
'''simple docstring'''






from __future__ import annotations

from scipy.special import comb  # type: ignore




class     __snake_case		:
					def __init__(     self,    A      ):

									"""simple docstring"""


									lowerCamelCase					:			str									= list_of_points
									# Degree determines the flexibility of the curve.
									# Degree = 1 will produce a straight line.
									lowerCamelCase					:			str									= len(A      ) - 1
					def     UpperCAmelCase_							(     self,    A      ):

									"""simple docstring"""


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

									"""simple docstring"""


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

									lowerCamelCase					:			str									= self.basis_function(A      )
									lowerCamelCase					:			Union[str, Any]									= 0.0
									lowerCamelCase					:			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     UpperCAmelCase_							(     self,    A = 0.01      ):

									"""simple docstring"""


									from matplotlib import pyplot as plt  # type: ignore

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

									lowerCamelCase					:			int									= 0.0
									while t <= 1:
													lowerCamelCase					:			Dict									= self.bezier_curve_function(A      )
													to_plot_x.append(value[0]      )
													to_plot_y.append(value[1]      )
													t += step_size

									lowerCamelCase					:			Tuple									= [i[0] for i in self.list_of_points]
									lowerCamelCase					:			Optional[Any]									= [i[1] for i in self.list_of_points]

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


'''simple docstring'''






from __future__ import annotations





def    UpperCAmelCase							(  UpperCAmelCase__							:							int):
				lowerCamelCase					:			List[Any]									= str(UpperCAmelCase__)
				return len(UpperCAmelCase__) == 9 and set(UpperCAmelCase__) == set('123456789')





def    UpperCAmelCase							(  ):
				for base_num in range(99_99       ,							49_99       ,							-1):
								lowerCamelCase					:			Tuple									= 10_00_02 * base_num
								if is_9_pandigital(UpperCAmelCase__):
												return candidate

				for base_num in range(3_33       ,							99       ,							-1):
								lowerCamelCase					:			List[Any]									= 1_00_20_03 * base_num
								if is_9_pandigital(UpperCAmelCase__):
												return candidate

				return None


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