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: Time Limit Exceeded)

def rewrite_count(vi_list):
    if len(set(vi_list)) != 1:
        vi_count_list = [(i, vi_list.count(i)) for i in set(vi_list)]
        vi_count_list = sorted(vi_count_list, key=lambda x: x[1])
        return vi_count_list[-1][0], len(vi_list) - vi_count_list[-1][1], len(vi_list) - vi_count_list[-2][1]
    else:
        return vi_list, 0, 0

N = int(input())
v_list = input().split()

if len(set(v_list)) == 1:
    print(len(v_list) // 2)
    exit()

v1_list = [v_list[i] for i in range(0, len(v_list), 2)]
v2_list = [v_list[i] for i in range(1, len(v_list), 2)]
max_v1, max_value_v1, second_value_v1 = rewrite_count(v1_list)
max_v2, max_value_v2, second_value_v2 = rewrite_count(v2_list)

if max_v1 != max_v2:
    ans = max_value_v1 + max_value_v2
elif max_value_v1 > max_value_v2:
    ans = max_value_v2 + second_value_v1
else:
    ans = max_value_v1 + second_value_v2
print(ans)