


from __future__ import annotations



def       _lowerCAmelCase    (				lowerCAmelCase_				:int				)->list[int]:
   '''simple docstring'''






   snake_case_            =       [True] * limit
   snake_case_            =       False
   snake_case_            =       False
   snake_case_            =       True

   for i in range(3		,    int(limit**0.5 + 1				)		,    2				):
      snake_case_            =       i * 2
      while index < limit:
         snake_case_            =       False
         snake_case_            =       index + i

   snake_case_            =       [2]

   for i in range(3		,    lowerCAmelCase_		,    2				):
      if is_prime[i]:
         primes.append(lowerCAmelCase_				)

   return primes



def       _lowerCAmelCase    (				lowerCAmelCase_				:int = 1_000_000				)->int:
   '''simple docstring'''






   snake_case_            =       prime_sieve(lowerCAmelCase_				)
   snake_case_            =       0
   snake_case_            =       0

   for i in range(len(lowerCAmelCase_				)				):
      for j in range(i + length		,    len(lowerCAmelCase_				)				):
         snake_case_            =       sum(primes[i:j]				)
         if sol >= ceiling:
            break

         if sol in primes:
            snake_case_            =       j - i
            snake_case_            =       sol

   return largest


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








from math import factorial



def       _lowerCAmelCase    (				lowerCAmelCase_				:int = 20				)->int:
   '''simple docstring'''






   snake_case_            =       2 * n  # middle entry of odd rows starting at row 3 is the solution for n = 1,
   # 2, 3,...
   snake_case_            =       n // 2

   return int(factorial(lowerCAmelCase_				) / (factorial(lowerCAmelCase_				) * factorial(n - k				))				)


if __name__ == "__main__":
   import sys

   if len(sys.argv) == 1:
      print(solution(20))
   else:
      try:
         SCREAMING_SNAKE_CASE						:Any			=  int(sys.argv[1])
         print(solution(n))
      except ValueError:
         print('''Invalid entry - please enter a number.''')




