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   = gets.to_i
ary = gets.split.map &:to_i

aryEVEN = {}
aryODD  = {}

n.times do |i|
  x = ary[i]
  if i % 2 == 0
    if aryEVEN[x] == nil
      aryEVEN[x]  = 1
    else
      aryEVEN[x] += 1
    end
  else
    if aryODD[x] == nil
      aryODD[x]  = 1
    else
      aryODD[x] += 1
    end
  end
end

aryEVEN = aryEVEN.sort{|a| a[1]}
aryODD  = aryODD.sort{|a| a[1]}

pEVEN = 0
pODD  = 0

while aryEVEN[pEVEN][0] == aryODD[pODD][0]
  if pEVEN < aryEVEN.size - 1 && aryEVEN[pEVEN + 1][1] > aryODD[pODD + 1][1]
    pEVEN += 1
  elsif pODD < aryODD.size - 1
    pODD  += 1
  else
    puts n / 2
    exit
  end
end

puts n - aryEVEN[pEVEN][1] - aryODD[pODD][1]