[1]]
  puts d
else
  d = n - a[as[1]] - b[bs[0]]
  puts d
end