


'''simple docstring'''



def 			_a			(		_lowercase      :			int = 200						):





     '''simple docstring'''






     __UpperCAmelCase			:				Optional[Any]													=    [1, 2, 5, 10, 20, 50, 100, 200]
     __UpperCAmelCase			:				int													=    [0] * (pence + 1)
     __UpperCAmelCase			:				Union[str, Any]													=    1  # base case: 1 way to make 0 pence

     for coin in coins:
          for i in range(_lowercase    ,      pence + 1    ,      1						):
               number_of_ways[i] += number_of_ways[i - coin]
     return number_of_ways[pence]


if __name__ == "__main__":
      assert solution(2_0_0) == 7_3_6_8_2



'''simple docstring'''



from __future__ import annotations




def 			_a			(		_lowercase      :			int						):





     '''simple docstring'''






     __UpperCAmelCase			:				str													=    [True] * limit
     __UpperCAmelCase			:				Tuple													=    False
     __UpperCAmelCase			:				List[str]													=    False
     __UpperCAmelCase			:				List[Any]													=    True

     for i in range(3    ,      int(limit**0.5 + 1						)    ,      2						):
          __UpperCAmelCase			:				Dict													=    i * 2
          while index < limit:
               __UpperCAmelCase			:				Optional[int]													=    False
               __UpperCAmelCase			:				Union[str, Any]													=    index + i

     __UpperCAmelCase			:				Optional[Any]													=    [2]

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

     return primes




def 			_a			(		_lowercase      :			int = 1000000						):





     '''simple docstring'''






     __UpperCAmelCase			:				List[str]													=    prime_sieve(_lowercase						)
     __UpperCAmelCase			:				Optional[Any]													=    0
     __UpperCAmelCase			:				int													=    0

     for i in range(len(_lowercase						)						):
          for j in range(i + length    ,      len(_lowercase						)						):
               __UpperCAmelCase			:				Optional[Any]													=    sum(primes[i:j]						)
               if sol >= ceiling:
                    break

               if sol in primes:
                    __UpperCAmelCase			:				Any													=    j - i
                    __UpperCAmelCase			:				List[Any]													=    sol

     return largest


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