






"""simple docstring"""



def       snake_case__		(   _SCREAMING_SNAKE_CASE       ,	_SCREAMING_SNAKE_CASE			)    ->list[list[int]]:
 UpperCAmelCase__ 						=				[]
 UpperCAmelCase__ 						=				len(lowerCamelCase__			)
 for i in range(lowerCamelCase__			):
  UpperCAmelCase__ 						=				[]
  for j in range(lowerCamelCase__			):
   UpperCAmelCase__ 						=				0
   for k in range(lowerCamelCase__			):
    UpperCAmelCase__ 						=				val + matrix_a[i][k] * matrix_b[k][j]
   list_a.append(lowerCamelCase__			)
  matrix_c.append(lowerCamelCase__			)
 return matrix_c




def       snake_case__		(   _SCREAMING_SNAKE_CASE			)    ->list[list[int]]:
 return [[int(row == column			) for column in range(lowerCamelCase__			)] for row in range(lowerCamelCase__			)]




def       snake_case__		(   _SCREAMING_SNAKE_CASE			)    ->int:
 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(lowerCamelCase__       ,	lowerCamelCase__			)
  UpperCAmelCase__ 						=				multiply(lowerCamelCase__       ,	lowerCamelCase__			)
  UpperCAmelCase__ 						=				int(n / 2			)
 return res_matrix[0][0]




def       snake_case__		(   _SCREAMING_SNAKE_CASE			)    ->int:
 if n <= 1:
  return n
 UpperCAmelCase__ 						=				0
 UpperCAmelCase__ 						=				1
 for _ in range(2       ,	n + 1			):
  UpperCAmelCase__ 						=				fiba, fiba + fiba
 return fiba




def       snake_case__		(   )    ->None:
 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(lowerCamelCase__			)} and using bruteforce is '''
      F'''{nth_fibonacci_bruteforce(lowerCamelCase__			)}\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()









'''simple docstring'''




from itertools import permutations




def     snake_case__     (			lowerCamelCase__					: int = 5      ) -> int:
					if gon_side < 3 or gon_side > 5:
										raise ValueError('''gon_side must be in the range [3, 5]'''      )

					# Since it's 16, we know 10 is on the outer ring
					# Put the big numbers at the end so that they are never the first number
					A_			:  int			=				list(range(gon_side + 1      ,		0      ,		-1      )      )
					A_			:  List[Any]			=				list(range(gon_side + 2      ,		gon_side * 2 + 1      )      )

					for perm in permutations(small_numbers + big_numbers      ):
										A_			:  Optional[int]			=				generate_gon_ring(lowerCamelCase__      ,		list(lowerCamelCase__      )      )
										if is_magic_gon(lowerCamelCase__      ):
															return int(''''''.join(str(lowerCamelCase__      ) for n in numbers      )      )

					A_			:  Optional[Any]			=				f'Magic {gon_side}-gon ring is impossible'
					raise ValueError(lowerCamelCase__      )




def     snake_case__     (			lowerCamelCase__					: int      ,		lowerCamelCase__					: list[int]      ) -> list[int]:
					A_			:  List[Any]			=				[0] * (gon_side * 3)
					A_			:  Optional[Any]			=				perm[0:3]
					perm.append(perm[1]      )

					A_			:  Optional[Any]			=				1 if gon_side < 5 else 2

					for i in range(1      ,		len(lowerCamelCase__      ) // 3 + magic_number      ):
										A_			:  List[str]			=				perm[2 * i + 1]
										A_			:  str			=				result[3 * i - 1]
										A_			:  Union[str, Any]			=				perm[2 * i + 2]

					return result




def     snake_case__     (			lowerCamelCase__					: list[int]      ) -> bool:
					if len(lowerCamelCase__      ) % 3 != 0:
										raise ValueError('''a gon ring should have a length that is a multiple of 3'''      )

					if min(numbers[::3]      ) != numbers[0]:
										return False

					A_			:  Union[str, Any]			=				sum(numbers[:3]      )

					return all(sum(numbers[i : i + 3]      ) == total for i in range(3      ,		len(lowerCamelCase__      )      ,		3      )      )


if __name__ == "__main__":
							print(solution())



