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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <algorithm>
#include <iostream>
#include <map>
#include <numeric>
#include <vector>

using namespace std;

int main() {
  int n, v;
  cin >> n;
  vector<vector<int>> V(2, vector<int>(100001));
  for (int i = 0; i != n; ++i) {
    cin >> v;
    ++V[i % 2][v];
  }

  vector<vector<int>> I(2, vector<int>(100001));
  for (auto i : {0, 1}) {
    iota(begin(I[i]), end(I[i]), 1);
    sort(begin(I[i]), end(I[i]),
         [&](int a, int b) { return V[i][a] > V[i][b]; });
  }
  auto ans = n - ((I[0][0] != I[1][0]) ? V[0][I[0][0]] + V[1][I[1][0]]
                                    : max(V[0][I[0][0]] + V[1][I[1][1]],
                                          V[0][I[0][1]] + V[1][I[1][0]]));
  cout << ans << endl;
}