




'''simple docstring'''







from functools import lru_cache






@lru_cache
def 		_lowercase		(	lowercase_  ):



		'''simple docstring'''







		if not isinstance(lowercase_						,							lowercase_  ):
				raise TypeError("k must be an integer."  )
		if k < 0:
				raise ValueError("k integer must be greater or equal to zero."  )
		if k == 0:
				return 0
		elif k == 1:
				return 1
		else:
				return fibonacci(k - 1  ) + fibonacci(k - 2  )






def 		_lowercase		(	lowercase_						,							lowercase_  ):



		'''simple docstring'''







		_snake_case	       =       len(lowercase_  )
		# Find m such that F_m >= n where F_i is the i_th fibonacci number.
		_snake_case	       =       0
		while True:
				if fibonacci(lowercase_  ) >= len_list:
						_snake_case	       =       i
						break
				i += 1
		_snake_case	       =       0
		while fibb_k > 0:
				_snake_case	       =       min(
				    offset + fibonacci(fibb_k - 1  )						,							len_list - 1  )  # Prevent out of range
				_snake_case	       =       arr[index_k]
				if item_k_1 == val:
						return index_k
				elif val < item_k_1:
						fibb_k -= 1
				elif val > item_k_1:
						offset += fibonacci(fibb_k - 1  )
						fibb_k -= 2
		else:
				return -1


if __name__ == "__main__":
						import doctest

						doctest.testmod()











'''simple docstring'''







from __future__ import annotations

import math
from itertools import permutations






def 		_lowercase		(	lowercase_  ):



		'''simple docstring'''







		if 1 < number < 4:
				# 2 and 3 are primes
				return True
		elif number < 2 or number % 2 == 0 or number % 3 == 0:
				# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
				return False

		# All primes number are in format of 6k +/- 1
		for i in range(5						,							int(math.sqrt(lowercase_  ) + 1  )						,							6  ):
				if number % i == 0 or number % (i + 2) == 0:
						return False
		return True






def 		_lowercase		(	lowercase_ = 7  ):



		'''simple docstring'''







		_snake_case	       =       "".join(str(lowercase_  ) for i in range(1						,							n + 1  )  )
		_snake_case	       =       [int("".join(lowercase_  )  ) for i in permutations(lowercase_						,							lowercase_  )]
		_snake_case	       =       [num for num in perm_list if is_prime(lowercase_  )]
		return max(lowercase_  ) if pandigitals else 0


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





