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.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    Map<Integer, Integer> even = new HashMap<>();
    Map<Integer, Integer> odd = new HashMap<>();
    for (int i = 0; i < n; i++) {
      int v = sc.nextInt();
      if (i % 2 == 0) {
        even.put(v, even.getOrDefault(v, 0) + 1);
      } else {
        odd.put(v, odd.getOrDefault(v, 0) + 1);
      }
    }
    
    int[][] evenSorted = sortMapByValue(even);
    int[][] oddSorted = sortMapByValue(odd);
    
    if (evenSorted[0][0] != oddSorted[0][0]) {
      int ans = 0;
      for (int i = 1; i < evenSorted.length; i++) {
        ans += evenSorted[i][1];
      }
      for (int i = 1; i < oddSorted.length; i++) {
        ans += oddSorted[i][1];
      }
      System.out.println(ans);
      return;
    }

    // use evenSorted[0][0]
    int ans1 = 0;
    for (int i = 1; i < evenSorted.length; i++)  {
      ans1 += evenSorted[i][1];
    }
    for (int i = 0; i < oddSorted.length; i++) {
      if (i == 1) {
        // skip
        continue;
      }
      ans1 += oddSorted[i][1];
    }

    // use oddSorted[0][0]
    int ans2 = 0;
    for (int i = 0; i < evenSorted.length; i++) {
      if (i == 1)  {
        // skip
        continue;
      }
      ans2 += evenSorted[i][1];
    }
    for (int i = 1; i < oddSorted.length; i++) {
      ans2 += oddSorted[i][1];
    }
    
    System.out.println(Math.min(ans1, ans2));
  }
  
  private static int[][] sortMapByValue(Map<Integer, Integer> map) {
    int[][] ret = new int[map.size()][2];
    int i = 0;
    for (Map.Entry<Integer, Integer> entry : map.entrySet()) {
      ret[i][0] = entry.getKey();
      ret[i][1] = entry.getValue();
      i++;
    }
    Arrays.sort(ret, (a, b) -> b[1] - a[1]);
    
    return ret;
  }
}