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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);

    Map<Integer, Integer> odds = new HashMap<>();
    Map<Integer, Integer> evens = new HashMap<>();
    int N = scanner.nextInt();
    for (int i = 0; i < N; i++) {
      int a = scanner.nextInt();
      if (i % 2 == 0) {
        evens.put(a, evens.getOrDefault(a, 0) + 1);
      } else {
        odds.put(a, odds.getOrDefault(a, 0) + 1);
      }
    }

    List<Map.Entry<Integer, Integer>> o = new ArrayList<>(odds.entrySet());
    List<Map.Entry<Integer, Integer>> e = new ArrayList<>(evens.entrySet());
    o.sort((o1, o2) -> o2.getValue() - o1.getValue());
    e.sort((o1, o2) -> o2.getValue() - o1.getValue());

    int o1 = o.get(0).getValue();
    int o2 = o.size() == 1 ? 0 : o.get(1).getValue();
    int e1 = e.get(0).getValue();
    int e2 = e.size() == 1 ? 0 : e.get(1).getValue();

    if (!o.get(0).getKey().equals(e.get(0).getKey())) {
      System.out.println(N - o1 - e1);
    } else {
      System.out.println(N - Math.max(o1 + e2, o2 + e1));
    }
  }
}