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 Lua (5.3.2) (judge verdict: Accepted)


n = io.read("*n")
v1 = {}
v2 = {}
for i = 1, n do
	x = io.read("*n")
	if i % 2 == 1 then
		v1[x] = v1[x] and v1[x]+1 or 1
	else
		v2[x] = v2[x] and v2[x]+1 or 1
	end
end

v1[-1] = 0
v2[-1] = 0
s1 = {}
s2 = {}
for k, v in pairs(v1) do
	s1[#s1+1] = {k, v}
end
for k, v in pairs(v2) do
	s2[#s2+1] = {k, v}
end
table.sort(s1, function(a, b) return a[2] > b[2] end)
table.sort(s2, function(a, b) return a[2] > b[2] end)
-- print_r(s1)
-- print_r(s2)

if s1[1][1] ~= s2[1][1] then
	print(n - s1[1][2] - s2[1][2])
else
	print(n - math.max(s1[1][2]+s2[2][2], s1[2][2]+s2[1][2]))
end