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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Main main = new Main();
        main.solve();
    }
    public void solve() {
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int N = scan.nextInt();
        int[] v = new int[N];
        HashMap<Integer, Integer> map = new HashMap<>();
        for (int i = 0; i < N; i++) {
            v[i] = scan.nextInt();
            if (!map.containsKey(v[i])) {
                map.put(v[i], 0);
            }
            int count = map.get(v[i]);
            map.put(v[i], count+1);
        }
        int[] c = new int[map.size()];
        long answer = Long.MAX_VALUE;
        for (int x : map.keySet()) {
            int a1 = map.get(x);
            for (int y : map.keySet()) {
                if (x == y) {
                    continue;
                }
                int a2 = map.get(y);
                long t = Math.abs(a1-N/2) + Math.abs(a2-N/2);
                answer = Math.min(answer, t);
            }
            long t = Math.abs(a1-N/2) + N/2;
            answer = Math.min(answer, t);
        }
        if (map.size() == 1) {
            long t = N / 2;
            answer = Math.min(answer, t);
        }
        System.out.println(answer);
    }
}