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.Scanner;

 class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] arr = new int[n];
//		HashSet<Integer> set = new HashSet<>();
		HashMap<Integer, Integer> map = new HashMap<>();
		for (int i = 0; i < n; i++) {
			arr[i] = sc.nextInt();
			if (map.containsKey(arr[i]))
				map.put(arr[i], map.get(arr[i]) + 1);
			else
				map.put(arr[i], 1);

		}
		int mx = map.get(arr[0]), mx2 = map.get(arr[1]);
		for (int i = 0; i < n - 2; i += 2) {
			if (arr[i] != arr[i + 2]) {
				int cnt = map.get(arr[i]);
				if (cnt > mx)
					mx = cnt;
			}
		}
		for (int i = 1; i < n - 3; i += 2) {
			if (arr[i] != arr[i + 2]) {
				int cnt = map.get(arr[i]);
				if (cnt > mx)
					mx2 = cnt;
			}
		}
		if (map.size() == 1)
			System.out.println(n / 2);
		else
			System.out.println(n - mx - mx2);
	}
}