





from collections.abc import Callable

import numpy as np





def     _UpperCamelCase     (a__   :Callable   ,			a__   :float   ,			a__   :float   ,			a__   :float   ,			a__   :float       ):






							"""simple docstring"""





							UpperCamelCase__				     =			int(np.ceil((x_end - xa) / step_size       )       )
							UpperCamelCase__				     =			np.zeros((n + 1,)       )
							UpperCamelCase__				     =			ya
							UpperCamelCase__				     =			xa

							for k in range(a__       ):
														UpperCamelCase__				     =			y[k] + step_size * ode_func(a__   ,			y[k]       )
														x += step_size

							return y


if __name__ == "__main__":
					import doctest

					doctest.testmod()











import math





def     _UpperCamelCase     (a__   :int       ):






							"""simple docstring"""





							UpperCamelCase__				     =			[True] * n
							UpperCamelCase__				     =			False
							UpperCamelCase__				     =			False
							UpperCamelCase__				     =			True

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

							UpperCamelCase__				     =			[2]

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

							return primes





def     _UpperCamelCase     (a__   :int = 9999_6666_3333       ):






							"""simple docstring"""





							UpperCamelCase__				     =			math.floor(math.sqrt(a__       )       ) + 100
							UpperCamelCase__				     =			prime_sieve(a__       )

							UpperCamelCase__				     =			0
							UpperCamelCase__				     =			0
							UpperCamelCase__				     =			primes[prime_index]

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

														UpperCamelCase__				     =			last_prime**2
														UpperCamelCase__				     =			next_prime**2

														# Get numbers divisible by lps(current)
														UpperCamelCase__				     =			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)
														UpperCamelCase__				     =			upper_bound - next_prime
														while current > lower_bound:
																					matches_sum += current
																					current -= next_prime

														# Remove the numbers divisible by both ups and lps
														UpperCamelCase__				     =			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
														UpperCamelCase__				     =			next_prime
														prime_index += 1

							return matches_sum


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




