


import functools






def 							__lowercase     (				__lowerCAmelCase							:       str      ,					__lowerCAmelCase							:       str     ):
							a__    =  len(__lowerCAmelCase     )
							a__    =  len(__lowerCAmelCase     )

							@functools.cache
							def min_distance(__lowerCAmelCase							:       int      ,					__lowerCAmelCase							:       int     ) -> int:
														# if first word index is overflow - delete all from the second word
														if indexa >= len_worda:
																					return len_worda - indexa
														# if second word index is overflow - delete all from the first word
														if indexa >= len_worda:
																					return len_worda - indexa
														a__    =  int(worda[indexa] != worda[indexa]     )  # current letters not identical
														return min(
														    1 + min_distance(indexa + 1      ,					__lowerCAmelCase     )      ,					1 + min_distance(__lowerCAmelCase      ,					indexa + 1     )      ,					diff + min_distance(indexa + 1      ,					indexa + 1     )      ,					)

							return min_distance(0      ,					0     )


if __name__ == "__main__":
						import doctest

						doctest.testmod()








from decimal import Decimal, getcontext
from math import ceil, factorial






def 							__lowercase     (				__lowerCAmelCase							:       int     ):

							if not isinstance(__lowerCAmelCase      ,					__lowerCAmelCase     ):
														raise TypeError('Undefined for non-integers'     )
							elif precision < 1:
														raise ValueError('Undefined for non-natural numbers'     )

							a__    =  precision
							a__    =  ceil(precision / 1_4     )
							a__    =  4_2_6_8_8_0 * Decimal(1_0_0_0_5     ).sqrt()
							a__    =  1
							a__    =  1_3_5_9_1_4_0_9
							a__    =  Decimal(__lowerCAmelCase     )
							for k in range(1      ,					__lowerCAmelCase     ):
														a__    =  factorial(6 * k     ) // (factorial(3 * k     ) * factorial(__lowerCAmelCase     ) ** 3)
														linear_term += 5_4_5_1_4_0_1_3_4
														exponential_term *= -2_6_2_5_3_7_4_1_2_6_4_0_7_6_8_0_0_0
														partial_sum += Decimal(multinomial_term * linear_term     ) / exponential_term
							return str(constant_term / partial_sum     )[:-1]


if __name__ == "__main__":
						snake_case							: Tuple      =   50
						print(f"""The first {n} digits of pi is: {pi(n)}""")




