'''simple docstring'''

from math import sqrt
def      __UpperCamelCase			(  UpperCAmelCase	):
 assert isinstance(a__						,	a__	) and (
     number >= 0
 ), "'number' must been an int and positive"

 lowercase__							:       Union[str, Any]										=   True

 # 0 and 1 are none primes.
 if number <= 1:
  lowercase__							:       Tuple										=   False

 for divisor in range(2						,	int(round(sqrt(a__	)	)	) + 1	):
  # if 'number' divisible by 'divisor' then sets 'status'
  # of false and break up the loop.
  if number % divisor == 0:
   lowercase__							:       List[str]										=   False
   break

    # precondition
 assert isinstance(a__						,	a__	), "'status' must been from type bool"

 return status
def      __UpperCamelCase			(  UpperCAmelCase	):
 assert isinstance(a__						,	a__	) and (n > 2), "'N' must been an int and > 2"

 # beginList: contains all natural numbers from 2 up to N
 lowercase__							:       int										=   list(range(2						,	n + 1	)	)

 lowercase__							:       Any										=   []  # this list will be returns.

 # actual sieve of erathostenes
 for i in range(len(a__	)	):
  for j in range(i + 1						,	len(a__	)	):
   if (begin_list[i] != 0) and (begin_list[j] % begin_list[i] == 0):
    lowercase__							:       Any										=   0

    # filters actual prime numbers.
 lowercase__							:       List[str]										=   [x for x in begin_list if x != 0]

 # precondition
 assert isinstance(a__						,	a__	), "'ans' must been from type list"

 return ans
def      __UpperCamelCase			(  UpperCAmelCase	):
 assert isinstance(a__						,	a__	) and (n > 2), "'N' must been an int and > 2"

 lowercase__							:       List[Any]										=   []

 # iterates over all numbers between 2 up to N+1
 # if a number is prime then appends to list 'ans'
 for number in range(2						,	n + 1	):
  if is_prime(a__	):
   ans.append(a__	)

    # precondition
 assert isinstance(a__						,	a__	), "'ans' must been from type list"

 return ans
def      __UpperCamelCase			(  UpperCAmelCase	):
 assert isinstance(a__						,	a__	) and number >= 0, "'number' must been an int and >= 0"

 lowercase__							:       Any										=   []  # this list will be returns of the function.

 # potential prime number factors.

 lowercase__							:       Dict										=   2

 lowercase__							:       List[Any]										=   number

 if number == 0 or number == 1:
  ans.append(a__	)

 # if 'number' not prime then builds the prime factorization of 'number'
 elif not is_prime(a__	):
  while quotient != 1:
   if is_prime(a__	) and (quotient % factor == 0):
    ans.append(a__	)
    quotient /= factor
   else:
    factor += 1

 else:
  ans.append(a__	)

 # precondition
 assert isinstance(a__						,	a__	), "'ans' must been from type list"

 return ans
def      __UpperCamelCase			(  UpperCAmelCase	):
 assert isinstance(a__						,	a__	) and (
     number >= 0
 ), "'number' bust been an int and >= 0"

 lowercase__							:       Any										=   0

 # prime factorization of 'number'
 lowercase__							:       Union[str, Any]										=   prime_factorization(a__	)

 lowercase__							:       List[str]										=   max(a__	)

 # precondition
 assert isinstance(a__						,	a__	), "'ans' must been from type int"

 return ans
def      __UpperCamelCase			(  UpperCAmelCase	):
 assert isinstance(a__						,	a__	) and (
     number >= 0
 ), "'number' bust been an int and >= 0"

 lowercase__							:       List[Any]										=   0

 # prime factorization of 'number'
 lowercase__							:       List[Any]										=   prime_factorization(a__	)

 lowercase__							:       Optional[int]										=   min(a__	)

