from random import randint
from tempfile import TemporaryFile

import numpy as np







def      _a					(   lowercase__	:      List[Any]  ,	lowercase__	:      List[Any]  ,	lowercase__	:      Optional[int]			):







     '''simple docstring'''


     SCREAMING_SNAKE_CASE__					:					Tuple      =		0
     if start < end:
          SCREAMING_SNAKE_CASE__					:					List[str]      =		randint(lowercase__  ,	lowercase__			)
          SCREAMING_SNAKE_CASE__					:					Dict      =		a[end]
          SCREAMING_SNAKE_CASE__					:					Tuple      =		a[pivot]
          SCREAMING_SNAKE_CASE__					:					Optional[Any]      =		temp

          SCREAMING_SNAKE_CASE__      ,				SCREAMING_SNAKE_CASE__					:					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      _a					(   lowercase__	:      Optional[Any]  ,	lowercase__	:      List[str]  ,	lowercase__	:      Union[str, Any]			):







     '''simple docstring'''


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

     SCREAMING_SNAKE_CASE__					:					Optional[int]      =		a[new_pivot_index + 1]
     SCREAMING_SNAKE_CASE__					:					Union[str, Any]      =		a[end]
     SCREAMING_SNAKE_CASE__					:					Dict      =		temp
     return new_pivot_index + 1, count


SCREAMING_SNAKE_CASE__		:       Union[str, Any]       						=       TemporaryFile()
SCREAMING_SNAKE_CASE__		:       Any       						=       100  # 1000 elements are to be sorted


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


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

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







print(z)







from __future__ import annotations

import math
def 	_UpperCamelCase					(    lowerCAmelCase_ )    ->bool:

   if 1 < number < 4:
      # 2 and 3 are primes
      return True
   elif number < 2 or number % 2 == 0 or number % 3 == 0:
      # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
      return False

   # All primes number are in format of 6k +/- 1
   for i in range(5	,    int(math.sqrt(lowerCAmelCase_ ) + 1 )	,    6 ):
      if number % i == 0 or number % (i + 2) == 0:
         return False
   return True


__a	 =      [num for num in range(3, 10_0001, 2) if not is_prime(num)]
def 	_UpperCamelCase					(    lowerCAmelCase_ )    ->list[int]:
   if not isinstance(lowerCAmelCase_	,    lowerCAmelCase_ ):
      raise ValueError("""n must be an integer""" )
   if n <= 0:
      raise ValueError("""n must be >= 0""" )

   UpperCAmelCase      					=  []
   for num in range(len(lowerCAmelCase_ ) ):
      UpperCAmelCase      					=  0
      while 2 * i * i <= odd_composites[num]:
         UpperCAmelCase      					=  odd_composites[num] - 2 * i * i
         if is_prime(lowerCAmelCase_ ):
            break
         i += 1
      else:
         list_nums.append(odd_composites[num] )
         if len(lowerCAmelCase_ ) == n:
            return list_nums

   return []
def 	_UpperCamelCase					(    )    ->int:
   return compute_nums(1 )[0]


if __name__ == "__main__":
 print(F"""{solution() = }""")



