


def 				UpperCAmelCase_					(							__snake_case     ,						__snake_case						)     ->			tuple[float, float]:







 """simple docstring"""


 if not len(__snake_case						) == len(__snake_case						) == 3:
  raise ValueError('''Please enter a valid equation.'''						)
 if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
  raise ValueError('''Both a & b of two equations can\'t be zero.'''						)

 # Extract the coefficients
 _lowercase      ,    _lowercase      ,    _lowercase							      =equationa
 _lowercase      ,    _lowercase      ,    _lowercase							      =equationa

 # Calculate the determinants of the matrices
 _lowercase							      =aa * ba - aa * ba
 _lowercase							      =ca * ba - ca * ba
 _lowercase							      =aa * ca - aa * ca

 # Check if the system of linear equations has a solution (using Cramer's rule)
 if determinant == 0:
  if determinant_x == determinant_y == 0:
   raise ValueError('''Infinite solutions. (Consistent system)'''						)
  else:
   raise ValueError('''No solution. (Inconsistent system)'''						)
 else:
  if determinant_x == determinant_y == 0:
   # Trivial solution (Inconsistent system)
   return (0.0, 0.0)
  else:
   _lowercase							      =determinant_x / determinant
   _lowercase							      =determinant_y / determinant
   # Non-Trivial Solution (Consistent system)
   return (x, y)






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

   # Validation
   if not isinstance(snake_case__       ,     snake_case__	) or len(snake_case__	) == 0:
      raise ValueError('the string should be not empty string'	)

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

   # Build trie
   UpperCamelCase    :  dict[str, Any]							=	{}
   UpperCamelCase    :  List[str]							=	'WORD_KEEPER'

   for word in words:
      UpperCamelCase    :  List[str]							=	trie
      for c in word:
         if c not in trie_node:
            UpperCamelCase    :  int							=	{}

         UpperCamelCase    :  str							=	trie_node[c]

      UpperCamelCase    :  Tuple							=	True

   UpperCamelCase    :  List[Any]							=	len(snake_case__	)

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

      UpperCamelCase    :  Dict							=	trie
      for i in range(snake_case__       ,     snake_case__	):
         UpperCamelCase    :  List[Any]							=	trie_node.get(string[i]       ,     snake_case__	)

         if trie_node is None:
            return False

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

      return False

   return is_breakable(0	)


if __name__ == "__main__":
    import doctest

    doctest.testmod()