 # precondition
 assert isinstance(a__						,	a__	), "'ans' must been from type int"

 return ans
def      __UpperCamelCase			(  UpperCAmelCase	):
 assert isinstance(a__						,	a__	), "'number' must been an int"
 assert isinstance(number % 2 == 0						,	a__	), "compare bust been from type bool"

 return number % 2 == 0
def      __UpperCamelCase			(  UpperCAmelCase	):
 assert isinstance(a__						,	a__	), "'number' must been an int"
 assert isinstance(number % 2 != 0						,	a__	), "compare bust been from type bool"

 return number % 2 != 0
def      __UpperCamelCase			(  UpperCAmelCase	):
 assert (
     isinstance(a__						,	a__	) and (number > 2) and is_even(a__	)
 ), "'number' must been an int, even and > 2"

 lowercase__							:       List[str]										=   []  # this list will returned

 # creates a list of prime numbers between 2 up to 'number'
 lowercase__							:       List[Any]										=   get_prime_numbers(a__	)
 lowercase__							:       Optional[int]										=   len(a__	)

 # run variable for while-loops.
 lowercase__							:       List[Any]										=   0
 lowercase__							:       List[Any]										=   None

 # exit variable. for break up the loops
 lowercase__							:       Any										=   True

 while i < len_pn and loop:
  lowercase__							:       Union[str, Any]										=   i + 1

  while j < len_pn and loop:
   if prime_numbers[i] + prime_numbers[j] == number:
    lowercase__							:       Any										=   False
    ans.append(prime_numbers[i]	)
    ans.append(prime_numbers[j]	)

   j += 1

  i += 1

 # precondition
 assert (
     isinstance(a__						,	a__	)
     and (len(a__	) == 2)
     and (ans[0] + ans[1] == number)
     and is_prime(ans[0]	)
     and is_prime(ans[1]	)
 ), "'ans' must contains two primes. And sum of elements must been eq 'number'"

 return ans
def      __UpperCamelCase			(  UpperCAmelCase						,	UpperCAmelCase	):
 assert (
     isinstance(a__						,	a__	)
     and isinstance(a__						,	a__	)
     and (numbera >= 0)
     and (numbera >= 0)
 ), "'number1' and 'number2' must been positive integer."

 lowercase__							:       List[str]										=   0

 while numbera != 0:
  lowercase__							:       Tuple										=   numbera % numbera
  lowercase__							:       List[Any]										=   numbera
  lowercase__							:       Union[str, Any]										=   rest

 # precondition
 assert isinstance(a__						,	a__	) and (
     numbera >= 0
 ), "'number' must been from type int and positive"

 return numbera
def      __UpperCamelCase			(  UpperCAmelCase						,	UpperCAmelCase	):
 assert (
     isinstance(a__						,	a__	)
     and isinstance(a__						,	a__	)
     and (numbera >= 1)
     and (numbera >= 1)
 ), "'number1' and 'number2' must been positive integer."

 lowercase__							:       List[Any]										=   1  # actual answer that will be return.

 # for kgV (x,1)
 if numbera > 1 and numbera > 1:
  # builds the prime factorization of 'number1' and 'number2'
  lowercase__							:       List[str]										=   prime_factorization(a__	)
  lowercase__							:       Tuple										=   prime_factorization(a__	)

 elif numbera == 1 or numbera == 1:
  lowercase__							:       List[Any]										=   []
  lowercase__							:       int										=   []
  lowercase__							:       List[Any]										=   max(a__						,	a__	)

 lowercase__							:       str										=   0
 lowercase__							:       Any										=   0

 lowercase__							:       int										=   []  # captured numbers int both 'primeFac1' and 'primeFac2'

 # iterates through primeFac1
 for n in prime_fac_a:
  if n not in done:
   if n in prime_fac_a:
    lowercase__							:       int										=   prime_fac_a.count(a__	)
    lowercase__							:       Optional[Any]										=   prime_fac_a.count(a__	)

    for _ in range(max(a__						,	a__	)	):
     ans *= n

   else:
    lowercase__							:       Union[str, Any]										=   prime_fac_a.count(a__	)

    for _ in range(a__	):
     ans *= n

   done.append(a__	)

    # iterates through primeFac2
 for n in prime_fac_a:
  if n not in done:
   lowercase__							:       str										=   prime_fac_a.count(a__	)

   for _ in range(a__	):
    ans *= n

   done.append(a__	)

