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, *VS = $stdin.read.split.map(&:to_i)
occ = [{}, {}]
for i in 0...(N/2)
  occ[0][VS[i*2  ]] = (occ[0][VS[i*2  ]] || 0) + 1
  occ[1][VS[i*2+1]] = (occ[1][VS[i*2+1]] || 0) + 1
end
ranking = [
  occ[0].sort_by(&:last),
  occ[1].sort_by(&:last),
]
def ans(na, nb); p (N/2 - na) + (N/2 - nb); end
a1, na1 = *ranking[0][-1]
b1, nb1 = *ranking[1][-1]
a2, na2 = *ranking[0][-2]
b2, nb2 = *ranking[1][-2]
if a1 != b1
  ans(na1, nb1)
else
  if na1 < nb1
    ans(na2, nb1)
  elsif na1 > nb1
    ans(na1, nb2)
  else # 1位が同数
    if na2.nil?  # 全部同じ数
      p N/2
    else
      ans(na1, [na2, nb2].max)
    end
  end
end