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 Python (3.4.3) (judge verdict: Wrong Answer)

n = int(input())
sequence = [int(x) for x in input().split(" ")]
odds = sequence[::2]
evens = sequence[1::2]
odd_counts = {}
even_counts = {}
for i in odds:
    odd_counts[i] = odd_counts.get(i, 0) + 1
for i in evens:
    even_counts[i] = even_counts.get(i, 0) + 1
odd_sorted = sorted(odd_counts.items(), key=lambda x: x[1])
even_sorted = sorted(even_counts.items(), key=lambda x: x[1])
best_even_num, best_even_count = even_sorted[0]
best_odd_num, best_odd_count = odd_sorted[0]
if best_even_num == best_odd_num:
    if best_odd_count >= best_even_count:
        if len(even_sorted) > 1:
            best_even_num, best_even_count = even_sorted[1]
        else:
            best_even_count = 0
    else:
        if len(odd_sorted) > 1:
            best_odd_count = odd_sorted[1][1]
        else:
            best_odd_count = 0
print(n - best_even_count - best_odd_count)