






from __future__ import annotations





class __lowerCamelCase :





	"""simple docstring"""






	def __init__(							self       ,    UpperCAmelCase    ):
							"""simple docstring"""







							_UpperCAmelCase									=			TypeError(
							    'Matrices must be formed from a list of zero or more lists containing at '
							    'least one and the same number of values, each of which must be of type '
							    'int or float.'    )
							if len(_a    ) != 0:
													_UpperCAmelCase									=			len(rows[0]    )
													if cols == 0:
																			raise error
													for row in rows:
																			if len(_a    ) != cols:
																									raise error
																			for value in row:
																									if not isinstance(_a       ,    (int, float)    ):
																															raise error
													_UpperCAmelCase									=			rows
							else:
													_UpperCAmelCase									=			[]

	def        UpperCamelCase    (							self    ):
							"""simple docstring"""







							return [[row[i] for row in self.rows] for i in range(len(self.rows[0]    )    )]

	@property
	def        UpperCamelCase    (							self    ):
							"""simple docstring"""







							return len(self.rows    )

	@property
	def        UpperCamelCase    (							self    ):
							"""simple docstring"""







							return len(self.rows[0]    )

	@property
	def        UpperCamelCase    (							self    ):
							"""simple docstring"""







							return (self.num_rows, self.num_columns)

	@property
	def        UpperCamelCase    (							self    ):
							"""simple docstring"""







							return self.order[0] == self.order[1]

	def        UpperCamelCase    (							self    ):
							"""simple docstring"""







							_UpperCAmelCase									=			[
							    [0 if column_num != row_num else 1 for column_num in range(self.num_rows    )]
							    for row_num in range(self.num_rows    )
							]
							return Matrix(_a    )

	def        UpperCamelCase    (							self    ):
							"""simple docstring"""







							if not self.is_square:
													return 0
							if self.order == (0, 0):
													return 1
							if self.order == (1, 1):
													return int(self.rows[0][0]    )
							if self.order == (2, 2):
													return int(
													    (self.rows[0][0] * self.rows[1][1])
													    - (self.rows[0][1] * self.rows[1][0])    )
							else:
													return sum(
													    self.rows[0][column] * self.cofactors().rows[0][column]
													    for column in range(self.num_columns    )    )

	def        UpperCamelCase    (							self    ):
							"""simple docstring"""







							return bool(self.determinant()    )

	def        UpperCamelCase    (							self       ,    UpperCAmelCase       ,    UpperCAmelCase    ):
							"""simple docstring"""







							_UpperCAmelCase									=			[
							    [
							        self.rows[other_row][other_column]
							        for other_column in range(self.num_columns    )
							        if other_column != column
							    ]
							    for other_row in range(self.num_rows    )
							    if other_row != row
							]
							return Matrix(_a    ).determinant()

	def        UpperCamelCase    (							self       ,    UpperCAmelCase       ,    UpperCAmelCase    ):
							"""simple docstring"""







							if (row + column) % 2 == 0:
													return self.get_minor(_a       ,    _a    )
							return -1 * self.get_minor(_a       ,    _a    )

	def        UpperCamelCase    (							self    ):
							"""simple docstring"""







							return Matrix(
							    [
							        [self.get_minor(_a       ,    _a    ) for column in range(self.num_columns    )]
							        for row in range(self.num_rows    )
							    ]    )

	def        UpperCamelCase    (							self    ):
							"""simple docstring"""







							return Matrix(
							    [
							        [
							            self.minors().rows[row][column]
							            if (row + column) % 2 == 0
							            else self.minors().rows[row][column] * -1
							            for column in range(self.minors().num_columns    )
							        ]
							        for row in range(self.minors().num_rows    )
							    ]    )

	def        UpperCamelCase    (							self    ):
							"""simple docstring"""







							_UpperCAmelCase									=			[
							    [self.cofactors().rows[column][row] for column in range(self.num_columns    )]
							    for row in range(self.num_rows    )
							]
							return Matrix(_a    )

	def        UpperCamelCase    (							self    ):
							"""simple docstring"""







							_UpperCAmelCase									=			self.determinant()
							if not determinant:
													raise TypeError('Only matrices with a non-zero determinant have an inverse'    )
							return self.adjugate() * (1 / determinant)

	def __repr__(							self    ):
							"""simple docstring"""







							return str(self.rows    )

	def __str__(							self    ):
							"""simple docstring"""







							if self.num_rows == 0:
													return "[]"
							if self.num_rows == 1:
													return "[[" + ". ".join(str(self.rows[0]    )    ) + "]]"
							return (
							    "["
							    + "\n ".join(
							        [
							            '[' + '. '.join([str(_a    ) for value in row]    ) + '.]'
							            for row in self.rows
							        ]    )
							    + "]"
							)

	def        UpperCamelCase    (							self       ,    UpperCAmelCase       ,    UpperCAmelCase = None    ):
							"""simple docstring"""







							_UpperCAmelCase									=			TypeError('Row must be a list containing all ints and/or floats'    )
							if not isinstance(_a       ,    _a    ):
													raise type_error
							for value in row:
													if not isinstance(_a       ,    (int, float)    ):
																			raise type_error
							if len(_a    ) != self.num_columns:
													raise ValueError(
													    'Row must be equal in length to the other rows in the matrix'    )
							if position is None:
													self.rows.append(_a    )
							else:
													_UpperCAmelCase									=			self.rows[0:position] + [row] + self.rows[position:]

	def        UpperCamelCase    (							self       ,    UpperCAmelCase       ,    UpperCAmelCase = None    ):
							"""simple docstring"""







