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 (2.4.0) (judge verdict: Accepted)

from collections import defaultdict

def main():
    n = int(input())
    V = [int(e) for e in input().split()]

    De, Do = defaultdict(int), defaultdict(int)
    for i in range(0, n, 2):
        De[V[i]] += 1

    for i in range(1, n + 1, 2):
        Do[V[i]] += 1

    Des = sorted(De.items(), key=lambda x: -x[1])
    Dos = sorted(Do.items(), key=lambda x: -x[1])

    Des.append((-1, 0))
    Dos.append((-1, 0))

    ans = n - Des[0][1] - Dos[0][1]

    if Des[0][0] == Dos[0][0]:
        ans += min(Des[0][1] - Des[1][1], Dos[0][1] - Dos[1][1])

    print(ans)

if __name__ == "__main__":
    main()