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 = gets.to_i, gets.chomp.split.map(&:to_i)
os, es = vs.partition.with_index {|_, i| i.odd? }
# 奇数番目の頻度表
ohi = os.group_by{|i| i }.map{|k, v| [k, v.length] }
# 偶数番目の頻度表
ehi = es.group_by{|i| i }.map{|k, v| [k, v.length]  }
# 奇数準拠のとき -> 偶数列は opop 以外で一番頻度が高いものがepop
opop = ohi.max_by {|pr| pr[1] }
# p opop
ehi_excluded_opop = ehi.select{|pr| pr[0] != opop[0] }
epop = ehi_excluded_opop.empty? ? [nil, 0] : ehi_excluded_opop.max_by{|pr| pr[1] }
# p epop
ans_based_odd = os.length - opop[1] + es.length - epop[1]
# p ans_based_odd
# 偶数準拠
epop = ehi.max_by {|pr| pr[1] }
# p epop
ohi_excluded_epop = ohi.select{|pr| pr[0] != epop[0] }
opop = ohi_excluded_epop.empty? ? [nil, 0] : ohi_excluded_epop.max_by{|pr| pr[1] }
# p opop
ans_based_even = os.length - opop[1] + es.length - epop[1]
# p ans_based_even

p [ans_based_odd, ans_based_even].min