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)

n, vs = $stdin.read.lines
n = n.to_i
odd_vs, even_vs = vs.split(' ').map(&:to_i).partition.with_index { |_, i| i.odd? }
odd_freq  = odd_vs.group_by(&:itself).map { |v, vs| [v, vs.size] }.to_h
even_freq = even_vs.group_by(&:itself).map { |v, vs| [v, vs.size] }.to_h

max_odd_v, odd_cnt = odd_freq.max_by { |v, count| count }
max_even_v, even_cnt = even_freq.max_by { |v, count| count }

if odd_cnt > even_cnt
  even_freq.delete(max_odd_v)
  puts((n/2 - odd_cnt) + (n/2 - (even_freq.values.max || 0)))
else
  odd_freq.delete(max_even_v)
  puts((n/2 - even_cnt) + (n/2 - (odd_freq.values.max || 0)))
end