






from __future__ import annotations

from typing import Any



class    _a     :






							"""simple docstring"""

							def __init__(      self				:     Tuple							,	a				:     int							,	a				:     int							,	a				:     float = 0    )	->None:
													SCREAMING_SNAKE_CASE__     :				List[str]   =					row, column
													SCREAMING_SNAKE_CASE__     :				List[Any]   =					[[default_value for c in range(a    )] for r in range(a    )]

							def __str__(      self				:     List[Any]    )	->str:
													SCREAMING_SNAKE_CASE__     :				Optional[int]   =					f"""Matrix consist of {self.row} rows and {self.column} columns\n"""

													# Make string identifier
													SCREAMING_SNAKE_CASE__     :				Tuple   =					0
													for row_vector in self.array:
																			for obj in row_vector:
																									SCREAMING_SNAKE_CASE__     :				int   =					max(a							,	len(str(a    )    )    )
													SCREAMING_SNAKE_CASE__     :				Dict   =					f"""%{max_element_length}s"""

													# Make string and return
													def single_line(a				:     list[float]    ) -> str:
																			nonlocal string_format_identifier
																			SCREAMING_SNAKE_CASE__     :				Dict   =					"["
																			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				:     int    )	->str:
													return str(self    )

							def      A_  (      self				:     str							,	a				:     tuple[int, int]    )	->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				:     Tuple							,	a				:     tuple[int, int]    )	->Any:
													assert self.validate_indicies(a    )
													return self.array[loc[0]][loc[1]]

							def __setitem__(      self				:     Optional[int]							,	a				:     tuple[int, int]							,	a				:     float    )	->None:
													assert self.validate_indicies(a    )
													SCREAMING_SNAKE_CASE__     :				Optional[Any]   =					value

							def __add__(      self				:     List[str]							,	a				:     Matrix    )	->Matrix:
													assert isinstance(a							,	a    )
													assert self.row == another.row and self.column == another.column

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

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

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

							def __mul__(      self				:     Dict							,	a				:     int | float | Matrix    )	->Matrix:

													if isinstance(a							,	(int, float)    ):  # Scalar multiplication
																			SCREAMING_SNAKE_CASE__     :				Optional[int]   =					Matrix(self.row							,	self.column    )
																			for r in range(self.row    ):
																									for c in range(self.column    ):
																															SCREAMING_SNAKE_CASE__     :				Tuple   =					self[r, c] * another
																			return result
													elif isinstance(a							,	a    ):  # Matrix multiplication
																			assert self.column == another.row
																			SCREAMING_SNAKE_CASE__     :				Optional[Any]   =					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:
																			SCREAMING_SNAKE_CASE__     :				Optional[int]   =					f"""Unsupported type given for another ({type(a    )})"""
																			raise TypeError(a    )

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






							def      A_  (      self				:     int							,	a				:     Matrix							,	a				:     Matrix    )	->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
													SCREAMING_SNAKE_CASE__     :				Optional[int]   =					v.transpose()
													SCREAMING_SNAKE_CASE__     :				Dict   =					(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							(     ):





										'''simple docstring'''


										SCREAMING_SNAKE_CASE__     :				Dict   =					Matrix(3			,   3			,   0     )
										for i in range(3     ):
																SCREAMING_SNAKE_CASE__     :				int   =					1
										print(f"""a^(-1) is {ainv}"""     )
										# u, v
										SCREAMING_SNAKE_CASE__     :				Optional[Any]   =					Matrix(3			,   1			,   0     )
										SCREAMING_SNAKE_CASE__     :				Optional[int]   =					1, 2, -3
										SCREAMING_SNAKE_CASE__     :				List[Any]   =					Matrix(3			,   1			,   0     )
										SCREAMING_SNAKE_CASE__     :				Optional[int]   =					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(_lowerCamelCase			,   _lowerCamelCase     )}"""     )







				def       UpperCAmelCase							(     ):





										'''simple docstring'''


										import doctest

										doctest.testmod()



				testa()






from __future__ import annotations







def       UpperCAmelCase							(     _lowerCamelCase      :  list[int]			,   _lowerCamelCase      :  int     ):





						'''simple docstring'''


						if len(_lowerCamelCase     ) < k or k < 0:
												raise ValueError("Invalid Input"     )
						SCREAMING_SNAKE_CASE__     :				int   =					sum(array[:k]     )
						for i in range(len(_lowerCamelCase     ) - k     ):
												SCREAMING_SNAKE_CASE__     :				str   =					current_sum - array[i] + array[i + k]
												SCREAMING_SNAKE_CASE__     :				Union[str, Any]   =					max(_lowerCamelCase			,   _lowerCamelCase     )
						return max_sum


if __name__ == "__main__":
				from doctest import testmod
				from random import randint

				testmod()
				__lowercase       :List[str]       =  [randint(-1_000, 1_000) for i in range(100)]
				__lowercase       :Any       =  randint(0, 110)
				print(f"The maximum sum of {k} consecutive elements is {max_sum_in_array(array,k)}")