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)

inputs = STDIN.readlines.map{|line|line.strip.split()}
line = inputs.shift

n = line[0].to_i
v_list = inputs.shift
v_counts = [Hash.new(0), Hash.new(0)]
n.times do |i|
    v_counts[i % 2][v_list[i].to_i] += 1
end

sorted0 = v_counts[0].sort do |a, b|
    b[1] <=> a[1]
end
sorted1 = v_counts[1].sort do |a, b|
    b[1] <=> a[1]
end
whole = n >> 1
if sorted0[0][0] != sorted1[0][0] then
    puts(whole - sorted0[0][1] + whole - sorted1[0][1])
else
    if sorted0.size > 1 && sorted1.size > 1 then
        puts([
            whole - sorted0[0][1] + whole - sorted1[1][1],
            whole - sorted0[1][1] + whole - sorted1[0][1],
        ].min)
    elsif sorted0.size > 1 then
        puts(whole - sorted1[1][1])
    elsif sorted1.size > 1 then
        puts(whole - sorted1[0][1])
    else
        puts(whole)
    end
end