



from __future__ import annotations



class 						UpperCAmelCase_					:







							def __init__(     self,    __a):

														'''simple docstring'''

														_lowerCAmelCase  :							str				     =					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:
																					_lowerCAmelCase  :							List[str]				     =					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
																					_lowerCAmelCase  :							Union[str, Any]				     =					rows
														else:
																					_lowerCAmelCase  :							Optional[int]				     =					[]







							def      snake_case__   (     self):

														'''simple docstring'''

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







							@property
							def      snake_case__   (     self):

														'''simple docstring'''

														return len(self.rows)







							@property
							def      snake_case__   (     self):

														'''simple docstring'''

														return len(self.rows[0])







							@property
							def      snake_case__   (     self):

														'''simple docstring'''

														return (self.num_rows, self.num_columns)







							@property
							def      snake_case__   (     self):

														'''simple docstring'''

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







							def      snake_case__   (     self):

														'''simple docstring'''

														_lowerCAmelCase  :							Optional[Any]				     =					[
														    [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      snake_case__   (     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      snake_case__   (     self):

														'''simple docstring'''

														return bool(self.determinant())







							def      snake_case__   (     self,    __a,    __a):

														'''simple docstring'''

														_lowerCAmelCase  :							Union[str, Any]				     =					[
														    [
														        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      snake_case__   (     self,    __a,    __a):

														'''simple docstring'''

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







							def      snake_case__   (     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      snake_case__   (     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      snake_case__   (     self):

														'''simple docstring'''

														_lowerCAmelCase  :							Union[str, Any]				     =					[
														    [self.cofactors().rows[column][row] for column in range(self.num_columns)]
														    for row in range(self.num_rows)
														]
														return Matrix(__a)







							def      snake_case__   (     self):

														'''simple docstring'''

														_lowerCAmelCase  :							str				     =					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      snake_case__   (     self,    __a,    __a = None):

														'''simple docstring'''

														_lowerCAmelCase  :							int				     =					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:
																					_lowerCAmelCase  :							Tuple				     =					self.rows[0:position] + [row] + self.rows[position:]







							def      snake_case__   (     self,    __a,    __a = None):

														'''simple docstring'''

														_lowerCAmelCase  :							Tuple				     =					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:
																					_lowerCAmelCase  :							str				     =					[self.rows[i] + [column[i]] for i in range(self.num_rows)]
														else:
																					_lowerCAmelCase  :							str				     =					[
																					    self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
																					    for i in range(self.num_rows)
																					]







							def __eq__(     self,    __a):

														'''simple docstring'''

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







							def __ne__(     self,    __a):

														'''simple docstring'''

														return not self == other







							def __neg__(     self):

														'''simple docstring'''

														return self * -1







							def __add__(     self,    __a):

														'''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,    __a):

														'''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,    __a):

														'''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,    __a):

														'''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")
														_lowerCAmelCase  :							Any				     =					self
														for _ in range(other - 1):
																					result *= self
														return result







							@classmethod
							def      snake_case__   (     cls,    __a,    __a):

														'''simple docstring'''

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


if __name__ == "__main__":
						import doctest

						doctest.testmod()





def        A       (      _lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase						):





							'''simple docstring'''




							def count_of_possible_combinations(_lowerCamelCase						) -> 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(_lowerCamelCase						)






def        A       (      _lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase						):





							'''simple docstring'''




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

							_lowerCAmelCase  :							List[Any]				     =					[-1] * (target + 1)
							return count_of_possible_combinations_with_dp_array(_lowerCamelCase       ,				_lowerCamelCase						)






def        A       (      _lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase						):





							'''simple docstring'''




							_lowerCAmelCase  :							List[Any]				     =					[0] * (target + 1)
							_lowerCAmelCase  :							List[str]				     =					1

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

							return dp_array[target]


if __name__ == "__main__":
						import doctest

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