





"""simple docstring"""






from __future__ import annotations

from collections.abc import Callable

A 			=  list[list[float | int]]

def     __A      (			a_						:Matrix   ,       a_						:Matrix)		->		Matrix:
				__a :						int			       =  len(a_)
				__a :						Matrix			       =  [[0 for _ in range(size + 1)] for _ in range(a_)]
				__a :						int
				__a :						int
				__a :						int
				__a :						int
				__a :						int
				__a :						float

				for row in range(a_):
								for col in range(a_):
												__a :						Any			       =  matrix[row][col]

								__a :						Optional[Any]			       =  vector[row][0]

				__a :						int			       =  0
				__a :						int			       =  0
				while row < size and col < size:
								# pivoting
								__a :						int			       =  max((abs(augmented[rowa][col]), rowa) for rowa in range(a_   ,       a_))[
								    1
								]
								if augmented[pivot_row][col] == 0:
												col += 1
												continue
								else:
												__a       ,						__a :						str			       =  augmented[pivot_row], augmented[row]

								for rowa in range(row + 1   ,       a_):
												__a :						Tuple			       =  augmented[rowa][col] / augmented[row][col]
												__a :						Union[str, Any]			       =  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   ,       a_):
								for row in range(a_):
												__a :						List[Any]			       =  augmented[row][col] / augmented[col][col]
												for cola in range(a_   ,       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(a_)
				]

def     __A      (			a_						:list[int])		->		Callable[[int], int]:
				__a :						int			       =  len(a_)
				__a :						Matrix			       =  [[0 for _ in range(a_)] for _ in range(a_)]
				__a :						Matrix			       =  [[0] for _ in range(a_)]
				__a :						Matrix
				__a :						int
				__a :						int
				__a :						int

				for x_val, y_val in enumerate(a_):
								for col in range(a_):
												__a :						str			       =  (x_val + 1) ** (size - col - 1)
								__a :						Dict			       =  y_val

				__a :						Union[str, Any]			       =  solve(a_   ,       a_)

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

				return interpolated_func

def     __A      (			a_						:int)		->		int:
				return (
				    1
				    - variable
				    + variable**2
				    - variable**3
				    + variable**4
				    - variable**5
				    + variable**6
				    - variable**7
				    + variable**8
				    - variable**9
				    + variable**10
				)

def     __A      (			a_						:Callable[[int], int] = question_function   ,       a_						:int = 10)		->		int:
				__a :						list[int]			       =  [func(a_) 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 :						Tuple			       =  1
								while func(a_) == poly(a_):
												x_val += 1

								ret += poly(a_)

				return ret


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






"""simple docstring"""






from __future__ import annotations

import typing
from collections import Counter

def     __A      (			a_						:int)		->		typing.Counter[int]:
				__a :						typing.Counter[int]			       =  Counter()
				for base in range(1   ,       max_perimeter + 1):
								for perpendicular in range(a_   ,       max_perimeter + 1):
												__a :						Any			       =  (base * base + perpendicular * perpendicular) ** 0.5
												if hypotenuse == int(a_):
																__a :						List[Any]			       =  int(base + perpendicular + hypotenuse)
																if perimeter > max_perimeter:
																				continue
																triplets[perimeter] += 1
				return triplets

def     __A      (			a_						:int = 10_00)		->		int:
				__a :						Dict			       =  pythagorean_triple(a_)
				return triplets.most_common(1)[0][0]


if __name__ == "__main__":
		print(F'Perimeter {solution()} has maximum solutions')