






"""simple docstring"""



from __future__ import annotations

from decimal import Decimal

from numpy import array

def 			_snake_case    (					lowerCamelCase__     :   list[list[float]]  )    ->     list[list[float]]:
							lowerCamelCase_	:							List[str]									=Decimal

							# Check if the provided matrix has 2 rows and 2 columns
							# since this implementation only works for 2x2 matrices
							if len(lowerCamelCase__  ) == 2 and len(matrix[0]  ) == 2 and len(matrix[1]  ) == 2:
														# Calculate the determinant of the matrix
														lowerCamelCase_	:							Any									=float(
														    d(matrix[0][0]  ) * d(matrix[1][1]  ) - d(matrix[1][0]  ) * d(matrix[0][1]  )  )
														if determinant == 0:
																					raise ValueError("This matrix has no inverse."  )

														# Creates a copy of the matrix with swapped positions of the elements
														lowerCamelCase_	:							str									=[[0.0, 0.0], [0.0, 0.0]]
														lowerCamelCase_							,						lowerCamelCase_	:							Optional[Any]									=matrix[1][1], matrix[0][0]
														lowerCamelCase_							,						lowerCamelCase_	:							int									=-matrix[1][0], -matrix[0][1]

														# Calculate the inverse of the matrix
														return [
														    [(float(d(lowerCamelCase__  )  ) / determinant) or 0.0 for n in row] for row in swapped_matrix
														]
							elif (
							    len(lowerCamelCase__  ) == 3
							    and len(matrix[0]  ) == 3
							    and len(matrix[1]  ) == 3
							    and len(matrix[2]  ) == 3
							):
														# Calculate the determinant of the matrix using Sarrus rule
														lowerCamelCase_	:							int									=float(
														    (
														        (d(matrix[0][0]  ) * d(matrix[1][1]  ) * d(matrix[2][2]  ))
														        + (d(matrix[0][1]  ) * d(matrix[1][2]  ) * d(matrix[2][0]  ))
														        + (d(matrix[0][2]  ) * d(matrix[1][0]  ) * d(matrix[2][1]  ))
														    )
														    - (
														        (d(matrix[0][2]  ) * d(matrix[1][1]  ) * d(matrix[2][0]  ))
														        + (d(matrix[0][1]  ) * d(matrix[1][0]  ) * d(matrix[2][2]  ))
														        + (d(matrix[0][0]  ) * d(matrix[1][2]  ) * d(matrix[2][1]  ))
														    )  )
														if determinant == 0:
																					raise ValueError("This matrix has no inverse."  )

														# Creating cofactor matrix
														lowerCamelCase_	:							Optional[Any]									=[
														    [d(0.0  ), d(0.0  ), d(0.0  )],
														    [d(0.0  ), d(0.0  ), d(0.0  )],
														    [d(0.0  ), d(0.0  ), d(0.0  )],
														]
														lowerCamelCase_	:							Union[str, Any]									=(d(matrix[1][1]  ) * d(matrix[2][2]  )) - (
														    d(matrix[1][2]  ) * d(matrix[2][1]  )
														)
														lowerCamelCase_	:							Any									=-(
														    (d(matrix[1][0]  ) * d(matrix[2][2]  )) - (d(matrix[1][2]  ) * d(matrix[2][0]  ))
														)
														lowerCamelCase_	:							List[str]									=(d(matrix[1][0]  ) * d(matrix[2][1]  )) - (
														    d(matrix[1][1]  ) * d(matrix[2][0]  )
														)
														lowerCamelCase_	:							int									=-(
														    (d(matrix[0][1]  ) * d(matrix[2][2]  )) - (d(matrix[0][2]  ) * d(matrix[2][1]  ))
														)
														lowerCamelCase_	:							Any									=(d(matrix[0][0]  ) * d(matrix[2][2]  )) - (
														    d(matrix[0][2]  ) * d(matrix[2][0]  )
														)
														lowerCamelCase_	:							str									=-(
														    (d(matrix[0][0]  ) * d(matrix[2][1]  )) - (d(matrix[0][1]  ) * d(matrix[2][0]  ))
														)
														lowerCamelCase_	:							List[str]									=(d(matrix[0][1]  ) * d(matrix[1][2]  )) - (
														    d(matrix[0][2]  ) * d(matrix[1][1]  )
														)
														lowerCamelCase_	:							Optional[Any]									=-(
														    (d(matrix[0][0]  ) * d(matrix[1][2]  )) - (d(matrix[0][2]  ) * d(matrix[1][0]  ))
														)
														lowerCamelCase_	:							List[str]									=(d(matrix[0][0]  ) * d(matrix[1][1]  )) - (
														    d(matrix[0][1]  ) * d(matrix[1][0]  )
														)

