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.*;
import java.util.stream.Collectors;
import java.util.stream.Stream;

public class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int num = sc.nextInt();

        Map<Integer, Integer> map1 = new HashMap<>();
        Map<Integer, Integer> map2 = new HashMap<>();
        for( int i=1;i<= num; i++ ) {
            int val = Integer.valueOf(sc.nextInt());
            if( i%2 == 0 ) {
                map2.put( val, map2.getOrDefault( val, 0 ) + 1 );
                continue;
            }
            map1.put( val, map1.getOrDefault( val, 0 ) + 1 );
        }
        Stream<Map.Entry<Integer, Integer>> s1 = map1.entrySet().stream().sorted((o1, o2) -> Integer.compare(o2.getValue(), o1.getValue()));
        int aNum = s1.map(Map.Entry::getValue).collect(Collectors.toList()).get(0);
        s1 = map1.entrySet().stream().sorted((o1, o2) -> Integer.compare(o2.getValue(), o1.getValue()));
        int aKey = s1.map(Map.Entry::getKey).collect(Collectors.toList()).get(0);

        Stream<Map.Entry<Integer, Integer>> s2 = map2.entrySet().stream().sorted((o1, o2) -> Integer.compare(o2.getValue(), o1.getValue()));
        int bNum = s2.map(Map.Entry::getValue).collect(Collectors.toList()).get(0);
        s2 = map2.entrySet().stream().sorted((o1, o2) -> Integer.compare(o2.getValue(), o1.getValue()));
        int bKey = s2.map(Map.Entry::getKey).collect(Collectors.toList()).get(0);

        aNum = (num%2 == aNum) ? 0 : Math.abs( (num%2) - aNum );
        bNum = (num%2 == bNum) ? 0 : Math.abs( (num%2) - bNum );

        if( aKey == bKey ) {
            aNum = num%2;
            bNum = 0;
        }
        System.out.println( aNum + bNum );
    }
}