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)

N,*vs=$<.read.split.map(&:to_i)

es,os = vs.zip((1..N)).partition {|v,i| i%2 == 0}

def f(xs)
  xs.group_by {|v,i|v}.map{|k,v|[k,v.length]}.sort_by {|k,v|-v}
end

es = f(es)
os = f(os)

if es[0][0] != os[0][0]
    puts vs.length - es[0][1] - os[0][1]
elsif es[0][0] == os[0][0] && es.length == 1 && os.length == 1
    puts vs.length / 2
elsif es[0][1]-es[1][1] < os[0][1]-os[1][1]
    puts vs.length - es[1][1] - os[0][1]
else
    puts vs.length - es[0][1] - os[1][1]
end