





from __future__ import annotations

from typing import Any

class       __A     :


				def __init__(		self   , UpperCAmelCase_   , UpperCAmelCase_   , UpperCAmelCase_ = 0							):
								lowerCamelCase ,  lowerCamelCase	 =row, column
								lowerCamelCase	 =[[default_value for c in range(UpperCAmelCase_							)] for r in range(UpperCAmelCase_							)]


				def __str__(		self							):
								lowerCamelCase	 =f"""Matrix consist of {self.row} rows and {self.column} columns\n"""

								# Make string identifier
								lowerCamelCase	 =0
								for row_vector in self.array:
												for obj in row_vector:
																lowerCamelCase	 =max(UpperCAmelCase_   , len(str(UpperCAmelCase_							)							)							)
								lowerCamelCase	 =f"""%{max_element_length}s"""

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

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


				def __repr__(		self							):
								return str(self							)


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


				def __getitem__(		self   , UpperCAmelCase_							):
								assert self.validate_indicies(UpperCAmelCase_							)
								return self.array[loc[0]][loc[1]]


				def __setitem__(		self   , UpperCAmelCase_   , UpperCAmelCase_							):
								assert self.validate_indicies(UpperCAmelCase_							)
								lowerCamelCase	 =value


				def __add__(		self   , UpperCAmelCase_							):
								assert isinstance(UpperCAmelCase_   , UpperCAmelCase_							)
								assert self.row == another.row and self.column == another.column

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


				def __neg__(		self							):
								lowerCamelCase	 =Matrix(self.row   , self.column							)
								for r in range(self.row							):
												for c in range(self.column							):
																lowerCamelCase	 =-self[r, c]
								return result


				def __sub__(		self   , UpperCAmelCase_							):
								return self + (-another)


				def __mul__(		self   , UpperCAmelCase_							):

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


				def _snake_case       (		self							):
								lowerCamelCase	 =Matrix(self.column   , self.row							)
								for r in range(self.row							):
												for c in range(self.column							):
																lowerCamelCase	 =self[r, c]
								return result


				def _snake_case       (		self   , UpperCAmelCase_   , UpperCAmelCase_							):
								assert isinstance(UpperCAmelCase_   , UpperCAmelCase_							) and isinstance(UpperCAmelCase_   , UpperCAmelCase_							)
								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
								lowerCamelCase	 =v.transpose()
								lowerCamelCase	 =(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      _lowercase					(						)						->  None:
											# a^(-1)
											lowerCamelCase	 =Matrix(3			,      3			,      0				)
											for i in range(3				):
															lowerCamelCase	 =1
											print(F"""a^(-1) is {ainv}"""				)
											# u, v
											lowerCamelCase	 =Matrix(3			,      1			,      0				)
											lowerCamelCase ,  lowerCamelCase ,  lowerCamelCase	 =1, 2, -3
											lowerCamelCase	 =Matrix(3			,      1			,      0				)
											lowerCamelCase ,  lowerCamelCase ,  lowerCamelCase	 =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(_UpperCAmelCase			,      _UpperCAmelCase				)}"""				)





							def      _lowercase					(						)						->  None:
											import doctest

											doctest.testmod()




							testa()












def      _lowercase					(						_UpperCAmelCase			,      _UpperCAmelCase				)						->  List[str]:
				lowerCamelCase	 =[0 for i in range(r + 1				)]
				# nc0 = 1
				lowerCamelCase	 =1
				for i in range(1			,      n + 1				):
								# to compute current row from previous row.
								lowerCamelCase	 =min(_UpperCAmelCase			,      _UpperCAmelCase				)
								while j > 0:
												c[j] += c[j - 1]
												j -= 1
				return c[r]




print(binomial_coefficient(n=10, r=5))





