





from __future__ import annotations





def      _UpperCamelCase  (a__ :list[int] ,      a__ :list[int] ,      a__ :list[int] ,      a__ :list[list[str]] ,      a__ :int ,      ):






							"""simple docstring"""





							UpperCamelCase__					  =      len(a__							)

							# If row is equal to the size of the board it means there are a queen in each row in
							# the current board (possible_board)
							if row == n:
														# We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
														# this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
														boards.append([""". """ * i + """Q """ + """. """ * (n - 1 - i) for i in possible_board]							)
														return

							# We iterate each column in the row to find all possible results in each row
							for col in range(a__							):
														# We apply that we learned previously. First we check that in the current board
														# (possible_board) there are not other same value because if there is it means
														# that there are a collision in vertical. Then we apply the two formulas we
														# learned before:
														#
														# 45º: y - x = b or 45: row - col = b
														# 135º: y + x = b or row + col = b.
														#
														# And we verify if the results of this two formulas not exist in their variables
														# respectively.  (diagonal_right_collisions, diagonal_left_collisions)
														#
														# If any or these are True it means there is a collision so we continue to the
														# next value in the for loop.
														if (
														    col in possible_board
														    or row - col in diagonal_right_collisions
														    or row + col in diagonal_left_collisions
														):
																					continue

														# If it is False we call dfs function again and we update the inputs
														depth_first_search(
														    [*possible_board, col] ,      [*diagonal_right_collisions, row - col] ,      [*diagonal_left_collisions, row + col] ,      a__ ,      a__ ,      )





def      _UpperCamelCase  (a__ :int							):






							"""simple docstring"""





							UpperCamelCase__					  =      []
							depth_first_search([] ,      [] ,      [] ,      a__ ,      a__							)

							# Print all the boards
							for board in boards:
														for column in board:
																					print(a__							)
														print(""""""							)

							print(len(a__							) ,      """solutions were found."""							)


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					n_queens_solution(4)











from __future__ import annotations

from math import pi





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






							"""simple docstring"""





							if (inductance, frequency, reactance).count(0							) != 1:
														raise ValueError("""One and only one argument must be 0"""							)
							if inductance < 0:
														raise ValueError("""Inductance cannot be negative"""							)
							if frequency < 0:
														raise ValueError("""Frequency cannot be negative"""							)
							if reactance < 0:
														raise ValueError("""Inductive reactance cannot be negative"""							)
							if inductance == 0:
														return {"inductance": reactance / (2 * pi * frequency)}
							elif frequency == 0:
														return {"frequency": reactance / (2 * pi * inductance)}
							elif reactance == 0:
														return {"reactance": 2 * pi * frequency * inductance}
							else:
														raise ValueError("""Exactly one argument must be 0"""							)


if __name__ == "__main__":
					import doctest

					doctest.testmod()




