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)

p $<.to_a[1].split.map(&:to_i).each_slice(2).to_a.transpose
.map{|a|a.group_by{|x|x}.map{|k,v|[k,v.size]}.sort_by{|x|-x[1]}}
.map{|a|[a[0][0]] + [a[1]&.slice(0)] + [a.flat_map{|(x,c)|[x] * c}]}
.transpose
.tap{|a|break a[0].uniq.size == 2 ?
  a[2][0].count{|x|x != a[0][0]} + a[2][1].count{|x|x != a[0][1]}:
  [
    a[2][0].count{|x|x != a[1][0]} + a[2][1].count{|x|x != a[0][1]},
    a[2][0].count{|x|x != a[0][0]} + a[2][1].count{|x|x != a[1][1]}
  ].min
}