

from __future__ import annotations

import math
import random







def  UpperCAmelCase_   (_lowerCAmelCase :		Tuple     ,			_lowerCAmelCase :		Optional[Any]     ,			_lowerCAmelCase :		Dict		):
			__UpperCamelCase    :    int								=      d * e - 1
			__UpperCamelCase    :    Optional[int]								=      0
			__UpperCamelCase    :    Optional[Any]								=      0
			while p == 0:
						__UpperCamelCase    :    str								=      random.randint(2     ,			n - 1		)
						__UpperCamelCase    :    int								=      k
						while True:
									if t % 2 == 0:
												__UpperCamelCase    :    str								=      t // 2
												__UpperCamelCase    :    Tuple								=      (g**t) % n
												__UpperCamelCase    :    Dict								=      math.gcd(x - 1     ,			snake_case__		)
												if x > 1 and y > 1:
															__UpperCamelCase    :    int								=      y
															__UpperCamelCase    :    Tuple								=      n // y
															break  # find the correct factors
									else:
												break  # t is not divisible by 2, break and choose another g
			return sorted([p, q]		)


if __name__ == "__main__":
					import doctest

					doctest.testmod()


from __future__ import annotations







def  UpperCAmelCase_   (_lowerCAmelCase :		int     ,			_lowerCAmelCase :		list[int]     ,			_lowerCAmelCase :		list[int]     ,			_lowerCAmelCase :		int		):

			# Base Case
			if counter == 0 or capacity == 0:
						return 0

			# If weight of the nth item is more than Knapsack of capacity,
			#   then this item cannot be included in the optimal solution,
			# else return the maximum of two cases:
			#   (1) nth item included
			#   (2) not included
			if weights[counter - 1] > capacity:
						return knapsack(_lowerCAmelCase     ,			_lowerCAmelCase     ,			_lowerCAmelCase     ,			counter - 1		)
			else:
						__UpperCamelCase    :    Tuple								=      capacity - weights[counter - 1]
						__UpperCamelCase    :    List[str]								=      values[counter - 1] + knapsack(
						    _lowerCAmelCase     ,			_lowerCAmelCase     ,			_lowerCAmelCase     ,			counter - 1		)
						__UpperCamelCase    :    Dict								=      knapsack(_lowerCAmelCase     ,			_lowerCAmelCase     ,			_lowerCAmelCase     ,			counter - 1		)
						return max(_lowerCAmelCase     ,			_lowerCAmelCase		)


if __name__ == "__main__":
					import doctest

					doctest.testmod()