





'''simple docstring'''




import functools
from typing import Any
def 	UpperCAmelCase_							(					__lowercase							:      str			,     __lowercase							:      list[str]       )		->       bool:


     '''simple docstring'''



     if not isinstance(__lowercase			,     __lowercase       ) or len(__lowercase       ) == 0:
          raise ValueError("the string should be not empty string"       )

     if not isinstance(__lowercase			,     __lowercase       ) or not all(
         isinstance(__lowercase			,     __lowercase       ) and len(__lowercase       ) > 0 for item in words       ):
          raise ValueError("the words should be a list of non-empty strings"       )

     # Build trie
     _UpperCAmelCase     							=   {}
     _UpperCAmelCase     							=   "WORD_KEEPER"

     for word in words:
          _UpperCAmelCase     							=   trie
          for c in word:
               if c not in trie_node:
                    _UpperCAmelCase     							=   {}

               _UpperCAmelCase     							=   trie_node[c]

          _UpperCAmelCase     							=   True

     _UpperCAmelCase     							=   len(__lowercase       )

     # Dynamic programming method
     @functools.cache
     def is_breakable(__lowercase							:      int       ) -> bool:
          if index == len_string:
               return True

          _UpperCAmelCase     							=   trie
          for i in range(__lowercase			,     __lowercase       ):
               _UpperCAmelCase     							=   trie_node.get(string[i]			,     __lowercase       )

               if trie_node is None:
                    return False

               if trie_node.get(__lowercase			,     __lowercase       ) and is_breakable(i + 1       ):
                    return True

          return False

     return is_breakable(0       )


if __name__ == "__main__":
  import doctest

  doctest.testmod()











'''simple docstring'''

from __future__ import annotations

from decimal import Decimal

from numpy import array





def 						UpperCamelCase				(							_lowerCamelCase					:					list[list[float]]       ):
    A__				=			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
        A__				=			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
        A__				=			[[0.0, 0.0], [0.0, 0.0]]
        A__,	A__				=			matrix[1][1], matrix[0][0]
        A__,	A__				=			-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
        A__				=			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
        A__				=			[
            [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       )],
        ]
        A__				=			(d(matrix[1][1]       ) * d(matrix[2][2]       )) - (
            d(matrix[1][2]       ) * d(matrix[2][1]       )
        )
        A__				=			-(
            (d(matrix[1][0]       ) * d(matrix[2][2]       )) - (d(matrix[1][2]       ) * d(matrix[2][0]       ))
        )
        A__				=			(d(matrix[1][0]       ) * d(matrix[2][1]       )) - (
            d(matrix[1][1]       ) * d(matrix[2][0]       )
        )
        A__				=			-(
            (d(matrix[0][1]       ) * d(matrix[2][2]       )) - (d(matrix[0][2]       ) * d(matrix[2][1]       ))
        )
        A__				=			(d(matrix[0][0]       ) * d(matrix[2][2]       )) - (
            d(matrix[0][2]       ) * d(matrix[2][0]       )
        )
        A__				=			-(
            (d(matrix[0][0]       ) * d(matrix[2][1]       )) - (d(matrix[0][1]       ) * d(matrix[2][0]       ))
        )
        A__				=			(d(matrix[0][1]       ) * d(matrix[1][2]       )) - (
            d(matrix[0][2]       ) * d(matrix[1][1]       )
        )
        A__				=			-(
            (d(matrix[0][0]       ) * d(matrix[1][2]       )) - (d(matrix[0][2]       ) * d(matrix[1][0]       ))
        )
        A__				=			(d(matrix[0][0]       ) * d(matrix[1][1]       )) - (
            d(matrix[0][1]       ) * d(matrix[1][0]       )
        )

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

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
        A__				=			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."       )



