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 = STDIN.gets.to_i
vs = STDIN.gets.strip.split(" ").map(&:to_i)

def count(a)
  cnt = {}
  a.each { |v| cnt[v] ||= 0; cnt[v] += 1 }
  cnt.sort_by { |v, cnt| cnt }.reverse
end

def reverse?(a, b, n)
  return true if a[0][1] < b[0][1]
  return false unless a[0][1] == b[0][1]
  aa = a[1] ? a[1][1] : n/2
  bb = b[1] ? b[1][1] : n/2
  return true if aa > bb
  false
end

a = []
b = []
vs.each_with_index do |v, i|
  if i % 2 == 0
    a << v
  else
    b << v
  end
end

ca = count(a)
cb = count(b)
ans = 0

# aa = [
#   ca,
#   cb
# ]
aa = [
  cb.reverse,
  ca
]
if reverse?(aa[0], aa[1], n)
  aa = aa.reverse
end

used = {}
aa.each do |c|
  no_ans = true

  c.each do |v, cnt|
    next if used[v]
    used[v] = true
    ans += n/2 - cnt
    no_ans = false
    break
  end

  if no_ans
    ans += n / 2
  end
end
puts ans