
"""simple docstring"""





def  lowerCamelCase__						(     __snake_case = 1_00_00_00      )				->						int:


					"""simple docstring"""





					_UpperCamelCase									=    [i - 1 for i in range(limit + 1      )]

					for i in range(2,	limit + 1      ):
										if phi[i] == i - 1:
															for j in range(2 * i,	limit + 1,	__snake_case      ):
																				phi[j] -= phi[j] // i

					return sum(phi[2 : limit + 1]      )


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








"""simple docstring"""





from collections.abc import Callable

import numpy as np



def  lowerCamelCase__						(     __snake_case,	__snake_case,	__snake_case,	__snake_case,	__snake_case      )				->						np.array:


					"""simple docstring"""





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

					for k in range(__snake_case      ):
										_UpperCamelCase									=    y[k] + step_size * ode_func(__snake_case,	y[k]      )
										_UpperCamelCase									=    y[k] + (
										    (step_size / 2) * (ode_func(__snake_case,	y[k]      ) + ode_func(x + step_size,	__snake_case      ))
										)
										x += step_size

					return y


if __name__ == "__main__":
				import doctest

				doctest.testmod()






