
def 		UpperCamelCase     (       _UpperCAmelCase  :   int = 200  )   ->			int:






						'''simple docstring'''

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

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


if __name__ == "__main__":
							assert solution(200) == 7_3682






def 		UpperCamelCase     (       _UpperCAmelCase  :   list[int] ,			_UpperCAmelCase  :   list[int]  )   ->			tuple[float, float]:






						'''simple docstring'''

						if not len(_UpperCAmelCase  ) == len(_UpperCAmelCase  ) == 3:
												raise ValueError("Please enter a valid equation."  )
						if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
												raise ValueError("Both a & b of two equations can't be zero."  )

						# Extract the coefficients
						_lowercase      ,    _lowercase      ,    _lowercase       :	List[str]           =   equationa
						_lowercase      ,    _lowercase      ,    _lowercase       :	List[str]           =   equationa

						# Calculate the determinants of the matrices
						_lowercase       :	List[Any]           =   aa * ba - aa * ba
						_lowercase       :	Tuple           =   ca * ba - ca * ba
						_lowercase       :	Union[str, Any]           =   aa * ca - aa * ca

						# Check if the system of linear equations has a solution (using Cramer's rule)
						if determinant == 0:
												if determinant_x == determinant_y == 0:
																		raise ValueError("Infinite solutions. (Consistent system)"  )
												else:
																		raise ValueError("No solution. (Inconsistent system)"  )
						else:
												if determinant_x == determinant_y == 0:
																		# Trivial solution (Inconsistent system)
																		return (0.0, 0.0)
												else:
																		_lowercase       :	str           =   determinant_x / determinant
																		_lowercase       :	Union[str, Any]           =   determinant_y / determinant
																		# Non-Trivial Solution (Consistent system)
																		return (x, y)




