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)

n = int(input())
a = list(map(int, input().split()))

u, v = [], []
for i in range(0, n, 2):
    u.append(a[i])
for i in range(1, n, 2):
    v.append(a[i])
cu = dict()
for i in u:
    if i in cu:
        cu[i] += 1
    else:
        cu[i] = 1
cv = dict()
for i in v:
    if i in cv:
        cv[i] += 1
    else:
        cv[i] = 1
ua, ub = (sorted(cu.items(), key=lambda x: x[1], reverse=True) + [(-1, 0)])[:2]
va, vb = (sorted(cv.items(), key=lambda x: x[1], reverse=True) + [(-2, 0)])[:2]
if ua[0] == va[0]:
    print(min(len(u) - ua[1] + len(v) - vb[1], len(u) - ub[1] + len(v) - va[1]))
else:
    print(len(u) - ua[1] + len(v) - va[1])