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())
VV = list(map(int, input().split()))
v_even = VV[::2]
v_odd = VV[1::2]

e = collections.Counter(v_even)
o = collections.Counter(v_odd)
e_common = e.most_common()
o_common = o.most_common()


if (e_common[0] != o_common[0]):
    tmp = e_common[0][1] + o_common[0][1]
    answer = N - tmp

elif (len(e_common) == 1 or len(o_common) == 1): # case one type
    if (len(e_common) == 1 and len(o_common) == 1):
        answer = N // 2
    elif (len(e_common) == 1):
        answer = N // 2 - o_common[1][1]
    elif (len(o_common) == 1):
        answer = N // 2 - e_common[1][1]

else:
    tmp1 = e_common[0][1] + o_common[1][1]
    tmp2 = e_common[1][1] + o_common[0][1]
    tmp = max(tmp1, tmp2)
    answer = N - tmp

print(answer)