




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

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


if __name__ == "__main__":
		assert solution(200) == 73682







def        lowerCAmelCase_			(  snake_case_ = 1000000  ):
      _A							:  Any    =		limit + 1
      _A							:  Tuple    =		[0] * limit
      for first_term in range(1,snake_case_  ):
            for n in range(snake_case_,snake_case_,snake_case_  ):
                  _A							:  Optional[int]    =		first_term + n / first_term
                  if common_difference % 4:  # d must be divisble by 4
                        continue
                  else:
                        common_difference /= 4
                        if (
                            first_term > common_difference
                            and first_term < 4 * common_difference
                        ):  # since x,y,z are positive integers
                              frequency[n] += 1  # so z>0 and a>d ,also 4d<a

      _A							:  List[str]    =		sum(1 for x in frequency[1:limit] if x == 10  )

      return count


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