							_UpperCAmelCase									=			TypeError(
							    'Column must be a list containing all ints and/or floats'    )
							if not isinstance(_a       ,    _a    ):
													raise type_error
							for value in column:
													if not isinstance(_a       ,    (int, float)    ):
																			raise type_error
							if len(_a    ) != self.num_rows:
													raise ValueError(
													    'Column must be equal in length to the other columns in the matrix'    )
							if position is None:
													_UpperCAmelCase									=			[self.rows[i] + [column[i]] for i in range(self.num_rows    )]
							else:
													_UpperCAmelCase									=			[
													    self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
													    for i in range(self.num_rows    )
													]

	def __eq__(							self       ,    UpperCAmelCase    ):
							"""simple docstring"""







							if not isinstance(_a       ,    _a    ):
													return NotImplemented
							return self.rows == other.rows

	def __ne__(							self       ,    UpperCAmelCase    ):
							"""simple docstring"""







							return not self == other

	def __neg__(							self    ):
							"""simple docstring"""







							return self * -1

	def __add__(							self       ,    UpperCAmelCase    ):
							"""simple docstring"""







							if self.order != other.order:
													raise ValueError('Addition requires matrices of the same order'    )
							return Matrix(
							    [
							        [self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns    )]
							        for i in range(self.num_rows    )
							    ]    )

	def __sub__(							self       ,    UpperCAmelCase    ):
							"""simple docstring"""







							if self.order != other.order:
													raise ValueError('Subtraction requires matrices of the same order'    )
							return Matrix(
							    [
							        [self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns    )]
							        for i in range(self.num_rows    )
							    ]    )

	def __mul__(							self       ,    UpperCAmelCase    ):
							"""simple docstring"""







							if isinstance(_a       ,    (int, float)    ):
													return Matrix(
													    [[int(element * other    ) for element in row] for row in self.rows]    )
							elif isinstance(_a       ,    _a    ):
													if self.num_columns != other.num_rows:
																			raise ValueError(
																			    'The number of columns in the first matrix must '
																			    'be equal to the number of rows in the second'    )
													return Matrix(
													    [
													        [Matrix.dot_product(_a       ,    _a    ) for column in other.columns()]
													        for row in self.rows
													    ]    )
							else:
													raise TypeError(
													    'A Matrix can only be multiplied by an int, float, or another matrix'    )

	def __pow__(							self       ,    UpperCAmelCase    ):
							"""simple docstring"""







							if not isinstance(_a       ,    _a    ):
													raise TypeError('A Matrix can only be raised to the power of an int'    )
							if not self.is_square:
													raise ValueError('Only square matrices can be raised to a power'    )
							if other == 0:
													return self.identity()
							if other < 0:
													if self.is_invertable():
																			return self.inverse() ** (-other)
													raise ValueError(
													    'Only invertable matrices can be raised to a negative power'    )
							_UpperCAmelCase									=			self
							for _ in range(other - 1    ):
													result *= self
							return result

	@classmethod
	def        UpperCamelCase    (							cls       ,    UpperCAmelCase       ,    UpperCAmelCase    ):
							"""simple docstring"""







							return sum(row[i] * column[i] for i in range(len(_a    )    )    )


if __name__ == "__main__":
		import doctest

		doctest.testmod()



def    __UpperCAmelCase (	__a      :			int		,__a      :			list[int]		,__a      :			int	)			->     int:

					"""simple docstring"""

					def count_of_possible_combinations(__a      :			int	) -> int:
										if target < 0:
															return 0
										if target == 0:
															return 1
										return sum(count_of_possible_combinations(target - item	) for item in array	)

					return count_of_possible_combinations(__a	)



def    __UpperCAmelCase (	__a      :			int		,__a      :			list[int]		,__a      :			int	)			->     int:

					"""simple docstring"""

					def count_of_possible_combinations_with_dp_array(
					    __a      :			int		,__a      :			list[int]	) -> int:
										if target < 0:
															return 0
										if target == 0:
															return 1
										if dp_array[target] != -1:
															return dp_array[target]
										_a	:    Union[str, Any]         =		sum(
										    count_of_possible_combinations_with_dp_array(target - item		,__a	)
										    for item in array	)
										_a	:    Optional[int]         =		answer
										return answer

					_a	:    int         =		[-1] * (target + 1)
					return count_of_possible_combinations_with_dp_array(__a		,__a	)



def    __UpperCAmelCase (	__a      :			int		,__a      :			list[int]		,__a      :			int	)			->     int:

					"""simple docstring"""

					_a	:    str         =		[0] * (target + 1)
					_a	:    Optional[Any]         =		1

					for i in range(1		,target + 1	):
										for j in range(__a	):
															if i - array[j] >= 0:
																				dp_array[i] += dp_array[i - array[j]]

					return dp_array[target]


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			a__				=		3
			a__				=		5
			a__				=		[1, 2, 5]
			print(combination_sum_iv(n, array, target))



