






def 		A_			(		lowercase_					,       lowercase_	)							->str:







 """simple docstring"""

 SCREAMING_SNAKE_CASE							  =						[]
 SCREAMING_SNAKE_CASE							  =						len(lowercase_	)
 for i in range(lowercase_	):
  SCREAMING_SNAKE_CASE							  =						[]
  for j in range(lowercase_	):
   SCREAMING_SNAKE_CASE							  =						0
   for k in range(lowercase_	):
    SCREAMING_SNAKE_CASE							  =						val + matrix_a[i][k] * matrix_b[k][j]
   list_a.append(lowercase_	)
  matrix_c.append(lowercase_	)
 return matrix_c





def 		A_			(		lowercase_	)							->List[Any]:







 """simple docstring"""

 return [[int(row == column	) for column in range(lowercase_	)] for row in range(lowercase_	)]





def 		A_			(		lowercase_	)							->List[str]:







 """simple docstring"""

 if n <= 1:
  return n
 SCREAMING_SNAKE_CASE							  =						identity(2	)
 SCREAMING_SNAKE_CASE							  =						[[1, 1], [1, 0]]
 SCREAMING_SNAKE_CASE							  =						n - 1
 while n > 0:
  if n % 2 == 1:
   SCREAMING_SNAKE_CASE							  =						multiply(lowercase_					,       lowercase_	)
  SCREAMING_SNAKE_CASE							  =						multiply(lowercase_					,       lowercase_	)
  SCREAMING_SNAKE_CASE							  =						int(n / 2	)
 return res_matrix[0][0]





def 		A_			(		lowercase_	)							->Any:







 """simple docstring"""

 if n <= 1:
  return n
 SCREAMING_SNAKE_CASE							  =						0
 SCREAMING_SNAKE_CASE							  =						1
 for _ in range(2					,       n + 1	):
  SCREAMING_SNAKE_CASE  , SCREAMING_SNAKE_CASE							  =						fiba, fiba + fiba
 return fiba





def 		A_			(		)							->Tuple:







 """simple docstring"""

 for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
  SCREAMING_SNAKE_CASE							  =						int(''.join(c for c in ordinal if c in '0123456789'	)	)  # 1000th --> 1000
  print(
      f'''{ordinal} fibonacci number using matrix exponentiation is '''
      f'''{nth_fibonacci_matrix(lowercase_	)} and using bruteforce is '''
      f'''{nth_fibonacci_bruteforce(lowercase_	)}\n'''	)
 # from timeit import timeit
 # print(timeit("nth_fibonacci_matrix(1000000)",
 #              "from main import nth_fibonacci_matrix", number=5))
 # print(timeit("nth_fibonacci_bruteforce(1000000)",
 #              "from main import nth_fibonacci_bruteforce", number=5))
 # 2.3342058970001744
 # 57.256506615000035


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      main()












def 		A_			(		lowercase_	)							->int:







 """simple docstring"""

 if not isinstance(lowercase_					,       lowercase_	):
  SCREAMING_SNAKE_CASE							  =						f'''Input value of [number={number}] must be an integer'''
  raise TypeError(lowercase_	)
 if number < 1:
  raise ValueError('Input must be a positive integer'	)
 return number * (2 * number - 1)


if __name__ == "__main__":
      import doctest

      doctest.testmod()




