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: Accepted)


import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.Scanner;

class Main {

    static final int MOD = 1000000007;

    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();
        }
        HashMap<Integer, Integer> evenmap = new HashMap<Integer, Integer>();
        HashMap<Integer, Integer> oddmap = new HashMap<Integer, Integer>();
        for (int i = 0; i < N; i++) {
            if (i % 2 == 0) {
                int cnt;
                if (evenmap.containsKey(v[i]))
                    cnt = evenmap.get(v[i]) + 1;
                else
                    cnt = 1;

                evenmap.put(v[i], cnt);
            } else {
                int cnt;
                if (oddmap.containsKey(v[i]))
                    cnt = oddmap.get(v[i]) + 1;
                else
                    cnt = 1;

                oddmap.put(v[i], cnt);
            }
        }
        int evmax = 0, evsec = 0, evmaxnum = 0;
        int odmax = 0, odsec = 0, odmaxnum = 0;
        for (int i = 0; i < N; i++) {
            if (i % 2 == 0) {
                int cnt = evenmap.get(v[i]);
                if (cnt > evmax) {
                    evsec = evmax;
                    evmax = cnt;
                    evmaxnum = v[i];
                } else if (v[i] != evmaxnum && cnt > evsec) {
                    evsec = cnt;
                }
            } else {
                int cnt = oddmap.get(v[i]);
                if (cnt > odmax) {
                    odsec = odmax;
                    odmax = cnt;
                    odmaxnum = v[i];
                } else if (v[i] != odmaxnum && cnt > odsec) {
                    odsec = cnt;
                }
            }
        }
        // ArrayList<Integer> evcnt = new ArrayList<Integer>(evenmap.values());
        // Collections.sort(evcnt, Comparator.reverseOrder());
        // ArrayList<Integer> odcnt = new ArrayList<Integer>(oddmap.values());
        // Collections.sort(odcnt, Comparator.reverseOrder());
        if (evmaxnum != odmaxnum) {
            System.out.println(N - evmax - odmax);
        } else {
            System.out.println(Math.min(N - evmax - odsec, N - evsec - odmax));
        }

    }
}