
"""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())










'''simple docstring'''

from __future__ import annotations

import math





def 		UpperCamelCase							(				_lowerCamelCase   :   int		,			_lowerCamelCase   :   int		,			_lowerCamelCase   :   bool		,			_lowerCamelCase   :   list[int]		,			_lowerCamelCase   :   float			):

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

    if len(_lowerCamelCase			) == 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		,			_lowerCamelCase		,			_lowerCamelCase		,			_lowerCamelCase			)		,			minimax(depth + 1		,			node_index * 2 + 1		,			_lowerCamelCase		,			_lowerCamelCase		,			_lowerCamelCase			)		,			)

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





def 		UpperCamelCase							(				):
    A__							=     [90, 23, 6, 33, 21, 65, 1_23, 3_44_23]
    A__							=     math.log(len(_lowerCamelCase			)		,			2			)
    print("Optimal value : "		,			end=""			)
    print(minimax(0		,			0		,			_lowerCamelCase		,			_lowerCamelCase		,			_lowerCamelCase			)			)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()



