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.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.Scanner;

public class Main {

  public static void main(String[] args) {

    Scanner sc = new Scanner(System.in);

    int N = Integer.parseInt(sc.next());

    Map<Integer, Integer> oMap = new HashMap<>();
    Map<Integer, Integer> eMap = new HashMap<>();

    for (int i = 0; i < N; i++) {
      int v = Integer.parseInt(sc.next());
      if (i % 2 == 0) {
        oMap.merge(v, 1, Integer::sum);
      } else {
        eMap.merge(v, 1, Integer::sum);
      }
    }

    List<Entry<Integer, Integer>> list_entries_o = new ArrayList<Entry<Integer, Integer>>(oMap.entrySet());
    Collections.sort(list_entries_o, new Comparator<Entry<Integer, Integer>>() {
      //compareを使用して値を比較する
      public int compare(Entry<Integer, Integer> obj1, Entry<Integer, Integer> obj2) {
        //降順
        return obj2.getValue().compareTo(obj1.getValue());
      }
    });

    List<Entry<Integer, Integer>> list_entries_e = new ArrayList<Entry<Integer, Integer>>(eMap.entrySet());
    Collections.sort(list_entries_e, new Comparator<Entry<Integer, Integer>>() {
      //compareを使用して値を比較する
      public int compare(Entry<Integer, Integer> obj1, Entry<Integer, Integer> obj2) {
        //降順
        return obj2.getValue().compareTo(obj1.getValue());
      }
    });

    int ans = 0;
    if (list_entries_o.get(0).getKey() != list_entries_e.get(0).getKey()) {
      ans = N - list_entries_o.get(0).getValue() - list_entries_e.get(0).getValue();
    } else {
      int e = 0, o = 0;
      if (eMap.size() > 1) {
        e = list_entries_e.get(1).getValue();
      }
      if (oMap.size() > 1) {
        o = list_entries_o.get(1).getValue();
      }

      ans = Math.min(N - list_entries_o.get(0).getValue() - e, N - o - list_entries_e.get(0).getValue());

    }
    System.out.println(ans);
  }
}