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)

from collections import defaultdict

n = int(input())
v = list(map(int, input().split(' ')))

odd = defaultdict(int)
even = defaultdict(int)
al = defaultdict(int)

for i in range(len(v)):
  al[v[i]] += 1
  if(i % 2 == 0): # even
    even[v[i]] += 1
  else: # odd
    odd[v[i]] += 1

if(len(al) == 1):
  print(n // 2)
  exit()

even_sorted = sorted(even.items(), key=lambda x: x[1], reverse=True)
odd_sorted = sorted(odd.items(), key=lambda x: x[1], reverse=True)

#print(even_sorted[0:4])
#print(odd_sorted[0:4])


if(len(even_sorted) == 1): # what if either of them had only one uniq num..
  if(odd_sorted[0][0] == even_sorted[0][0]):
    print(n - odd_sorted[1][1]  - even_sorted[0][1])
  else:
    print(n - odd_sorted[0][1] - even_sorted[0][1])
elif(len(odd_sorted) == 1):
  if(odd_sorted[0][0] == even_sorted[0][0]):
    print(n - even_sorted[1][1] - odd_sorted[0][1])
  else:
    print(n - odd_sorted[0][1] - even_sorted[0][1])


else: # both of them have more than 1 uniq num..
  if(odd_sorted[0][0] == even_sorted[0][0]):
    if(odd_sorted[0][1] == even_sorted[0][1]):
      if(odd_sorted[1][1] < even_sorted[1][1]):
        print(n - odd_sorted[0][1] - even_sorted[1][1])
      else:
        print(n - odd_sorted[1][1] - even_sorted[0][1])
    elif(odd_sorted[0][1] < even_sorted[0][1]): # odd to be changed (even stays)
      print(n - odd_sorted[1][1] - even_sorted[0][1])
    else:
      print(n - odd_sorted[0][1] - even_sorted[1][1])
  else: # both has more than 1 uniq num, and most freq values aren't the same
    print(n - odd_sorted[0][1] - even_sorted[0][1])