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)

gets
arr = gets.split.map(&:to_i)
odds = (0...arr.size).step(2).map{|i| arr[i]}
evens = (1...arr.size).step(2).map{|i| arr[i]}

odds_count = {}
evens_count = {}
odds_count.default = 0
evens_count.default = 0

odds.each{|it| odds_count[it] += 1}
evens.each{|it| evens_count[it] += 1}

odds_count_arr = odds_count.to_a.sort_by{|it| -it[1]}
evens_count_arr = evens_count.to_a.sort_by{|it| -it[1]}
odds_count_arr.push [nil, 0]
evens_count_arr.push [nil, 0]


p odds_count_arr
p evens_count_arr

answer = arr.size
if odds_count_arr[0][0] == evens_count_arr[0][0]
    answer -= (odds_count_arr[0][1] + [odds_count_arr[1][1], evens_count_arr[1][1]].max)
else
    answer -= (odds_count_arr[0][1] + evens_count_arr[0][1])
end

puts answer