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 Q {
  public int key ;
  public int val ;
  public Q( int k , int v ) {key=k;val=v;}
}

class M { static void Main(String[] _) {
  var N = int.Parse( Console.ReadLine() );
  var A = Console.ReadLine().Split(' ');
  
  var B0 = A.Where( (a,i) => i % 2 == 0 );
  var B1 = A.Where( (a,i) => i % 2 == 1 );
  var C0 = B0.GroupBy(i => i).Where(g => g.Count() >= 1).Select(g => new Q( int.Parse(g.Key), g.Count() ) );
  var C1 = B1.GroupBy(i => i).Where(g => g.Count() >= 1).Select(g => new Q( int.Parse(g.Key), g.Count() ) );
  
  while(true) {
    var D0 = C0.Aggregate( new Q(0,0) , (x, y) => x.val > y.val ? x : y );
    var D1 = C1.Aggregate( new Q(0,0) , (x, y) => x.val > y.val ? x : y );
    var N0 = B0.Count() - D0.val;
    var N1 = B1.Count() - D1.val;
    
  	if ( D0.key == D1.key ) {
      int W = (int)(10e5);
      if ( N0 < N1 ) {
      C1 = C1.Select( a => new Q( a.key + W , a.val ) );
        continue;
      }      
      C0 = C0.Select( a => new Q( a.key + W , a.val ) );
      continue;      
    }
    
    var result = N0 + N1;
    Console.WriteLine(result);
    return;
  }
  
  
}}