

from __future__ import annotations

from typing import Any

class 				UpperCAmelCase_		:
							"""simple docstring"""







							def __init__(			self       ,							_a       ,							_a       ,							_a = 0       )    ->    None:
												_a      ,					_a	:    str         =		row, column
												_a	:    Any         =		[[default_value for c in range(_a       )] for r in range(_a       )]


							def __str__(			self       )    ->    str:
												_a	:    str         =		F"""Matrix consist of {self.row} rows and {self.column} columns\n"""

												# Make string identifier
												_a	:    str         =		0
												for row_vector in self.array:
																	for obj in row_vector:
																						_a	:    Optional[Any]         =		max(_a       ,							len(str(_a       )       )       )
												_a	:    List[Any]         =		F"""%{max_element_length}s"""

												# Make string and return
												def single_line(_a       ) -> str:
																	nonlocal string_format_identifier
																	_a	:    Union[str, Any]         =		'''['''
																	line += ", ".join(string_format_identifier % (obj,) for obj in row_vector       )
																	line += "]"
																	return line

												s += "\n".join(single_line(_a       ) for row_vector in self.array       )
												return s


							def __repr__(			self       )    ->    str:
												return str(self       )


							def 				__lowercase				(			self       ,							_a       )    ->    bool:
												if not (isinstance(_a       ,							(list, tuple)       ) and len(_a       ) == 2):
																	return False
												elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
																	return False
												else:
																	return True


							def __getitem__(			self       ,							_a       )    ->    Any:
												assert self.validate_indicies(_a       )
												return self.array[loc[0]][loc[1]]


							def __setitem__(			self       ,							_a       ,							_a       )    ->    None:
												assert self.validate_indicies(_a       )
												_a	:    int         =		value


							def __add__(			self       ,							_a       )    ->    Matrix:
												assert isinstance(_a       ,							_a       )
												assert self.row == another.row and self.column == another.column

												# Add
												_a	:    Union[str, Any]         =		Matrix(self.row       ,							self.column       )
												for r in range(self.row       ):
																	for c in range(self.column       ):
																						_a	:    Union[str, Any]         =		self[r, c] + another[r, c]
												return result


							def __neg__(			self       )    ->    Matrix:
												_a	:    Dict         =		Matrix(self.row       ,							self.column       )
												for r in range(self.row       ):
																	for c in range(self.column       ):
																						_a	:    Optional[int]         =		-self[r, c]
												return result


							def __sub__(			self       ,							_a       )    ->    Matrix:
												return self + (-another)


							def __mul__(			self       ,							_a       )    ->    Matrix:

												if isinstance(_a       ,							(int, float)       ):  # Scalar multiplication
																	_a	:    Optional[int]         =		Matrix(self.row       ,							self.column       )
																	for r in range(self.row       ):
																						for c in range(self.column       ):
																											_a	:    Union[str, Any]         =		self[r, c] * another
																	return result
												elif isinstance(_a       ,							_a       ):  # Matrix multiplication
																	assert self.column == another.row
																	_a	:    Dict         =		Matrix(self.row       ,							another.column       )
																	for r in range(self.row       ):
																						for c in range(another.column       ):
																											for i in range(self.column       ):
																																result[r, c] += self[r, i] * another[i, c]
																	return result
												else:
																	_a	:    int         =		F"""Unsupported type given for another ({type(_a       )})"""
																	raise TypeError(_a       )


							def 				__lowercase				(			self       )    ->    Matrix:
												_a	:    List[str]         =		Matrix(self.column       ,							self.row       )
												for r in range(self.row       ):
																	for c in range(self.column       ):
																						_a	:    Tuple         =		self[r, c]
												return result




							def 				__lowercase				(			self       ,							_a       ,							_a       )    ->    Any:
												assert isinstance(_a       ,							_a       ) and isinstance(_a       ,							_a       )
												assert self.row == self.column == u.row == v.row  # u, v should be column vector
												assert u.column == v.column == 1  # u, v should be column vector

												# Calculate
												_a	:    Dict         =		v.transpose()
												_a	:    Optional[Any]         =		(v_t * self * u)[0, 0] + 1
												if numerator_factor == 0:
																	return None  # It's not invertable
												return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":



			def    __UpperCAmelCase (	)			->     None:

								"""simple docstring"""

								_a	:    int         =		Matrix(3		,3		,0	)
								for i in range(3	):
													_a	:    Dict         =		1
								print(F"""a^(-1) is {ainv}"""	)
								# u, v
								_a	:    Dict         =		Matrix(3		,1		,0	)
								_a      ,					_a      ,					_a	:    Dict         =		1, 2, -3
								_a	:    Any         =		Matrix(3		,1		,0	)
								_a      ,					_a      ,					_a	:    Optional[Any]         =		4, -2, 5
								print(F"""u is {u}"""	)
								print(F"""v is {v}"""	)
								print(F"""uv^T is {u * v.transpose()}"""	)
								# Sherman Morrison
								print(F"""(a + uv^T)^(-1) is {ainv.sherman_morrison(__a		,__a	)}"""	)



			def    __UpperCAmelCase (	)			->     None:

								"""simple docstring"""

								import doctest

								doctest.testmod()







			testa()






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))



