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)

#!/usr/bin/env ruby
n = STDIN.readline.strip.to_i
v = STDIN.readline.strip.split(' ').map(&:to_i)
o = {}
e = {}
for i in 0..(n/2-1) do
  e[v[i*2]] = e[v[i*2]].nil? ? 1 : e[v[i*2]]+1
  o[v[i*2+1]] = o[v[i*2+1]].nil? ? 1 : o[v[i*2+1]]+1
end
e_s = e.sort_by{|k, _v| _v}
o_s = o.sort_by{|k, _v| _v}

def find_max(a, b)
  max_a = a[0][1]
  max_b = 0
  i = 0
  while i < a.length and a[i][1] == max_a do 
    max_i_b = a[i][0] != b[0][0] ? b[0][1] : b.length == 1 ? 0 : b[1][1]
    max_b = max_i_b if max_b < max_i_b
    i += 1
  end
  max_a + max_b
end
        
max_e = find_max(e_s, o_s)
max_o = find_max(o_s, e_s)
m = [max_e, max_o].max
puts n - m