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)

N = gets.to_i
V = gets.split.map &:to_i

VE = V.select.with_index(1){|v, i|v if i.even?}
VO = V.select.with_index(1){|v, i|v if i.odd?}

def count_desc(a)
  a.uniq.map{|v|a.count(v)}.sort_by{|v|v}.reverse
end

cve = count_desc(VE)
cvo = count_desc(VO)

if VE == VO
  puts N/2
elsif cve.size == 1 && cvo.size == 1
  puts 0
elsif cve.size == 1 && cvo.size != 1
  buf = cvo.drop(1).inject(:+)
  puts cvo[0] < buf ? N/2-cvo[0] : N/2-buf 
elsif cve.size != 1 && cvo.size == 1
  buf = cve.drop(1).inject(:+)
  puts cve[0] < buf ? N/2-cve[0] : N/2-buf 
else
  puts N   - cve[0] - cvo[0]
end