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.*;

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

        AbstractMap.SimpleEntry<Integer, Integer> a1 = new AbstractMap.SimpleEntry<>(0, 0);
        AbstractMap.SimpleEntry<Integer, Integer> b1 = new AbstractMap.SimpleEntry<>(0, 0);
        AbstractMap.SimpleEntry<Integer, Integer> a2 = new AbstractMap.SimpleEntry<>(0, 0);
        AbstractMap.SimpleEntry<Integer, Integer> b2 = new AbstractMap.SimpleEntry<>(0, 0);
        for( int i=1; i<= num; i++ ) {
            int val = sc.nextInt();
            if( i%4 == 0 ) {
                if( b1.getKey() == val ) {
                    b1 = new AbstractMap.SimpleEntry<>(val, b1.getValue()+1);
                } else {
                    b2 = new AbstractMap.SimpleEntry<>(val, 1);
                }
                continue;
            }
            if( i%3 == 0 && i%2 != 0 ) {
                if( a1.getKey() == val ) {
                    a1 = new AbstractMap.SimpleEntry<>(val, a1.getValue()+1);
                } else {
                    a2 = new AbstractMap.SimpleEntry<>(val, 1);
                }
                continue;
            }
            if( i%2 == 0 ) {
                if( b2.getKey() == val ) {
                    b2 = new AbstractMap.SimpleEntry<>(val, b2.getValue()+1);
                } else {
                    b1 = new AbstractMap.SimpleEntry<>(val, 1);
                }
                continue;
            }
            if( a2.getKey() == val ) {
                a2 = new AbstractMap.SimpleEntry<>(val, a2.getValue()+1);
            } else {
                a1 = new AbstractMap.SimpleEntry<>(val, 1);
            }
        }
        int a = 0, b = 0;
        if( a2.getValue() != 0 ) {
            a = (a1.getValue() > a2.getValue()) ? a1.getValue() : a2.getValue();
            if( a< 0 ) a *= -1;
            a = (num / 2) - a;
        }
        if( b2.getValue() != 0 ) {
            b = (b1.getValue() > b2.getValue()) ? b1.getValue() : b2.getValue();
            if( b< 0 ) b *= -1;
            b = (num / 2) - b;
        }
        int result = a + b;
        if( result == 0 && a1.getKey() == b1.getKey() ) result = num / 2;

        System.out.println( result );
    }
}