



'''simple docstring'''




from random import randint
from tempfile import TemporaryFile

import numpy as np



def    __lowerCamelCase						(      _lowercase			,       _lowercase			,       _lowercase	)   ->    List[Any]:
							UpperCAmelCase  :	Dict							  =	0
							if start < end:
														UpperCAmelCase  :	Optional[Any]							  =	randint(_lowercase			,       _lowercase	)
														UpperCAmelCase  :	Dict							  =	a[end]
														UpperCAmelCase  :	Any							  =	a[pivot]
														UpperCAmelCase  :	List[Any]							  =	temp

														UpperCAmelCase  ,  UpperCAmelCase  :	Optional[int]							  =	_in_place_partition(_lowercase			,       _lowercase			,       _lowercase	)
														count += _in_place_quick_sort(_lowercase			,       _lowercase			,       p - 1	)
														count += _in_place_quick_sort(_lowercase			,       p + 1			,       _lowercase	)
							return count



def    __lowerCamelCase						(      _lowercase			,       _lowercase			,       _lowercase	)   ->    int:
							UpperCAmelCase  :	Any							  =	0
							UpperCAmelCase  :	Optional[int]							  =	randint(_lowercase			,       _lowercase	)
							UpperCAmelCase  :	int							  =	a[end]
							UpperCAmelCase  :	Tuple							  =	a[pivot]
							UpperCAmelCase  :	str							  =	temp
							UpperCAmelCase  :	List[Any]							  =	start - 1
							for index in range(_lowercase			,       _lowercase	):
														count += 1
														if a[index] < a[end]:  # check if current val is less than pivot value
																					UpperCAmelCase  :	Dict							  =	new_pivot_index + 1
																					UpperCAmelCase  :	Dict							  =	a[new_pivot_index]
																					UpperCAmelCase  :	Optional[int]							  =	a[index]
																					UpperCAmelCase  :	Any							  =	temp

							UpperCAmelCase  :	List[Any]							  =	a[new_pivot_index + 1]
							UpperCAmelCase  :	Union[str, Any]							  =	a[end]
							UpperCAmelCase  :	Optional[Any]							  =	temp
							return new_pivot_index + 1, count


a     :    Any      						=					TemporaryFile()
a     :    Dict      						=					1_0_0  # 1000 elements are to be sorted


a						,   a     :    Union[str, Any]      						=					0, 1  # mean and standard deviation
a     :    Optional[int]      						=					np.random.normal(mu, sigma, p)
np.save(outfile, X)
print("""The array is""")
print(X)


outfile.seek(0)  # using the same array
a     :    List[str]      						=					np.load(outfile)
a     :    str      						=					len(M) - 1
a     :    List[str]      						=					_in_place_quick_sort(M, 0, r)

print(
    """No of Comparisons for 100 elements selected from a standard normal distribution"""
    """is :"""
)


print(z)






'''simple docstring'''




a     :    Tuple      						=					[sum(int(c, 1_0) ** 2 for c in i.__str__()) for i in range(1_0_0_0_0_0)]



def    __lowerCamelCase						(      _lowercase	)   ->    int:
							UpperCAmelCase  :	str							  =	0
							while number:
														# Increased Speed Slightly by checking every 5 digits together.
														sum_of_digits_squared += DIGITS_SQUARED[number % 1_0_0_0_0_0]
														number //= 1_0_0_0_0_0

							return sum_of_digits_squared


# There are 2 Chains made,
# One ends with 89 with the chain member 58 being the one which when declared first,
# there will be the least number of iterations for all the members to be checked.

# The other one ends with 1 and has only one element 1.

# So 58 and 1 are chosen to be declared at the starting.

# Changed dictionary to an array to quicken the solution
a     :    list[bool | None]      						=					[None] * 1_0_0_0_0_0_0_0
a     :    Optional[Any]      						=					True
a     :    List[Any]      						=					False



def    __lowerCamelCase						(      _lowercase	)   ->    bool:

							if CHAINS[number - 1] is not None:
														return CHAINS[number - 1]  # type: ignore

							UpperCAmelCase  :	List[str]							  =	chain(next_number(_lowercase	)	)
							UpperCAmelCase  :	Tuple							  =	number_chain

							while number < 1_0_0_0_0_0_0_0:
														UpperCAmelCase  :	List[str]							  =	number_chain
														number *= 1_0

							return number_chain



def    __lowerCamelCase						(      _lowercase = 1_0_0_0_0_0_0_0	)   ->    int:
							for i in range(1			,       _lowercase	):
														if CHAINS[i] is None:
																					chain(i + 1	)

							return CHAINS[:number].count(_lowercase	)


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							print(F'''{solution() = }''')

