

from __future__ import annotations





def 	__a     (      A__			:  list[int | str]       ):
    create_state_space_tree(A__			,  []			,  0			,  [0 for i in range(len(A__       )       )]       )





def 	__a     (      A__			:  list[int | str]			,  A__			:  list[int | str]			,  A__			:  int			,  A__			:  list[int]			,  ):

    if index == len(A__       ):
        print(A__       )
        return

    for i in range(len(A__       )       ):
        if not index_used[i]:
            current_sequence.append(sequence[i]       )
            SCREAMING_SNAKE_CASE										=   True
            create_state_space_tree(A__			,  A__			,  index + 1			,  A__       )
            current_sequence.pop()
            SCREAMING_SNAKE_CASE										=   False
__A			:					list[int | str]						=			[3, 1, 2, 4]
generate_all_permutations(sequence)

__A			:					list[int | str]						=			["A", "B", "C"]





generate_all_permutations(sequence_a)

"""simple docstring"""


import math






def  lowercase						(	lowerCAmelCase__						):
			lowerCamelCase_					=  [True] * n
			lowerCamelCase_					=  False
			lowerCamelCase_					=  False
			lowerCamelCase_					=  True

			for i in range(3	,int(n**0.5 + 1						)	,2						):
						lowerCamelCase_					=  i * 2
						while index < n:
									lowerCamelCase_					=  False
									lowerCamelCase_					=  index + i

			lowerCamelCase_					=  [2]

			for i in range(3	,lowerCAmelCase__	,2						):
						if is_prime[i]:
									primes.append(lowerCAmelCase__						)

			return primes






def  lowercase						(	lowerCAmelCase__ = 999_966_663_333						):
			lowerCamelCase_					=  math.floor(math.sqrt(lowerCAmelCase__						)						) + 100
			lowerCamelCase_					=  prime_sieve(lowerCAmelCase__						)

			lowerCamelCase_					=  0
			lowerCamelCase_					=  0
			lowerCamelCase_					=  primes[prime_index]

			while (last_prime**2) <= limit:
						lowerCamelCase_					=  primes[prime_index + 1]

						lowerCamelCase_					=  last_prime**2
						lowerCamelCase_					=  next_prime**2

						# Get numbers divisible by lps(current)
						lowerCamelCase_					=  lower_bound + last_prime
						while upper_bound > current <= limit:
									matches_sum += current
									current += last_prime

						# Reset the upper_bound
						while (upper_bound - next_prime) > limit:
									upper_bound -= next_prime

						# Add the numbers divisible by ups(current)
						lowerCamelCase_					=  upper_bound - next_prime
						while current > lower_bound:
									matches_sum += current
									current -= next_prime

						# Remove the numbers divisible by both ups and lps
						lowerCamelCase_					=  0
						while upper_bound > current <= limit:
									if current <= lower_bound:
												# Increment the current number
												current += last_prime * next_prime
												continue

									if current > limit:
												break

									# Remove twice since it was added by both ups and lps
									matches_sum -= current * 2

									# Increment the current number
									current += last_prime * next_prime

						# Setup for next pair
						lowerCamelCase_					=  next_prime
						prime_index += 1

			return matches_sum


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