    # precondition
 assert isinstance(a__						,	a__	) and (
     ans >= 0
 ), "'ans' must been from type int and positive"

 return ans
def      __UpperCamelCase			(  UpperCAmelCase	):
 assert isinstance(a__						,	a__	) and (n >= 0), "'number' must been a positive int"

 lowercase__							:       int										=   0
 lowercase__							:       str										=   2  # this variable holds the answer

 while index < n:
  index += 1

  ans += 1  # counts to the next number

  # if ans not prime then
  # runs to the next prime number.
  while not is_prime(a__	):
   ans += 1

    # precondition
 assert isinstance(a__						,	a__	) and is_prime(
     a__	), "'ans' must been a prime number and from type int"

 return ans
def      __UpperCamelCase			(  UpperCAmelCase						,	UpperCAmelCase	):
 assert (
     is_prime(a__	) and is_prime(a__	) and (p_number_a < p_number_a)
 ), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

 lowercase__							:       Optional[Any]										=   p_number_a + 1  # jump to the next number

 lowercase__							:       str										=   []  # this list will be returns.

 # if number is not prime then
 # fetch the next prime number.
 while not is_prime(a__	):
  number += 1

 while number < p_number_a:
  ans.append(a__	)

  number += 1

  # fetch the next prime number.
  while not is_prime(a__	):
   number += 1

    # precondition
 assert (
     isinstance(a__						,	a__	)
     and ans[0] != p_number_a
     and ans[len(a__	) - 1] != p_number_a
 ), "'ans' must been a list without the arguments"

 # 'ans' contains not 'pNumber1' and 'pNumber2' !
 return ans
def      __UpperCamelCase			(  UpperCAmelCase	):
 assert isinstance(a__						,	a__	) and (n >= 1), "'n' must been int and >= 1"

 lowercase__							:       Optional[Any]										=   []  # will be returned.

 for divisor in range(1						,	n + 1	):
  if n % divisor == 0:
   ans.append(a__	)

    # precondition
 assert ans[0] == 1 and ans[len(a__	) - 1] == n, "Error in function getDivisiors(...)"

 return ans
def      __UpperCamelCase			(  UpperCAmelCase	):
 assert isinstance(a__						,	a__	) and (
     number > 1
 ), "'number' must been an int and >= 1"

 lowercase__							:       int										=   get_divisors(a__	)

 # precondition
 assert (
     isinstance(a__						,	a__	)
     and (divisors[0] == 1)
     and (divisors[len(a__	) - 1] == number)
 ), "Error in help-function getDivisiors(...)"

 # summed all divisors up to 'number' (exclusive), hence [:-1]
 return sum(divisors[:-1]	) == number
def      __UpperCamelCase			(  UpperCAmelCase						,	UpperCAmelCase	):
 assert (
     isinstance(a__						,	a__	)
     and isinstance(a__						,	a__	)
     and (denominator != 0)
 ), "The arguments must been from type int and 'denominator' != 0"

 # build the greatest common divisor of numerator and denominator.
 lowercase__							:       Dict										=   gcd(abs(a__	)						,	abs(a__	)	)

 # precondition
 assert (
     isinstance(a__						,	a__	)
     and (numerator % gcd_of_fraction == 0)
     and (denominator % gcd_of_fraction == 0)
 ), "Error in function gcd(...,...)"

 return (numerator // gcd_of_fraction, denominator // gcd_of_fraction)
def      __UpperCamelCase			(  UpperCAmelCase	):
 assert isinstance(a__						,	a__	) and (n >= 0), "'n' must been a int and >= 0"

 lowercase__							:       Optional[Any]										=   1  # this will be return.

 for factor in range(1						,	n + 1	):
  ans *= factor

 return ans





def      __UpperCamelCase			(  UpperCAmelCase	):
 assert isinstance(a__						,	a__	) and (n >= 0), "'n' must been an int and >= 0"

 lowercase__							:       Any										=   0
 lowercase__							:       str										=   1
 lowercase__							:       str										=   1  # this will be return

 for _ in range(n - 1	):
  lowercase__							:       str										=   ans
  ans += fiba
  lowercase__							:       List[str]										=   tmp

 return ans








from manim import *

class 							__SCREAMING_SNAKE_CASE       (  _a							):






							def 					_lowerCamelCase		(    self	):
														UpperCamelCase__					  =      Rectangle(height=0.5	,			width=0.5	)
														UpperCamelCase__					  =      Rectangle(height=0.25	,			width=0.25	)
														UpperCamelCase__					  =      Rectangle(height=0.46	,			width=0.46	).set_stroke(width=0	)

