
"""simple docstring"""






from __future__ import annotations

from decimal import Decimal

from numpy import array



def      lowerCAmelCase__			(		__magic_name__      )						->list[list[float]]:
			__lowercase       =       Decimal

			# Check if the provided matrix has 2 rows and 2 columns
			# since this implementation only works for 2x2 matrices
			if len(__magic_name__      ) == 2 and len(matrix[0]      ) == 2 and len(matrix[1]      ) == 2:
						# Calculate the determinant of the matrix
						__lowercase       =       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
						__lowercase       =       [[0.0, 0.0], [0.0, 0.0]]
						__lowercase   ,					__lowercase       =       matrix[1][1], matrix[0][0]
						__lowercase   ,					__lowercase       =       -matrix[1][0], -matrix[0][1]

						# Calculate the inverse of the matrix
						return [
						    [(float(d(__magic_name__      )      ) / determinant) or 0.0 for n in row] for row in swapped_matrix
						]
			elif (
			    len(__magic_name__      ) == 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
						__lowercase       =       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
						__lowercase       =       [
						    [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      )],
						]
						__lowercase       =       (d(matrix[1][1]      ) * d(matrix[2][2]      )) - (
						    d(matrix[1][2]      ) * d(matrix[2][1]      )
						)
						__lowercase       =       -(
						    (d(matrix[1][0]      ) * d(matrix[2][2]      )) - (d(matrix[1][2]      ) * d(matrix[2][0]      ))
						)
						__lowercase       =       (d(matrix[1][0]      ) * d(matrix[2][1]      )) - (
						    d(matrix[1][1]      ) * d(matrix[2][0]      )
						)
						__lowercase       =       -(
						    (d(matrix[0][1]      ) * d(matrix[2][2]      )) - (d(matrix[0][2]      ) * d(matrix[2][1]      ))
						)
						__lowercase       =       (d(matrix[0][0]      ) * d(matrix[2][2]      )) - (
						    d(matrix[0][2]      ) * d(matrix[2][0]      )
						)
						__lowercase       =       -(
						    (d(matrix[0][0]      ) * d(matrix[2][1]      )) - (d(matrix[0][1]      ) * d(matrix[2][0]      ))
						)
						__lowercase       =       (d(matrix[0][1]      ) * d(matrix[1][2]      )) - (
						    d(matrix[0][2]      ) * d(matrix[1][1]      )
						)
						__lowercase       =       -(
						    (d(matrix[0][0]      ) * d(matrix[1][2]      )) - (d(matrix[0][2]      ) * d(matrix[1][0]      ))
						)
						__lowercase       =       (d(matrix[0][0]      ) * d(matrix[1][1]      )) - (
						    d(matrix[0][1]      ) * d(matrix[1][0]      )
						)

						# Transpose the cofactor matrix (Adjoint matrix)
						__lowercase       =       array(__magic_name__      )
						for i in range(3      ):
									for j in range(3      ):
												__lowercase       =       cofactor_matrix[j][i]

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

        # Calculate the inverse of the matrix
						return [[float(d(__magic_name__      )      ) 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"""






from __future__ import annotations

from random import random

class 					__a     :



							'''simple docstring'''







							def __init__(     self  ,    _lowerCamelCase = None       )			->							str:




										'''simple docstring'''
										__lowercase       =       value
										__lowercase       =       random()
										__lowercase       =       None
										__lowercase       =       None
							def __repr__(     self       )			->							str:




										'''simple docstring'''
										from pprint import pformat

										if self.left is None and self.right is None:
													return f'''\'{self.value}: {self.prior:.5}\''''
										else:
													return pformat(
													    {f'''{self.value}: {self.prior:.5}''': (self.left, self.right)}  ,    indent=1       )





							def __str__(     self       )			->							str:




										'''simple docstring'''
										__lowercase       =       str(self.value       ) + " "
										__lowercase       =       str(self.left or ""       )
										__lowercase       =       str(self.right or ""       )
										return value + left + right





def      lowerCAmelCase__			(		__magic_name__			,   __magic_name__      )						->tuple[Node | None, Node | None]:
			if root is None:  # None tree is split into 2 Nones
						return None, None
			elif root.value is None:
						return None, None
			else:
						if value < root.value:
									__lowercase   ,					__lowercase       =       split(root.left			,   __magic_name__      )
									return left, root
						else:
									__lowercase   ,					__lowercase       =       split(root.right			,   __magic_name__      )
									return root, right



def      lowerCAmelCase__			(		__magic_name__			,   __magic_name__      )						->Node | None:
			if (not left) or (not right):  # If one node is None, return the other
						return left or right
			elif left.prior < right.prior:
						__lowercase       =       merge(left.right			,   __magic_name__      )
						return left
			else:
						__lowercase       =       merge(__magic_name__			,   right.left      )
						return right



def      lowerCAmelCase__			(		__magic_name__			,   __magic_name__      )						->Node | None:
			__lowercase       =       Node(__magic_name__      )
			__lowercase   ,					__lowercase       =       split(__magic_name__			,   __magic_name__      )
			return merge(merge(__magic_name__			,   __magic_name__      )			,   __magic_name__      )



def      lowerCAmelCase__			(		__magic_name__			,   __magic_name__      )						->Node | None:
			__lowercase   ,					__lowercase       =       split(__magic_name__			,   value - 1      )
			__lowercase   ,					__lowercase       =       split(__magic_name__			,   __magic_name__      )
			return merge(__magic_name__			,   __magic_name__      )



def      lowerCAmelCase__			(		__magic_name__      )						->None:
			if not root:  # None
						return
			else:
						inorder(root.left      )
						print(root.value			,   end=","      )
						inorder(root.right      )



def      lowerCAmelCase__			(		__magic_name__			,   __magic_name__      )						->Node | None:
			for arg in args.split():
						if arg[0] == "+":
									__lowercase       =       insert(__magic_name__			,   int(arg[1:]      )      )

						elif arg[0] == "-":
									__lowercase       =       erase(__magic_name__			,   int(arg[1:]      )      )

						else:
									print("Unknown command"      )

			return root



def      lowerCAmelCase__			(		)						->None:
			__lowercase       =       None
			print(
			    "enter numbers to create a tree, + value to add value into treap, "
			    "- value to erase all nodes with value. 'q' to quit. "      )

			__lowercase       =       input()
			while args != "q":
						__lowercase       =       interact_treap(__magic_name__			,   __magic_name__      )
						print(__magic_name__      )
						__lowercase       =       input()

			print("good by!"      )


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					main()





