






from __future__ import annotations

import math





def 				snake_case  (     lowerCamelCase					):




 '''simple docstring'''







 if num <= 0:
  __lowercase             =  F'{num}: Invalid input, please enter a positive integer.'
  raise ValueError(SCREAMING_SNAKE_CASE__					)

 __lowercase             =  [True] * (num + 1)
 __lowercase             =  []
 __lowercase             =  2
 __lowercase             =  int(math.sqrt(SCREAMING_SNAKE_CASE__					)					)

 while start <= end:
  # If start is a prime
  if sieve[start] is True:
   prime.append(SCREAMING_SNAKE_CASE__					)

   # Set multiples of start be False
   for i in range(start * start				,  num + 1				,  SCREAMING_SNAKE_CASE__					):
    if sieve[i] is True:
     __lowercase             =  False

  start += 1

 for j in range(end + 1				,  num + 1					):
  if sieve[j] is True:
   prime.append(SCREAMING_SNAKE_CASE__					)

 return prime


if __name__ == "__main__":
      print(prime_sieve(int(input("""Enter a positive integer: """).strip())))









from __future__ import annotations

from scipy.special import comb  # type: ignore


class        __UpperCamelCase    :







	def __init__(  self      :							int       ,				_lowerCAmelCase      :							list[tuple[float, float]]			)		-> Any:
		"""simple docstring"""







		__lowercase             =  list_of_points
		# Degree determines the flexibility of the curve.
		# Degree = 1 will produce a straight line.
		__lowercase             =  len(_lowerCAmelCase			) - 1







	def  _a   (  self      :							Tuple       ,				_lowerCAmelCase      :							float			)		-> list[float]:
		"""simple docstring"""







		assert 0 <= t <= 1, "Time t must be between 0 and 1."
		__lowercase             =  []
		for i in range(len(self.list_of_points			)			):
			# basis function for each i
			output_values.append(
			    comb(self.degree       ,				_lowerCAmelCase			) * ((1 - t) ** (self.degree - i)) * (t**i)			)
		# the basis must sum up to 1 for it to produce a valid Bezier curve.
		assert round(sum(_lowerCAmelCase			)       ,				5			) == 1
		return output_values







	def  _a   (  self      :							List[str]       ,				_lowerCAmelCase      :							float			)		-> tuple[float, float]:
		"""simple docstring"""







		assert 0 <= t <= 1, "Time t must be between 0 and 1."

		__lowercase             =  self.basis_function(_lowerCAmelCase			)
		__lowercase             =  0.0
		__lowercase             =  0.0
		for i in range(len(self.list_of_points			)			):
			# For all points, sum up the product of i-th basis function and i-th point.
			x += basis_function[i] * self.list_of_points[i][0]
			y += basis_function[i] * self.list_of_points[i][1]
		return (x, y)







	def  _a   (  self      :							Optional[int]       ,				_lowerCAmelCase      :							float = 0.01			)		-> Union[str, Any]:
		"""simple docstring"""







		from matplotlib import pyplot as plt  # type: ignore

		__lowercase             =  []  # x coordinates of points to plot
		__lowercase             =  []  # y coordinates of points to plot

		__lowercase             =  0.0
		while t <= 1:
			__lowercase             =  self.bezier_curve_function(_lowerCAmelCase			)
			to_plot_x.append(value[0]			)
			to_plot_y.append(value[1]			)
			t += step_size

		__lowercase             =  [i[0] for i in self.list_of_points]
		__lowercase             =  [i[1] for i in self.list_of_points]

		plt.plot(
		    _lowerCAmelCase       ,				_lowerCAmelCase       ,				color="""blue"""       ,				label="""Curve of Degree """ + str(self.degree			)       ,				)
		plt.scatter(_lowerCAmelCase       ,				_lowerCAmelCase       ,				color="""red"""       ,				label="""Control Points"""			)
		plt.legend()
		plt.show()


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						BezierCurve([(1, 2), (3, 5)]).plot_curve()  # degree 1
						BezierCurve([(0, 0), (5, 5), (5, 0)]).plot_curve()  # degree 2
						BezierCurve([(0, 0), (5, 5), (5, 0), (2.5, -2.5)]).plot_curve()  # degree 3

