





"""simple docstring"""




from __future__ import annotations

import math





def 	a_    (							_lowercase       ):

						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 	a_    (							_lowercase       ):
						_UpperCamelCase      : List[str]         =   str(_lowercase       )
						_UpperCamelCase      : str         =   [n]
						for i in range(1	,						len(_lowercase       )       ):
												list_nums.append(int(str_num[i:]       )       )
												list_nums.append(int(str_num[:-i]       )       )
						return list_nums





def 	a_    (							_lowercase       ):
						if len(str(_lowercase       )       ) > 3:
												if not is_prime(int(str(_lowercase       )[-3:]       )       ) or not is_prime(int(str(_lowercase       )[:3]       )       ):
																		return False
						return True





def 	a_    (							_lowercase = 11       ):
						_UpperCamelCase      : list[int]         =   []
						_UpperCamelCase      : Optional[int]         =   13
						while len(_lowercase       ) != count:
												if validate(_lowercase       ):
																		_UpperCamelCase      : int         =   list_truncated_nums(_lowercase       )
																		if all(is_prime(_lowercase       ) for i in list_nums       ):
																								list_truncated_primes.append(_lowercase       )
												num += 2
						return list_truncated_primes





def 	a_    (							):
						return sum(compute_truncated_primes(11       )       )


if __name__ == "__main__":
						print(F"{sum(compute_truncated_primes(11)) = }")










"""simple docstring"""




from __future__ import annotations

import math





def 	a_    (							_lowercase	,						_lowercase	,						_lowercase	,						_lowercase	,						_lowercase       ):

						if depth < 0:
												raise ValueError('''Depth cannot be less than 0'''       )

						if len(_lowercase       ) == 0:
												raise ValueError('''Scores cannot be empty'''       )

						if depth == height:
												return scores[node_index]

						if is_max:
												return max(
												    minimax(depth + 1	,						node_index * 2	,						_lowercase	,						_lowercase	,						_lowercase       )	,						minimax(depth + 1	,						node_index * 2 + 1	,						_lowercase	,						_lowercase	,						_lowercase       )	,						)

						return min(
						    minimax(depth + 1	,						node_index * 2	,						_lowercase	,						_lowercase	,						_lowercase       )	,						minimax(depth + 1	,						node_index * 2 + 1	,						_lowercase	,						_lowercase	,						_lowercase       )	,						)





def 	a_    (							):
						_UpperCamelCase      : Dict         =   [90, 23, 6, 33, 21, 65, 123, 3_4423]
						_UpperCamelCase      : int         =   math.log(len(_lowercase       )	,						2       )
						print('''Optimal value : '''	,						end=''''''       )
						print(minimax(0	,						0	,						_lowercase	,						_lowercase	,						_lowercase       )       )


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()



