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

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] v = new int[n];
        for (int i = 0; i < n; i++) {
            v[i] = sc.nextInt();
        }
        Map<Integer, Integer> map1 = new HashMap<>();
        Map<Integer, Integer> map2 = new HashMap<>();
        for (int i = 0; i < n; i += 2) {
            int value1 = 1;
            int value2 = 1;
            if (map1.containsKey(v[i])) {
                value1 += map1.get(v[i]);
            }
            if (map2.containsKey(v[i + 1])) {
                value2 += map2.get(v[i + 1]);
            }
            map1.put(v[i], value1);
            map2.put(v[i + 1], value2);
        }
        int max1 = 0;
        int max_key1 = -1;
        for (int key : map1.keySet()) {
            max1 = Math.max(max1, map1.get(key));
            if (max1 == map1.get(key)) {
                max_key1 = key;
            }
        }
        int next_max1 = 0;
        int next_max_key1 = -1;
        for (int key : map1.keySet()) {
            if (map1.get(key) != max1 && key != max_key1) {
                next_max1 = Math.max(next_max1, map1.get(key));
                if (next_max1 == map1.get(key)) {
                    next_max_key1 = key;
                }
            }
        }

        int max2 = 0;
        int max_key2 = -1;
        for (int key : map2.keySet()) {
            max2 = Math.max(max2, map2.get(key));
            if (max2 == map2.get(key)) {
                max_key2 = key;
            }
        }
        int next_max2 = 0;
        int next_max_key2 = -1;
        for (int key : map2.keySet()) {
            if (map2.get(key) != max2 && key != max_key2) {
                next_max2 = Math.max(next_max2, map2.get(key));
                if (next_max2 == map2.get(key)) {
                    next_max_key2 = key;
                }
            }
        }
        int res1 = max1;
        int res2 = max2;
        if (max_key1 == max_key2) {
            res1 = Math.max(max1, max2);
            res2 = Math.max(next_max1, next_max2);
        }
        System.out.println(n / 2 - res1 + n / 2 - res2);
        sc.close();
    }
}