






from __future__ import annotations


class       __lowercase      :







     '''simple docstring'''




     def __init__(				self       :			Optional[Any] ,	UpperCamelCase_       :			Tuple				):


         """simple docstring"""



         __A         =	TypeError(
             """Matrices must be formed from a list of zero or more lists containing at """
             """least one and the same number of values, each of which must be of type """
             """int or float."""				)
         if len(_SCREAMING_SNAKE_CASE				) != 0:
             __A         =	len(rows[0]				)
             if cols == 0:
                 raise error
             for row in rows:
                 if len(_SCREAMING_SNAKE_CASE				) != cols:
                     raise error
                 for value in row:
                     if not isinstance(_SCREAMING_SNAKE_CASE ,	(int, float)				):
                         raise error
             __A         =	rows
         else:
             __A         =	[]




     def 		lowerCAmelCase_     (				self       :			List[str]				):


         """simple docstring"""



         return [[row[i] for row in self.rows] for i in range(len(self.rows[0]				)				)]




     @property
     def 		lowerCAmelCase_     (				self       :			Tuple				):


         """simple docstring"""



         return len(self.rows				)




     @property
     def 		lowerCAmelCase_     (				self       :			str				):


         """simple docstring"""



         return len(self.rows[0]				)




     @property
     def 		lowerCAmelCase_     (				self       :			Any				):


         """simple docstring"""



         return (self.num_rows, self.num_columns)




     @property
     def 		lowerCAmelCase_     (				self       :			str				):


         """simple docstring"""



         return self.order[0] == self.order[1]




     def 		lowerCAmelCase_     (				self       :			Dict				):


         """simple docstring"""



         __A         =	[
             [0 if column_num != row_num else 1 for column_num in range(self.num_rows				)]
             for row_num in range(self.num_rows				)
         ]
         return Matrix(_SCREAMING_SNAKE_CASE				)




     def 		lowerCAmelCase_     (				self       :			Union[str, Any]				):


         """simple docstring"""



         if not self.is_square:
             return 0
         if self.order == (0, 0):
             return 1
         if self.order == (1, 1):
             return int(self.rows[0][0]				)
         if self.order == (2, 2):
             return int(
                 (self.rows[0][0] * self.rows[1][1])
                 - (self.rows[0][1] * self.rows[1][0])				)
         else:
             return sum(
                 self.rows[0][column] * self.cofactors().rows[0][column]
                 for column in range(self.num_columns				)				)




     def 		lowerCAmelCase_     (				self       :			Union[str, Any]				):


         """simple docstring"""



         return bool(self.determinant()				)




     def 		lowerCAmelCase_     (				self       :			List[str] ,	UpperCamelCase_       :			List[Any] ,	UpperCamelCase_       :			str				):


         """simple docstring"""



         __A         =	[
             [
                 self.rows[other_row][other_column]
                 for other_column in range(self.num_columns				)
                 if other_column != column
             ]
             for other_row in range(self.num_rows				)
             if other_row != row
         ]
         return Matrix(_SCREAMING_SNAKE_CASE				).determinant()




     def 		lowerCAmelCase_     (				self       :			Dict ,	UpperCamelCase_       :			List[str] ,	UpperCamelCase_       :			List[Any]				):


         """simple docstring"""



         if (row + column) % 2 == 0:
             return self.get_minor(_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				)
         return -1 * self.get_minor(_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				)




     def 		lowerCAmelCase_     (				self       :			List[str]				):


         """simple docstring"""



         return Matrix(
             [
                 [self.get_minor(_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				) for column in range(self.num_columns				)]
                 for row in range(self.num_rows				)
             ]				)




     def 		lowerCAmelCase_     (				self       :			List[Any]				):


         """simple docstring"""



         return Matrix(
             [
                 [
                     self.minors().rows[row][column]
                     if (row + column) % 2 == 0
                     else self.minors().rows[row][column] * -1
                     for column in range(self.minors().num_columns				)
                 ]
                 for row in range(self.minors().num_rows				)
             ]				)




     def 		lowerCAmelCase_     (				self       :			Union[str, Any]				):


         """simple docstring"""



