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.to_i
v = gets.split.map(&:to_i)
p = Hash.new(0)
q = Hash.new(0)
n.times do |i|
  p[v[i]] += 1 if i.even?
  q[v[i]] += 1 if i.odd?
end
ps = Hash[p.sort_by{|k, v| -v}].keys
qs = Hash[q.sort_by{|k, v| -v}].keys
x, y, ans = 0, 0, 0
f = false
(n / 2).times do |i|
  x = ps[i]
  (n / 2).times do |j|
    if ps[i] != qs[j]
      y = qs[j]
      f = true
      break
    end
  end
  break if f
end
ans = n - p[x] - q[y] if f
x, y = 0, 0
f = false
(n / 2).times do |i|
  x = qs[i]
  (n / 2).times do |j|
    if qs[i] != ps[j]
      y = ps[j]
      f = true
      break
    end
  end
  break if f
end
ans = n - q[x] - p[y] if f && ans > n - q[x] - p[y]
puts ans