






def 			lowercase__  (				A_:	list[list[int]]     ,			A_:	list[list[int]]		)  ->							list[list[int]]:







       """simple docstring"""






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







def 			lowercase__  (				A_:	int		)  ->							list[list[int]]:







       """simple docstring"""






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







def 			lowercase__  (				A_:	int		)  ->							int:







       """simple docstring"""






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







def 			lowercase__  (				A_:	int		)  ->							int:







       """simple docstring"""






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







def 			lowercase__  (				)  ->							None:







       """simple docstring"""






       for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
              __UpperCAmelCase    							=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(A_		)} and using bruteforce is '''
                  F'''{nth_fibonacci_bruteforce(A_		)}\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()












__A  							=  [0.485, 0.456, 0.406]
__A  							=  [0.229, 0.224, 0.225]
__A  							=  [0.5, 0.5, 0.5]
__A  							=  [0.5, 0.5, 0.5]
__A  							=  [0.4814_5466, 0.457_8275, 0.4082_1073]
__A  							=  [0.2686_2954, 0.2613_0258, 0.2757_7711]




