


'''simple docstring'''
from __future__ import annotations


def     a   (    __a     )						->			bool:



					'''simple docstring'''






					UpperCamelCase__     :Tuple							      =				str(__a     )
					return len(__a     ) == 9 and set(__a     ) == set('''123456789'''     )


def     a   (    )						->			int | None:



					'''simple docstring'''






					for base_num in range(9999				,      4999				,      -1     ):
										UpperCamelCase__     :List[Any]							      =				100002 * base_num
										if is_9_pandigital(__a     ):
															return candidate

					for base_num in range(333				,      99				,      -1     ):
										UpperCamelCase__     :Optional[int]							      =				1002003 * base_num
										if is_9_pandigital(__a     ):
															return candidate

					return None


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



'''simple docstring'''
import numpy as np


def     a   (    __a				,      __a				,      __a				,      __a				,      __a     )						->			Union[str, Any]:



					'''simple docstring'''






					UpperCamelCase__     :Tuple							      =				int(np.ceil((x_end - xa) / h     )     )
					UpperCamelCase__     :Optional[int]							      =				np.zeros((n + 1,)     )
					UpperCamelCase__     :List[str]							      =				ya
					UpperCamelCase__     :Tuple							      =				xa

					for k in range(__a     ):
										UpperCamelCase__     :Dict							      =				f(__a				,      y[k]     )
										UpperCamelCase__     :List[Any]							      =				f(x + 0.5 * h				,      y[k] + 0.5 * h * ka     )
										UpperCamelCase__     :Dict							      =				f(x + 0.5 * h				,      y[k] + 0.5 * h * ka     )
										UpperCamelCase__     :List[Any]							      =				f(x + h				,      y[k] + h * ka     )
										UpperCamelCase__     :List[str]							      =				y[k] + (1 / 6) * h * (ka + 2 * ka + 2 * ka + ka)
										x += h

					return y


if __name__ == "__main__":
		import doctest

		doctest.testmod()