"""simple docstring"""



from __future__ import annotations

from collections.abc import Callable

_UpperCamelCase								=		list[list[float | int]]

def  _A(		lowerCAmelCase			,  lowerCAmelCase							):
							A__       :     int								=			len(lowerCAmelCase							)
							A__       :     Matrix								=			[[0 for _ in range(size + 1							)] for _ in range(lowerCAmelCase							)]
							A__       :     int
							A__       :     int
							A__       :     int
							A__       :     int
							A__       :     int
							A__       :     float

							for row in range(lowerCAmelCase							):
														for col in range(lowerCAmelCase							):
																					A__       :     List[str]								=			matrix[row][col]

														A__       :     Dict								=			vector[row][0]

							A__       :     Tuple								=			0
							A__       :     List[Any]								=			0
							while row < size and col < size:
														# pivoting
														A__       :     Tuple								=			max((abs(augmented[rowa][col]							), rowa) for rowa in range(lowerCAmelCase			,  lowerCAmelCase							)							)[
														    1
														]
														if augmented[pivot_row][col] == 0:
																					col += 1
																					continue
														else:
																					A__				,							A__       :     Any								=			augmented[pivot_row], augmented[row]

														for rowa in range(row + 1			,  lowerCAmelCase							):
																					A__       :     Tuple								=			augmented[rowa][col] / augmented[row][col]
																					A__       :     int								=			0
																					for cola in range(col + 1			,  size + 1							):
																												augmented[rowa][cola] -= augmented[row][cola] * ratio

														row += 1
														col += 1

							# back substitution
							for col in range(1			,  lowerCAmelCase							):
														for row in range(lowerCAmelCase							):
																					A__       :     Any								=			augmented[row][col] / augmented[col][col]
																					for cola in range(lowerCAmelCase			,  size + 1							):
																												augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
							return [
							    [round(augmented[row][size] / augmented[row][row]			,  10							)] for row in range(lowerCAmelCase							)
							]

def  _A(		lowerCAmelCase							):
							A__       :     int								=			len(lowerCAmelCase							)
							A__       :     Matrix								=			[[0 for _ in range(lowerCAmelCase							)] for _ in range(lowerCAmelCase							)]
							A__       :     Matrix								=			[[0] for _ in range(lowerCAmelCase							)]
							A__       :     Matrix
							A__       :     int
							A__       :     int
							A__       :     int

							for x_val, y_val in enumerate(lowerCAmelCase							):
														for col in range(lowerCAmelCase							):
																					A__       :     Any								=			(x_val + 1) ** (size - col - 1)
														A__       :     Tuple								=			y_val

							A__       :     Tuple								=			solve(lowerCAmelCase			,  lowerCAmelCase							)

							def interpolated_func(lowerCAmelCase							) -> int:
														return sum(
														    round(coeffs[x_val][0]							) * (var ** (size - x_val - 1))
														    for x_val in range(lowerCAmelCase							)							)

							return interpolated_func

def  _A(		lowerCAmelCase							):
							return (
							    1
							    - variable
							    + variable**2
							    - variable**3
							    + variable**4
							    - variable**5
							    + variable**6
							    - variable**7
							    + variable**8
							    - variable**9
							    + variable**10
							)

def  _A(		lowerCAmelCase = question_function			,  lowerCAmelCase = 10							):
							A__       :     list[int]								=			[func(lowerCAmelCase							) for x_val in range(1			,  order + 1							)]

							A__       :     list[Callable[[int], int]]								=			[
							    interpolate(data_points[:max_coeff]							) for max_coeff in range(1			,  order + 1							)
							]

							A__       :     int								=			0
							A__       :     Callable[[int], int]
							A__       :     int

							for poly in polynomials:
														A__       :     List[Any]								=			1
														while func(lowerCAmelCase							) == poly(lowerCAmelCase							):
																					x_val += 1

														ret += poly(lowerCAmelCase							)

							return ret


if __name__ == "__main__":
				print(F'{solution() = }')






"""simple docstring"""



import math
from collections.abc import Iterator
from itertools import takewhile

def  _A(		lowerCAmelCase							):

							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(lowerCAmelCase							) + 1							)			,  6							):
														if number % i == 0 or number % (i + 2) == 0:
																					return False
							return True

def  _A(		):
							A__       :     List[str]								=			2
							while True:
														if is_prime(lowerCAmelCase							):
																					yield num
														num += 1

def  _A(		lowerCAmelCase = 200_0000							):
							return sum(takewhile(lambda lowerCAmelCase							: x < n			,  prime_generator()							)							)


if __name__ == "__main__":
				print(F'{solution() = }')





