





import math




def 			lowerCAmelCase_			(				UpperCamelCase_	)  ->		Tuple:
       UpperCamelCase_ 							=	0
       if n % 2 == 0:
              count += 1
              while n % 2 == 0:
                     UpperCamelCase_ 							=	int(n / 2	)
    # the n input value must be odd so that
    # we can skip one element (ie i += 2)

       UpperCamelCase_ 							=	3

       while i <= int(math.sqrt(UpperCamelCase_	)	):
              if n % i == 0:
                     count += 1
                     while n % i == 0:
                            UpperCamelCase_ 							=	int(n / i	)
              UpperCamelCase_ 							=	i + 2

       # this condition checks the prime
       # number n is greater than 2

       if n > 2:
              count += 1
       return count


if __name__ == "__main__":
     _UpperCAmelCase										=					5_1_2_4_2_1_8_3
     print(f'''The number of distinct prime factors is/are {exact_prime_factor_count(n)}''')
     print(f'''The value of log(log(n)) is {math.log(math.log(n)):.4f}''')









"""simple docstring"""




UpperCamelCase											=     [
    [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0],
    [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
    [0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0],
    [0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0],
]






def 							lowerCAmelCase			(   UpperCamelCase_:				int  ,			UpperCamelCase_:				int  ,			UpperCamelCase_:				int  ,			UpperCamelCase_:				int       )							->				bool:







  '''simple docstring'''







  return 0 <= row < rows and 0 <= col < cols






def 							lowerCAmelCase			(   UpperCamelCase_:				int  ,			UpperCamelCase_:				int  ,			UpperCamelCase_:				set  ,			UpperCamelCase_:				list[list[int]]       )							->				int:







  '''simple docstring'''







  _a					      =						len(UpperCamelCase_       )
  _a					      =						len(mat[0]       )
  if is_safe(UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_       ) and (row, col) not in seen and mat[row][col] == 1:
    seen.add((row, col)       )
    return (
        1
        + depth_first_search(row + 1  ,			UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_       )
        + depth_first_search(row - 1  ,			UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_       )
        + depth_first_search(UpperCamelCase_  ,			col + 1  ,			UpperCamelCase_  ,			UpperCamelCase_       )
        + depth_first_search(UpperCamelCase_  ,			col - 1  ,			UpperCamelCase_  ,			UpperCamelCase_       )
    )
  else:
    return 0






def 							lowerCAmelCase			(   UpperCamelCase_:				list[list[int]]       )							->				int:







  '''simple docstring'''







  _a					      =						set()

  _a					      =						0
  for row, line in enumerate(UpperCamelCase_       ):
    for col, item in enumerate(UpperCamelCase_       ):
      if item == 1 and (row, col) not in seen:
        # Maximizing the area
        _a					      =						max(UpperCamelCase_  ,			depth_first_search(UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_       )       )
  return max_area


if __name__ == "__main__":
     import doctest

     print(find_max_area(matrix))  # Output -> 6
     doctest.testmod()


