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: Time Limit Exceeded)

# ちょうど2種類=>出来合いの要素数が一番多いほうがいい
# 偶数番目の数と奇数番目の数は別の処理で数えられる
n = gets.to_i
datas = gets.split(" ").map{|nn|nn.to_i}
need = 0
if (datas.count(datas[0]) == n)
  need = n / 2
else
gusus = []
0.step(n-1,2) do|i|
  gusus << datas[i]
end
uniqgusus = gusus.uniq
co = 0
gusumax = 0
uniqgusus.each do|num|
  co = gusus.count(num)
  if co > gusumax
    gusumax = co
  end
end
need += n/2 - gusumax

kisus = []
1.step(n-1,2) do|i|
  kisus << datas[i]
end
uniqkisus = kisus.uniq
co = 0
kisumax = 0
uniqkisus.each do|num|
  co = kisus.count(num)
  if co > kisumax
    kisumax = co
  end
end
need += n/2 - kisumax
end
puts need.to_s