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)

from collections import Counter
from heapq import heappop,heappush

N = int(input())
V = list(map(int, input().split()))
odd = Counter(V[::2])
odd[10**6] = 0
even = Counter(V[1::2])
even[10**6] = 0
heapodd = []
heapeven = []
for k,v in odd.items():
    heappush(heapodd,(-v,k))
for k,v in even.items():
    heappush(heapeven,(-v,k))

vo1,odd1 = heappop(heapodd)
vo2,odd2 = heappop(heapodd)
ve1,even1 = heappop(heapeven)
ve2,even2 = heappop(heapeven)

if odd1 != even1:
  print(N + vo1 + ve1)
else:
  print(min(N+ve1+vo2,N+vo1+ve2))