






"""simple docstring"""




def   a      (						lowerCamelCase_		,       lowerCamelCase_    ):






				'''simple docstring'''
				lowercase__       			=      []
				lowercase__       			=      len(_UpperCamelCase    )
				for i in range(_UpperCamelCase    ):
								lowercase__       			=      []
								for j in range(_UpperCamelCase    ):
												lowercase__       			=      0
												for k in range(_UpperCamelCase    ):
																lowercase__       			=      val + matrix_a[i][k] * matrix_b[k][j]
												list_a.append(_UpperCamelCase    )
								matrix_c.append(_UpperCamelCase    )
				return matrix_c






def   a      (						lowerCamelCase_    ):






				'''simple docstring'''
				return [[int(row == column    ) for column in range(_UpperCamelCase    )] for row in range(_UpperCamelCase    )]






def   a      (						lowerCamelCase_    ):






				'''simple docstring'''




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






def   a      (						lowerCamelCase_    ):






				'''simple docstring'''




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






def   a      (						):






				'''simple docstring'''




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












from collections import defaultdict






def   a      (						lowerCamelCase_ = 5    ):






				'''simple docstring'''
				lowercase__       			=      defaultdict(lowerCamelCase_    )
				lowercase__       			=      0

				while True:
								lowercase__       			=      get_digits(lowerCamelCase_    )
								freqs[digits].append(lowerCamelCase_    )

								if len(freqs[digits]    ) == max_base:
												lowercase__       			=      freqs[digits][0] ** 3
												return base

								num += 1






def   a      (						lowerCamelCase_    ):






				'''simple docstring'''
				return "".join(sorted(str(num**3    )    )    )


if __name__ == "__main__":
							print(F"{solution() = }")