														# Transpose the cofactor matrix (Adjoint matrix)
														lowerCamelCase_	:							Optional[int]									=array(lowerCamelCase__  )
														for i in range(3  ):
																					for j in range(3  ):
																												lowerCamelCase_	:							Optional[int]									=cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
														lowerCamelCase_	:							Tuple									=array(lowerCamelCase__  )
														for i in range(3  ):
																					for j in range(3  ):
																												inverse_matrix[i][j] /= d(lowerCamelCase__  )

        # Calculate the inverse of the matrix
														return [[float(d(lowerCamelCase__  )  ) or 0.0 for n in row] for row in inverse_matrix]
							raise ValueError("Please provide a matrix of size 2x2 or 3x3."  )











"""simple docstring"""



def 			_snake_case    (					lowerCamelCase__     :   Optional[Any]  )    ->     Optional[int]:
							if not head:
														return True
							# split the list to two parts
							lowerCamelCase_							,						lowerCamelCase_	:							Union[str, Any]									=head.next, head
							while fast and fast.next:
														lowerCamelCase_	:							Optional[Any]									=fast.next.next
														lowerCamelCase_	:							str									=slow.next
							lowerCamelCase_	:							Tuple									=slow.next
							lowerCamelCase_	:							Any									=None  # Don't forget here! But forget still works!
							# reverse the second part
							lowerCamelCase_	:							List[str]									=None
							while second:
														lowerCamelCase_	:							Any									=second.next
														lowerCamelCase_	:							Union[str, Any]									=node
														lowerCamelCase_	:							Union[str, Any]									=second
														lowerCamelCase_	:							Optional[Any]									=nxt
							# compare two parts
							# second part has the same or one less node
							while node:
														if node.val != head.val:
																					return False
														lowerCamelCase_	:							List[str]									=node.next
														lowerCamelCase_	:							Optional[Any]									=head.next
							return True

def 			_snake_case    (					lowerCamelCase__     :   str  )    ->     Optional[int]:
							if not head or not head.next:
														return True

							# 1. Get the midpoint (slow)
							lowerCamelCase_	:							List[str]									=head
							while fast and fast.next:
														lowerCamelCase_							,						lowerCamelCase_	:							Union[str, Any]									=fast.next.next, slow.next

							# 2. Push the second half into the stack
							lowerCamelCase_	:							List[Any]									=[slow.val]
							while slow.next:
														lowerCamelCase_	:							List[Any]									=slow.next
														stack.append(slow.val  )

							# 3. Comparison
							while stack:
														if stack.pop() != cur.val:
																					return False
														lowerCamelCase_	:							Union[str, Any]									=cur.next

							return True

def 			_snake_case    (					lowerCamelCase__     :   Dict  )    ->     Optional[Any]:
							if not head or not head.next:
														return True
							lowerCamelCase_	:							Union[str, Any]									={}
							lowerCamelCase_	:							List[Any]									=0
							while head:
														if head.val in d:
																					d[head.val].append(lowerCamelCase__  )
														else:
																					lowerCamelCase_	:							List[str]									=[pos]
														lowerCamelCase_	:							Optional[int]									=head.next
														pos += 1
							lowerCamelCase_	:							Union[str, Any]									=pos - 1
							lowerCamelCase_	:							Optional[int]									=0
							for v in d.values():
														if len(lowerCamelCase__  ) % 2 != 0:
																					middle += 1
														else:
																					lowerCamelCase_	:							Optional[Any]									=0
																					for i in range(0    ,						len(lowerCamelCase__  )  ):
																												if v[i] + v[len(lowerCamelCase__  ) - 1 - step] != checksum:
																																			return False
																												step += 1
														if middle > 1:
																					return False
							return True



