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
vs = gets.split.map(&:to_i)
even = {}
odd = {}
ev = []
ov = []
vs.each_with_index{|v, i|
  if i % 2 == 0
    t = even
    tv = ev
  else
    t = odd
    tv = ov
  end
  if t[v] == nil
    o = {:v => v, :c => 0}
    t[v] = o
    tv << o
  end
  t[v][:c] += 1
}
ev.sort!{|a, b|
  v = 0 if a[:c] == b[:c]
  v = -1 if a[:c] > b[:c]
  v = 1 if a[:c] < b[:c]
  v
}
ov.sort!{|a, b|
  v = 0 if a[:c] == b[:c]
  v = -1 if a[:c] > b[:c]
  v = 1 if a[:c] < b[:c]
  v
}

ei = 0
oi = 0
while(true)
  te = ev[ei]
  to = ov[oi]
  break if te[:v] != to[:v]
  break if ei == ev.length - 1 && oi == ov.length - 1
  if ei == ev.length - 1
    oi += 1
  elsif oi == ov.length - 1
    ei += 1
  else
    if ev[ei + 1][:c] > ov[oi + 1][:c]
      ei += 1
    else
      oi += 1
    end
  end
end
ans = n - ev[ei][:c] - ov[oi][:c] 
if vs[0] == vs[1] && ans == 0
  ans = n / 2
end
puts ans