





import math







def 			A__							(    SCREAMING_SNAKE_CASE__)   ->    bool:
  __snake_case:						Optional[Any]   =						math.loga(math.sqrt(4 * positive_integer + 1) / 2 + 1 / 2)

  return exponent == int(SCREAMING_SNAKE_CASE__)







def 			A__							(    SCREAMING_SNAKE_CASE__ = 1 / 1_2345)   ->    int:
  __snake_case:						Tuple   =						0
  __snake_case:						List[str]   =						0

  __snake_case:						Any   =						3
  while True:
    __snake_case:						Optional[int]   =						(integer**2 - 1) / 4
    # if candidate is an integer, then there is a partition for k
    if partition_candidate == int(SCREAMING_SNAKE_CASE__):
      __snake_case:						Optional[int]   =						int(SCREAMING_SNAKE_CASE__)
      total_partitions += 1
      if check_partition_perfect(SCREAMING_SNAKE_CASE__):
        perfect_partitions += 1
    if perfect_partitions > 0:
      if perfect_partitions / total_partitions < max_proportion:
        return int(SCREAMING_SNAKE_CASE__)
    integer += 1


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













def 			A__							(    SCREAMING_SNAKE_CASE__ = 200)   ->    int:
  __snake_case:						Optional[int]   =						[1, 2, 5, 10, 20, 50, 100, 200]
  __snake_case:						List[Any]   =						[0] * (pence + 1)
  __snake_case:						int   =						1  # base case: 1 way to make 0 pence

  for coin in coins:
    for i in range(SCREAMING_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) == 73_682






