



from maths.prime_check import is_prime


def    __lowerCamelCase   (  lowerCamelCase__		):

				"""simple docstring"""


				if not isinstance(lowerCamelCase_	,					lowerCamelCase_		):
								lowercase__	:       Dict						=	F"""Input value of [number={number}] must be an integer"""
								raise TypeError(lowerCamelCase_		)
				if is_prime(lowerCamelCase_		) and is_prime(number + 2		):
								return number + 2
				else:
								return -1


if __name__ == "__main__":
				import doctest

				doctest.testmod()










from __future__ import annotations

from scipy.special import comb  # type: ignore







class 				lowerCAmelCase_       :






				def __init__(			self      ,snake_case__ ):
							SCREAMING_SNAKE_CASE_   : Optional[int]					  =      list_of_points
							# Degree determines the flexibility of the curve.
							# Degree = 1 will produce a straight line.
							SCREAMING_SNAKE_CASE_   : Tuple					  =      len(snake_case__ ) - 1






				def 		snake_case	(			self      ,snake_case__ ):
							assert 0 <= t <= 1, "Time t must be between 0 and 1."
							SCREAMING_SNAKE_CASE_   : list[float]					  =      []
							for i in range(len(self.list_of_points ) ):
										# basis function for each i
										output_values.append(
										    comb(self.degree      ,snake_case__ ) * ((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(snake_case__ )      ,5 ) == 1
							return output_values






				def 		snake_case	(			self      ,snake_case__ ):
							assert 0 <= t <= 1, "Time t must be between 0 and 1."

							SCREAMING_SNAKE_CASE_   : int					  =      self.basis_function(snake_case__ )
							SCREAMING_SNAKE_CASE_   : List[Any]					  =      0.0
							SCREAMING_SNAKE_CASE_   : Union[str, Any]					  =      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 		snake_case	(			self      ,snake_case__ = 0.01 ):
							from matplotlib import pyplot as plt  # type: ignore

							SCREAMING_SNAKE_CASE_   : list[float]					  =      []  # x coordinates of points to plot
							SCREAMING_SNAKE_CASE_   : list[float]					  =      []  # y coordinates of points to plot

							SCREAMING_SNAKE_CASE_   : List[str]					  =      0.0
							while t <= 1:
										SCREAMING_SNAKE_CASE_   : int					  =      self.bezier_curve_function(snake_case__ )
										to_plot_x.append(value[0] )
										to_plot_y.append(value[1] )
										t += step_size

							SCREAMING_SNAKE_CASE_   : Dict					  =      [i[0] for i in self.list_of_points]
							SCREAMING_SNAKE_CASE_   : Union[str, Any]					  =      [i[1] for i in self.list_of_points]

							plt.plot(
							    snake_case__      ,snake_case__      ,color='blue'      ,label='Curve of Degree ' + str(self.degree )      ,)
							plt.scatter(snake_case__      ,snake_case__      ,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