         __A         =	[
             [self.cofactors().rows[column][row] for column in range(self.num_columns				)]
             for row in range(self.num_rows				)
         ]
         return Matrix(_SCREAMING_SNAKE_CASE				)




     def 		lowerCAmelCase_     (				self       :			List[Any]				):


         """simple docstring"""



         __A         =	self.determinant()
         if not determinant:
             raise TypeError("""Only matrices with a non-zero determinant have an inverse"""				)
         return self.adjugate() * (1 / determinant)




     def __repr__(				self       :			Dict				):


         """simple docstring"""



         return str(self.rows				)




     def __str__(				self       :			List[Any]				):


         """simple docstring"""



         if self.num_rows == 0:
             return "[]"
         if self.num_rows == 1:
             return "[[" + ". ".join(str(self.rows[0]				)				) + "]]"
         return (
             "["
             + "\n ".join(
                 [
                     """[""" + """. """.join([str(_SCREAMING_SNAKE_CASE				) for value in row]				) + """.]"""
                     for row in self.rows
                 ]				)
             + "]"
         )




     def 		lowerCAmelCase_     (				self       :			Optional[int] ,	UpperCamelCase_       :			Union[str, Any] ,	UpperCamelCase_       :			List[Any] = None				):


         """simple docstring"""



         __A         =	TypeError("""Row must be a list containing all ints and/or floats"""				)
         if not isinstance(_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
             raise type_error
         for value in row:
             if not isinstance(_SCREAMING_SNAKE_CASE ,	(int, float)				):
                 raise type_error
         if len(_SCREAMING_SNAKE_CASE				) != self.num_columns:
             raise ValueError(
                 """Row must be equal in length to the other rows in the matrix"""				)
         if position is None:
             self.rows.append(_SCREAMING_SNAKE_CASE				)
         else:
             __A         =	self.rows[0:position] + [row] + self.rows[position:]




     def 		lowerCAmelCase_     (				self       :			str ,	UpperCamelCase_       :			Tuple ,	UpperCamelCase_       :			Union[str, Any] = None				):


         """simple docstring"""



         __A         =	TypeError(
             """Column must be a list containing all ints and/or floats"""				)
         if not isinstance(_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
             raise type_error
         for value in column:
             if not isinstance(_SCREAMING_SNAKE_CASE ,	(int, float)				):
                 raise type_error
         if len(_SCREAMING_SNAKE_CASE				) != self.num_rows:
             raise ValueError(
                 """Column must be equal in length to the other columns in the matrix"""				)
         if position is None:
             __A         =	[self.rows[i] + [column[i]] for i in range(self.num_rows				)]
         else:
             __A         =	[
                 self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
                 for i in range(self.num_rows				)
             ]




     def __eq__(				self       :			List[str] ,	UpperCamelCase_       :			str				):


         """simple docstring"""



         if not isinstance(_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
             return NotImplemented
         return self.rows == other.rows




     def __ne__(				self       :			Tuple ,	UpperCamelCase_       :			Union[str, Any]				):


         """simple docstring"""



         return not self == other




     def __neg__(				self       :			Dict				):


         """simple docstring"""



         return self * -1




     def __add__(				self       :			List[str] ,	UpperCamelCase_       :			List[Any]				):


         """simple docstring"""



         if self.order != other.order:
             raise ValueError("""Addition requires matrices of the same order"""				)
         return Matrix(
             [
                 [self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns				)]
                 for i in range(self.num_rows				)
             ]				)




     def __sub__(				self       :			Any ,	UpperCamelCase_       :			int				):


         """simple docstring"""



         if self.order != other.order:
             raise ValueError("""Subtraction requires matrices of the same order"""				)
         return Matrix(
             [
                 [self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns				)]
                 for i in range(self.num_rows				)
             ]				)




     def __mul__(				self       :			List[str] ,	UpperCamelCase_       :			Optional[Any]				):


