bool Palindrome( const apstring & A )
     {
         for( int i = 0; i < A.length( ) / 2; i++ )
         {
             if( A[ i ] != A[ A.length( ) - ( i + 1 ) )
                 return false;
         }
 
         return true;
     }

     bool Equals( const apvector & v1, const apvector & v2 )
     {
         if( v1.length( ) != v2.length( ) )
             return false;

         for( int i = 0; i < v1.length( ); i++ )
         {
             if( v1[ i ] != v2[ i ] )
                 return false;
         }
 
         return true;
     }

     apvector WithoutDuplicates( const apvector & v )
     {
         apvector copy = v;
         apvector answer;
         int itemsCopied = 1;

         if( v.length( ) == 0 )
             return copy;

         sort( copy );
         answer.resize( copy.length( ) );

         answer[ 0 ] = copy[ 0 ];
         for( int i = 1; i < copy.length( ); i++ )
         {
             if( copy[ i ] != copy[ i - 1 ] )
             {
                 answer[ itemsCopied ] = copy[ i ];
                 itemsCopied++;
             }
         }

         answer.resize( itemsCopied ); 

         return answer;
     }