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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

class Solution
{
    static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        var v = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        var a = new Dictionary<int, int>();
        var b = new Dictionary<int, int>();

        for (int i = 0; i < v.Length; i++)
        {
            if (i % 2 == 0)
            {
                if (!a.ContainsKey(v[i]))
                {
                    a[v[i]] = 0;
                }
                a[v[i]]++;
            }
            else
            {
                if (!b.ContainsKey(v[i]))
                {
                    b[v[i]] = 0;
                }
                b[v[i]]++;
            }
        }

        var a1st = a.OrderByDescending(x => x.Value).First();
        KeyValuePair<int, int>? a2nd = null;
        if (a.Any(x => x.Key != a1st.Key))
        {
            a2nd = a.Where(x => x.Key != a1st.Key).OrderByDescending(x => x.Value).First();
        }
        var b1st = b.OrderByDescending(x => x.Value).First();
        KeyValuePair<int, int>? b2nd = null;
        if (b.Any(x => x.Key != b1st.Key))
        {
            b2nd = b.Where(x => x.Key != b1st.Key).OrderByDescending(x => x.Value).First();
        }

        int result;
        if (a1st.Key != b1st.Key
            || (a2nd != null && a1st.Value == ((KeyValuePair<int, int>)a2nd).Value)
            || (b2nd != null && b1st.Value == ((KeyValuePair<int, int>)b2nd).Value))
        {
            result = (n / 2 - a1st.Value) + (n / 2 - b1st.Value);
        }
        else
        {
            if (a2nd == null && b2nd == null)
            {
                result = n / 2;
            }
            else if (a2nd == null)
            {
                result = n / 2 - ((KeyValuePair<int, int>)b2nd).Value;
            }
            else if (b2nd == null)
            {
                result = n / 2 - ((KeyValuePair<int, int>)a2nd).Value;
            }
            else
            {
                var a2 = ((KeyValuePair<int, int>)a2nd);
                var b2 = ((KeyValuePair<int, int>)b2nd);

                if (a1st.Value == b1st.Value)
                {
                    result = Math.Min(n / 2 - a2.Value, 2 / n - b2.Value) + (n / 2 - a1st.Value);
                }
                if (a1st.Value > b1st.Value)
                {
                    result = (n / 2 - a1st.Value) + (n / 2 - a2.Value);
                }
                else
                {
                    result = (n / 2 - a2.Value) + (n / 2 - b1st.Value);
                }
            }
        }
        Console.WriteLine(result);
    }
}