														UpperCamelCase__					  =      [mem.copy() for i in range(6	)]
														UpperCamelCase__					  =      [mem.copy() for i in range(6	)]
														UpperCamelCase__					  =      VGroup(*__lowerCAmelCase	).arrange(__lowerCAmelCase	,			buff=0	)
														UpperCamelCase__					  =      VGroup(*__lowerCAmelCase	).arrange(__lowerCAmelCase	,			buff=0	)
														UpperCamelCase__					  =      VGroup(__lowerCAmelCase	,			__lowerCAmelCase	).arrange(__lowerCAmelCase	,			buff=0	)
														UpperCamelCase__					  =      Text("""CPU"""	,			font_size=24	)
														UpperCamelCase__					  =      Group(__lowerCAmelCase	,			__lowerCAmelCase	).arrange(__lowerCAmelCase	,			buff=0.5	,			aligned_edge=__lowerCAmelCase	)
														cpu.move_to([-2.5, -0.5, 0]	)
														self.add(__lowerCAmelCase	)

														UpperCamelCase__					  =      [mem.copy() for i in range(4	)]
														UpperCamelCase__					  =      VGroup(*__lowerCAmelCase	).arrange(__lowerCAmelCase	,			buff=0	)
														UpperCamelCase__					  =      Text("""GPU"""	,			font_size=24	)
														UpperCamelCase__					  =      Group(__lowerCAmelCase	,			__lowerCAmelCase	).arrange(__lowerCAmelCase	,			buff=0.5	,			aligned_edge=__lowerCAmelCase	)
														gpu.move_to([-1, -1, 0]	)
														self.add(__lowerCAmelCase	)

														UpperCamelCase__					  =      [mem.copy() for i in range(6	)]
														UpperCamelCase__					  =      VGroup(*__lowerCAmelCase	).arrange(__lowerCAmelCase	,			buff=0	)

														UpperCamelCase__					  =      Text("""Model"""	,			font_size=24	)
														UpperCamelCase__					  =      Group(__lowerCAmelCase	,			__lowerCAmelCase	).arrange(__lowerCAmelCase	,			buff=0.5	,			aligned_edge=__lowerCAmelCase	)
														model.move_to([3, -1.0, 0]	)
														self.add(__lowerCAmelCase	)

														UpperCamelCase__					  =      []
														UpperCamelCase__					  =      []
														UpperCamelCase__					  =      []

														for i, rect in enumerate(__lowerCAmelCase	):
																					rect.set_stroke(__lowerCAmelCase	)

																					UpperCamelCase__					  =      Rectangle(height=0.46 / 4	,			width=0.46 / 3	).set_stroke(width=0.0	).set_fill(__lowerCAmelCase	,			opacity=0.7	)

																					if i == 0:
																												cpu_target.next_to(cpu_left_col_base[0].get_corner(DOWN + LEFT	)	,			buff=0.02	,			direction=__lowerCAmelCase	)
																												cpu_target.set_x(cpu_target.get_x() + 0.1	)
																					elif i == 3:
																												cpu_target.next_to(model_cpu_arr[0]	,			direction=__lowerCAmelCase	,			buff=0.0	)
																					else:
																												cpu_target.next_to(model_cpu_arr[i - 1]	,			direction=__lowerCAmelCase	,			buff=0.0	)
																					self.add(__lowerCAmelCase	)
																					model_cpu_arr.append(__lowerCAmelCase	)

														self.add(*__lowerCAmelCase	,			*__lowerCAmelCase	,			*__lowerCAmelCase	)

														UpperCamelCase__					  =      [mem.copy() for i in range(6	)]
														UpperCamelCase__					  =      VGroup(*__lowerCAmelCase	).arrange(__lowerCAmelCase	,			buff=0	)

														UpperCamelCase__					  =      Text("""Loaded Checkpoint"""	,			font_size=24	)
														UpperCamelCase__					  =      Group(__lowerCAmelCase	,			__lowerCAmelCase	).arrange(__lowerCAmelCase	,			buff=0.5	,			aligned_edge=__lowerCAmelCase	)
														checkpoint.move_to([3, 0.5, 0]	)

														self.add(__lowerCAmelCase	)

