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 = gets.to_i
vs = gets.split.map(&:to_i)
evens = {}
odds  = {}
vs.map.with_index { |e, i|
  if i.even?
    if evens[e].nil?
      evens[e] = 1
    else
      evens[e] += 1
    end
  else # i.odd?
    if odds[e].nil?
      odds[e] = 1
    else
      odds[e] += 1
    end
  end
}

# {key => value} は {値 => 出現回数}。keyが値でvalueが出現回数。

# 偶数列と奇数列で、最頻値が衝突していないかのチェック
evens_top, evens_second = evens.max_by(2) { |key, value| value }
odds_top, odds_second   =  odds.max_by(2) { |key, value| value }
if evens_top[0] == odds_top[0]
  # 衝突している場合には2番目に頻度が高いものの出現回数を比較
  if evens_second.nil? && odds_second.nil?
    # どちらも2番目が存在していない場合
    evens_value = evens_top[0]
    odds_value = evens_value + 1
  elsif odds_second.nil? || evens_second[1] >= odds_second[1]
    evens_value = evens_second[0]
    odds_value = odds_top[0]
  else #evens_second[1] < odds_second[1]
    evens_value = evens_top[0]
    odds_value = odds_second[0]
  end
else
  # 衝突していない場合にはそれぞれの最頻値の値を採用
  evens_value = evens_top[0]
  odds_value = odds_top[0]
end

rewrite_count = 0
evens.each do |key, value|
  unless evens_value == key
    rewrite_count += value
  end
end
odds.each do |key, value|
  unless odds_value == key
    rewrite_count += value
  end
end
puts rewrite_count