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: Wrong Answer)

import java.util.*;
import java.util.function.Predicate;
import java.util.stream.Collectors;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt() / 2;
        List<Integer> u1 = new ArrayList<>(), u2 = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            u1.add(scanner.nextInt());
            u2.add(scanner.nextInt());
        }

        int e, f;

        Map<Integer, Long> a = u1.stream()
                .collect(Collectors.groupingBy(i -> i, Collectors.counting()))
                .entrySet()
                .stream()
                .sorted(Comparator.comparingLong(Map.Entry::getValue))
                .collect(Collectors.toMap(Map.Entry::getKey, Map.Entry::getValue, (a1, b2) -> null, LinkedHashMap::new));
        Map<Integer, Long> b = u2.stream()
                .collect(Collectors.groupingBy(i -> i, Collectors.counting()))
                .entrySet()
                .stream()
                .sorted(Comparator.comparingLong(Map.Entry::getValue))
                .collect(Collectors.toMap(Map.Entry::getKey, Map.Entry::getValue, (a1, b2) -> null, LinkedHashMap::new));

        List<Integer> c = new ArrayList<>(a.keySet());
        List<Integer> d = new ArrayList<>(b.keySet());

        if (c.get(0).equals(d.get(0))) {
            if (c.size() == 1 || d.size() == 1) {
                System.out.println(n);
                return;
            } else {
                if (a.get(c.get(1)) + b.get(d.get(0)) < a.get(c.get(0)) + b.get(d.get(1))) {
                    e = c.get(1);
                    f = d.get(0);
                } else {
                    e = c.get(0);
                    f = d.get(1);
                }
            }
        } else {
            e = c.get(0);
            f = d.get(0);
        }
        u1.removeIf(Predicate.isEqual(e));
        u2.removeIf(Predicate.isEqual(f));
        System.out.println(u1.size() + u2.size());
    }
}