





from __future__ import annotations

import numpy as np





def   lowerCAmelCase_				( __a	):







  """simple docstring"""





  lowerCamelCase__						,      lowerCamelCase__:   Optional[Any]    						=np.shape(_SCREAMING_SNAKE_CASE	)
  if rows != columns:
    lowerCamelCase__:   Dict    						=(
        "\'table\' has to be of square shaped array but got a "
        F"""{rows}x{columns} array:\n{table}"""
    )
    raise ValueError(_SCREAMING_SNAKE_CASE	)

  lowerCamelCase__:   int    						=np.zeros((rows, columns)	)
  lowerCamelCase__:   int    						=np.zeros((rows, columns)	)
  for i in range(_SCREAMING_SNAKE_CASE	):
    for j in range(_SCREAMING_SNAKE_CASE	):
      lowerCamelCase__:   str    						=sum(lower[i][k] * upper[k][j] for k in range(_SCREAMING_SNAKE_CASE	)	)
      if upper[j][j] == 0:
        raise ArithmeticError("No LU decomposition exists"	)
      lowerCamelCase__:   str    						=(table[i][j] - total) / upper[j][j]
    lowerCamelCase__:   int    						=1
    for j in range(_SCREAMING_SNAKE_CASE			,					_SCREAMING_SNAKE_CASE	):
      lowerCamelCase__:   Any    						=sum(lower[i][k] * upper[k][j] for k in range(_SCREAMING_SNAKE_CASE	)	)
      lowerCamelCase__:   Tuple    						=table[i][j] - total
  return lower, upper


if __name__ == "__main__":
     import doctest

     doctest.testmod()








# Lint as: python3
import dataclasses
import re
from dataclasses import dataclass
from functools import total_ordering
from typing import Optional, Union


__A             =       re.compile(R"^(?P<major>\d+)" R"\.(?P<minor>\d+)" R"\.(?P<patch>\d+)$")



@total_ordering
@dataclass
class      _SCREAMING_SNAKE_CASE		:







 '''simple docstring'''
 lowercase_	=    42
 lowercase_	=    None
 lowercase_	=    None
 lowercase_	=    None
 lowercase_	=    None

 def 							SCREAMING_SNAKE_CASE_      (self       :     List[Any]) ->Tuple:



   '''simple docstring'''



   lowerCamelCase__						,      lowerCamelCase__						,      lowerCamelCase__:   List[str]    						=_str_to_version_tuple(self.version_str)

 def __repr__(self       :     Union[str, Any]) ->Union[str, Any]:



   '''simple docstring'''



   return F"""{self.tuple[0]}.{self.tuple[1]}.{self.tuple[2]}"""

 @property
 def 							SCREAMING_SNAKE_CASE_      (self       :     Optional[Any]) ->Optional[Any]:



   '''simple docstring'''



   return self.major, self.minor, self.patch

 def 							SCREAMING_SNAKE_CASE_      (self       :     Dict ,				UpperCAmelCase_       :     Tuple) ->Any:



   '''simple docstring'''



   if isinstance(UpperCAmelCase_ ,				UpperCAmelCase_):
     return Version(UpperCAmelCase_)
   elif isinstance(UpperCAmelCase_ ,				UpperCAmelCase_):
     return other
   raise TypeError(F"""{other} (type {type(UpperCAmelCase_)}) cannot be compared to version.""")

 def __eq__(self       :     Optional[Any] ,				UpperCAmelCase_       :     Tuple) ->List[str]:



   '''simple docstring'''



   try:
     lowerCamelCase__:   List[Any]    						=self._validate_operand(UpperCAmelCase_)
   except (TypeError, ValueError):
     return False
   else:
     return self.tuple == other.tuple

 def __lt__(self       :     Dict ,				UpperCAmelCase_       :     List[str]) ->Union[str, Any]:



   '''simple docstring'''



   lowerCamelCase__:   Tuple    						=self._validate_operand(UpperCAmelCase_)
   return self.tuple < other.tuple

 def __hash__(self       :     Any) ->Dict:



   '''simple docstring'''



   return hash(_version_tuple_to_str(self.tuple))

 @classmethod
 def 							SCREAMING_SNAKE_CASE_      (cls       :     Union[str, Any] ,				UpperCAmelCase_       :     Optional[Any]) ->Union[str, Any]:



   '''simple docstring'''



   lowerCamelCase__:   str    						={f.name for f in dataclasses.fields(cls)}
   return cls(**{k: v for k, v in dic.items() if k in field_names})







 def 							SCREAMING_SNAKE_CASE_      (self       :     Optional[int]) ->str:



   '''simple docstring'''



   return self.version_str





def   lowerCAmelCase_				( __a	)  ->	List[Any]:







  """simple docstring"""





  lowerCamelCase__:   Optional[int]    						=_VERSION_REG.match(__a	)
  if not res:
    raise ValueError(F"""Invalid version '{version_str}'. Format should be x.y.z with {{x,y,z}} being digits."""	)
  return tuple(int(__a	) for v in [res.group("major"	), res.group("minor"	), res.group("patch"	)]	)






def   lowerCAmelCase_				( __a	)  ->	Dict:







  """simple docstring"""





  return ".".join(str(__a	) for v in version_tuple	)