         """simple docstring"""



         if isinstance(_SCREAMING_SNAKE_CASE ,	(int, float)				):
             return Matrix(
                 [[int(element * other				) for element in row] for row in self.rows]				)
         elif isinstance(_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
             if self.num_columns != other.num_rows:
                 raise ValueError(
                     """The number of columns in the first matrix must """
                     """be equal to the number of rows in the second"""				)
             return Matrix(
                 [
                     [Matrix.dot_product(_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				) for column in other.columns()]
                     for row in self.rows
                 ]				)
         else:
             raise TypeError(
                 """A Matrix can only be multiplied by an int, float, or another matrix"""				)




     def __pow__(				self       :			Optional[int] ,	UpperCamelCase_       :			Tuple				):


         """simple docstring"""



         if not isinstance(_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
             raise TypeError("""A Matrix can only be raised to the power of an int"""				)
         if not self.is_square:
             raise ValueError("""Only square matrices can be raised to a power"""				)
         if other == 0:
             return self.identity()
         if other < 0:
             if self.is_invertable():
                 return self.inverse() ** (-other)
             raise ValueError(
                 """Only invertable matrices can be raised to a negative power"""				)
         __A         =	self
         for _ in range(other - 1				):
             result *= self
         return result





     @classmethod
     def 		lowerCAmelCase_     (				cls       :			Union[str, Any] ,	UpperCamelCase_       :			Optional[int] ,	UpperCamelCase_       :			Dict				):


         """simple docstring"""



         return sum(row[i] * column[i] for i in range(len(_SCREAMING_SNAKE_CASE				)				)				)


if __name__ == "__main__":
   import doctest

   doctest.testmod()












import random
import sys

import numpy as np
from matplotlib import pyplot as plt
from matplotlib.colors import ListedColormap

__a      :       List[Any]				  =   "Usage of script: script_name <size_of_canvas:int>"

__a      :       Dict				  =   [0] * 100 + [1] * 10
random.shuffle(choice)



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			int    )						->      list[list[bool]]:





    """simple docstring"""

    __A         =	[[False for i in range(__lowercase    )] for j in range(__lowercase    )]
    return canvas



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			list[list[bool]]    )						->      None:





    """simple docstring"""

    for i, row in enumerate(__lowercase    ):
        for j, _ in enumerate(__lowercase    ):
            __A         =	bool(random.getrandbits(1    )    )



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			list[list[bool]]    )						->      list[list[bool]]:





    """simple docstring"""

    __A         =	np.array(__lowercase    )
    __A         =	np.array(create_canvas(current_canvas.shape[0]    )    )
    for r, row in enumerate(__lowercase    ):
        for c, pt in enumerate(__lowercase    ):
            __A         =	__judge_point(
                __lowercase			,				current_canvas[r - 1 : r + 2, c - 1 : c + 2]    )

    __A         =	next_gen_canvas
    del next_gen_canvas  # cleaning memory as we move on.
    __A         =	current_canvas.tolist()
    return return_canvas



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			bool			,				__lowercase   :			list[list[bool]]    )						->      bool:





    """simple docstring"""

    __A         =	0
    __A         =	0
    # finding dead or alive neighbours count.
    for i in neighbours:
        for status in i:
            if status:
                alive += 1
            else:
                dead += 1

    # handling duplicate entry for focus pt.
    if pt:
        alive -= 1
    else:
        dead -= 1

    # running the rules of game here.
    __A         =	pt
    if pt:
        if alive < 2:
            __A         =	False
        elif alive == 2 or alive == 3:
            __A         =	True
        elif alive > 3:
            __A         =	False
    else:
        if alive == 3:
            __A         =	True

    return state


if __name__ == "__main__":
  if len(sys.argv) != 2:
    raise Exception(usage_doc)

  __a      :       str				  =   int(sys.argv[1])
  # main working structure of this module.
  __a      :       List[Any]				  =   create_canvas(canvas_size)
  seed(c)
  __a  ,__a      :       int				  =   plt.subplots()
  fig.show()
  __a      :       Union[str, Any]				  =   ListedColormap(["w", "k"])
  try:
    while True:
      __a      :       Dict				  =   run(c)
      ax.matshow(c, cmap=cmap)
      fig.canvas.draw()
      ax.cla()
  except KeyboardInterrupt:
    # do nothing.
    pass




