





from __future__ import annotations




def 			__snake_case						(      __A ,__A    )		->				Optional[int]:
   lowercase    :			List[str]  =       [None] * (len(lowercase_    ) + len(lowercase_    ))

   lowercase    :			Dict  =       0  # pointer to current index for left Half
   lowercase    :			Any  =       0  # pointer to current index for the right Half
   lowercase    :			List[Any]  =       0  # pointer to current index for the sorted array Half

   while pointera < len(lowercase_    ) and pointera < len(lowercase_    ):
      if left_half[pointera] < right_half[pointera]:
         lowercase    :			Optional[int]  =       left_half[pointera]
         pointera += 1
         index += 1
      else:
         lowercase    :			List[Any]  =       right_half[pointera]
         pointera += 1
         index += 1
   while pointera < len(lowercase_    ):
      lowercase    :			Tuple  =       left_half[pointera]
      pointera += 1
      index += 1

   while pointera < len(lowercase_    ):
      lowercase    :			Optional[int]  =       right_half[pointera]
      pointera += 1
      index += 1

   return sorted_array




def 			__snake_case						(      __A    )		->				List[str]:







   if len(lowercase_    ) <= 1:
      return array
   # the actual formula to calculate the middle element = left + (right - left) // 2
   # this avoids integer overflow in case of large N
   lowercase    :			int  =       0 + (len(lowercase_    ) - 0) // 2

   # Split the array into halves till the array length becomes equal to One
   # merge the arrays of single length returned by mergeSort function and
   # pass them into the merge arrays function which merges the array
   lowercase    :			int  =       array[:middle]
   lowercase    :			Union[str, Any]  =       array[middle:]

   return merge(merge_sort(lowercase_    ) ,merge_sort(lowercase_    )    )


if __name__ == "__main__":
   import doctest

   doctest.testmod()









"""simple docstring"""
import math




def 			__snake_case						(      __A    )		->				float:
   lowercase    :			List[Any]  =       math.log(2 ,10    ) * number
   lowercase    :			Tuple  =       round((log_number - int(__A    )) ,15    )

   return difference




def 			__snake_case						(      __A = 678910    )		->				int:
   lowercase    :			Any  =       90
   lowercase    :			Optional[Any]  =       0

   lowercase    :			List[str]  =       math.log(1.23 ,10    )
   lowercase    :			str  =       math.log(1.24 ,10    )
   lowercase    :			str  =       0

   while position < number:
      lowercase    :			Optional[Any]  =       log_difference(__A    )

      if difference >= upper_limit:
         power_iterator += 93

      elif difference < lower_limit:
         power_iterator += 196

      else:
         lowercase    :			List[Any]  =       power_iterator
         power_iterator += 196
         position += 1

   return previous_power


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   print(F'{solution() = }')


