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.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC111C_cs
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var sq = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var x = new Sequence(n, sq);
            Console.WriteLine(x.MininumChange());
        }
    }
    public class Sequence
    {
        private readonly int n;
        private readonly int[] num;
        private int[] oddnum;
        private int[] evennum;
        public Sequence(int n, int[] num)
        {
            this.n = n;
            this.num = num;
            oddnum = num.Where((x, index) => index % 2 == 1).ToArray();
            evennum = num.Where((x, index) => index % 2 == 0).ToArray();
        }

        public int MininumChange()
        {
            var tmpOdd = oddnum.GroupBy(x => x).Select(x => new { Val = x.Key, Cnt = x.Count() }).OrderByDescending(x => x.Cnt);
            var oddnumFirstMode = tmpOdd.First();
            var tmpEven = evennum.GroupBy(x => x).Select(x => new { Val = x.Key, Cnt = x.Count() }).OrderByDescending(x => x.Cnt);
            var evennumFirstMode = tmpEven.First();
            if (oddnumFirstMode.Val != evennumFirstMode.Val)
            {
                return oddnum.Length - oddnumFirstMode.Cnt + evennum.Length - evennumFirstMode.Cnt;
            }
            else
            {
                int result1 = int.MaxValue;
                int result2 = int.MaxValue;
                if (tmpEven.Count() == 1 && tmpOdd.Count() == 1)
                {
                    return num.Length / 2;
                }
                if (tmpOdd.Count() > 1)
                {
                    var oddnumSecondModeCnt = tmpOdd.Skip(1).First().Cnt;
                    result1 = oddnum.Length - oddnumSecondModeCnt + evennum.Length - evennumFirstMode.Cnt;
                }
                if (tmpEven.Count() > 1)
                {
                    var evennumSecondModeCnt = tmpEven.Skip(1).First().Cnt;
                    result2 = oddnum.Length - oddnumFirstMode.Cnt + evennum.Length - evennumSecondModeCnt;
                }
                return Math.Min(result1, result2);
            }
        }
    }
}