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: Accepted)

import collections
n = int(input())
v = list(map(int, input().split()))
vo = [v[i] for i in range(n) if i%2 == 0]
ve = [v[i] for i in range(n) if i%2 == 1]
vo_dict = collections.Counter(vo)
ve_dict = collections.Counter(ve)
if vo_dict == ve_dict and len(vo_dict) == 1:
    ans = n//2
else:
    if vo_dict.most_common()[0][0] != ve_dict.most_common()[0][0]:
        ans = n - vo_dict.most_common()[0][1] - ve_dict.most_common()[0][1]
    else:
        ans = min(n - vo_dict.most_common()[0][1] - ve_dict.most_common(2)[1][1],
                  n - vo_dict.most_common(2)[1][1] - ve_dict.most_common()[0][1])
print(ans)