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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text;

class Program
{
    static int n;
    static int[] v;

    public static void Main(string[] args)
    {
        n = Input.NextInt();
        v = Input.LineInt();

        var d0 = SepBuket(0);
        var d1 = SepBuket(1);
        var dorderedbynum0 = d0.OrderBy(n => -n.Value).ToList();
        var dorderedbynum1 = d1.OrderBy(n => -n.Value).ToList();

        int min = int.MaxValue;
        min = Math.Min(min, NewMethod(dorderedbynum0, dorderedbynum1));
        min = Math.Min(min, NewMethod(dorderedbynum1, dorderedbynum0));

        Console.WriteLine(min);
    }

    private static int NewMethod(List<KeyValuePair<int, int>> dorderedbynum0, List<KeyValuePair<int, int>> dorderedbynum1)
    {
        int n_2 = v.Length / 2;
        int min = int.MaxValue;
        foreach (var do0 in dorderedbynum0)
        {
            if (do0.Key == 100000)
                continue;

            var nn = n_2 - do0.Value;
            if (nn > min)
                break;
            var okat1 = dorderedbynum1.FirstOrDefault(n => n.Key > do0.Key);
            if (default(KeyValuePair<int, int>).Equals(okat1))
            {
                min = Math.Min(min, nn + n_2);
            }
            else
            {
                min = Math.Min(min, nn + (n_2 - okat1.Value));
            }
        }

        return min;
    }

    private static Dictionary<int, int> SepBuket(int start)
    {
        var dic0 = new Dictionary<int, int>();
        for (int i = start; i < v.Length; i += 2)
        {
            if (!dic0.ContainsKey(v[i]))
                dic0[v[i]] = 0;
            dic0[v[i]]++;
        }
        return dic0;
    }
}

public static class Input
{
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}