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
v = gets.chomp.split(' ').map(&:to_i)
map1, map2 = Hash.new(0), Hash.new(0)
0.upto(n - 1) do |i|
  if i % 2 == 0
    map1[v[i]] = map1[v[i]] + 1
  else
    map2[v[i]] = map2[v[i]] + 1
  end
end
map1 = Hash[map1.sort_by{ |_, v| v }]
map2 = Hash[map2.sort_by{ |_, v| v }]
top1, top2 = map1.keys.take(2).map { |v| map1[v] }
top2 = 0 if top2.nil?
k1, v1 = map1.shift
k2, v2 = map2.shift
while k1 == k2 && map1.length > 0 && map2.length > 0
  if v1 > v2
    _, v2 = map2.shift
  elsif v1 < v2
    _, v1 = map1.shift
  else
    k1, v1 = map1.shift
    k2, v2 = map2.shift
  end
end
if k1 == k2
  puts (n / 2) - top1 + (n / 2) - top2
else
  puts (n / 2) - v1 + (n / 2) - v2
end