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 PyPy3 (7.3.0) (judge verdict: Accepted)

n = int(input())
v = list(input().split())
from collections import Counter
x, y = list(Counter(v[::2]).most_common(3)), list(Counter(v[1::2]).most_common(3))
x.sort(key=lambda i:i[1], reverse=True)
y.sort(key=lambda i:i[1], reverse=True)
r = []
for a, b in x[:max(len(x), 3)]:
    for aa, bb in y[:max(len(y), 3)]:
        if a == aa:
            r.append(n-max(b, bb))
        else:
            r.append(n-b-bb)
print(min(r))