




'''simple docstring'''



import math







def 	_UpperCamelCase       (_lowerCamelCase							:   int		)->      bool:




     '''simple docstring'''





     if 1 < number < 4:
          # 2 and 3 are primes
          return True
     elif number < 2 or number % 2 == 0 or number % 3 == 0:
          # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
          return False

     # All primes number are in format of 6k +/- 1
     for i in range(5      ,		int(math.sqrt(_lowerCamelCase		) + 1		)      ,		6		):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True







def 	_UpperCamelCase       (_lowerCamelCase							:   int = 60_08_51_47_51_43		)->      int:




     '''simple docstring'''





     try:
          __snake_case			    =     int(_lowerCamelCase		)
     except (TypeError, ValueError):
          raise TypeError('''Parameter n must be int or castable to int.'''		)
     if n <= 0:
          raise ValueError('''Parameter n must be greater than or equal to one.'''		)
     __snake_case			    =     0
     if is_prime(_lowerCamelCase		):
          return n
     while n % 2 == 0:
          n //= 2
     if is_prime(_lowerCamelCase		):
          return n
     for i in range(3      ,		int(math.sqrt(_lowerCamelCase		)		) + 1      ,		2		):
          if n % i == 0:
               if is_prime(n // i		):
                    __snake_case			    =     n // i
                    break
               elif is_prime(_lowerCamelCase		):
                    __snake_case			    =     i
     return max_number


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












'''simple docstring'''



from __future__ import annotations







def 	_UpperCamelCase       (_lowerCamelCase							:   int      ,		_lowerCamelCase							:   list[int]      ,		_lowerCamelCase							:   list[int]      ,		_lowerCamelCase							:   int		)->      int:




     '''simple docstring'''





     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:
          __snake_case			    =     capacity - weights[counter - 1]
          __snake_case			    =     values[counter - 1] + knapsack(
              _lowerCamelCase      ,		_lowerCamelCase      ,		_lowerCamelCase      ,		counter - 1		)
          __snake_case			    =     knapsack(_lowerCamelCase      ,		_lowerCamelCase      ,		_lowerCamelCase      ,		counter - 1		)
          return max(_lowerCamelCase      ,		_lowerCamelCase		)


if __name__ == "__main__":
     import doctest

     doctest.testmod()






