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
V = gets.split.map(&:to_i)

ls = V.partition.with_index {|v,i| i.even? }
a,b = ls.map.with_index {|v,i| v.group_by(&:itself).map {|k,v| [v.size, k] }.sort }

if a[-1][1] != b[-1][1]
  ans = N - a[-1][0] - b[-1][0]
elsif a[-2] == nil && b[-2] == nil
  ans = N - [a[-1][0], b[-1][0]].max
else
  ans = N - [a[-1][0] + (b[-2][0]||0), a[-2][0] + (b[-1][0]||0)].max
end
puts ans