														UpperCamelCase__					  =      []
														UpperCamelCase__					  =      []

														for i, rect in enumerate(__lowerCAmelCase	):
																					UpperCamelCase__					  =      fill.copy().set_fill(__lowerCAmelCase	,			opacity=0.7	)
																					target.move_to(__lowerCAmelCase	)
																					ckpt_arr.append(__lowerCAmelCase	)

																					UpperCamelCase__					  =      target.copy()
																					if i < 5:
																												cpu_target.move_to(cpu_left_col_base[i + 1]	)
																					else:
																												cpu_target.move_to(cpu_right_col_base[i - 5]	)
																					ckpt_cpu_arr.append(__lowerCAmelCase	)
														self.add(*__lowerCAmelCase	,			*__lowerCAmelCase	)

														UpperCamelCase__					  =      Square(side_length=2.2	)
														key.move_to([-5, 2, 0]	)

														UpperCamelCase__					  =      MarkupText(
														    f"""<b>Key:</b>\n\n<span fgcolor='{YELLOW}'>●</span> Empty Model"""	,			font_size=18	,			)

														key_text.move_to([-5, 2.4, 0]	)

														self.add(__lowerCAmelCase	,			__lowerCAmelCase	)

														UpperCamelCase__					  =      MarkupText(
														    f"""<span fgcolor='{BLUE}'>●</span> Checkpoint"""	,			font_size=18	,			)

														blue_text.next_to(__lowerCAmelCase	,			DOWN * 2.4	,			aligned_edge=key_text.get_left()	)
														self.add(__lowerCAmelCase	)

														UpperCamelCase__					  =      MarkupText(
														    f"""Based on the passed in configuration, weights are stored in\na variety of np.memmaps on disk or to a particular device."""	,			font_size=24	,			)
														step_a.move_to([2, 2, 0]	)

														UpperCamelCase__					  =      [meta_mem.copy() for i in range(6	)]
														UpperCamelCase__					  =      [meta_mem.copy() for i in range(6	)]
														UpperCamelCase__					  =      VGroup(*__lowerCAmelCase	).arrange(__lowerCAmelCase	,			buff=0	)
														UpperCamelCase__					  =      VGroup(*__lowerCAmelCase	).arrange(__lowerCAmelCase	,			buff=0	)
														UpperCamelCase__					  =      VGroup(__lowerCAmelCase	,			__lowerCAmelCase	).arrange(__lowerCAmelCase	,			buff=0	)
														UpperCamelCase__					  =      Text("""Disk"""	,			font_size=24	)
														UpperCamelCase__					  =      Group(__lowerCAmelCase	,			__lowerCAmelCase	).arrange(__lowerCAmelCase	,			buff=0.5	,			aligned_edge=__lowerCAmelCase	)
														disk.move_to([-4.0, -1.25, 0]	)
														self.play(Write(__lowerCAmelCase	,			run_time=3	)	,			Write(__lowerCAmelCase	,			run_time=1	)	,			Create(__lowerCAmelCase	,			run_time=1	)	)

														UpperCamelCase__					  =      []
														for i, rect in enumerate(__lowerCAmelCase	):
																					UpperCamelCase__					  =      rect.copy()
																					target.generate_target()
																					target.target.move_to(disk_left_col_base[i]	).scale(0.5	)
																					animations.append(MoveToTarget(__lowerCAmelCase	,			run_time=1.5	)	)
														self.play(*__lowerCAmelCase	)

														self.play(FadeOut(__lowerCAmelCase	)	)

														UpperCamelCase__					  =      MarkupText(f"""Then, the checkpoint is removed from memory\nthrough garbage collection."""	,			font_size=24	)
														step_a.move_to([2, 2, 0]	)

														self.play(Write(__lowerCAmelCase	,			run_time=3	)	)

														self.play(
														    FadeOut(__lowerCAmelCase	,			__lowerCAmelCase	,			*__lowerCAmelCase	,			*__lowerCAmelCase	)	,			)

														self.wait()




