





"""simple docstring"""




from __future__ import annotations

from math import pi

# Define the Reduced Planck Constant ℏ (H bar), speed of light C, value of
# Pi and the function
UpperCAmelCase_ 							=       1.054571817E-34  # unit of ℏ : J * s

UpperCAmelCase_ 							=       3E8  # unit of c : m * s^-1





def   lowerCamelCase__       (       UpperCamelCase__     :    float    ,      UpperCamelCase__     :    float    ,      UpperCamelCase__     :    float  )     ->	dict[str, float]:



					'''simple docstring'''




					if (force, area, distance).count(0  ) != 1:
										raise ValueError('One and only one argument must be 0'  )
					if force < 0:
										raise ValueError('Magnitude of force can not be negative'  )
					if distance < 0:
										raise ValueError('Distance can not be negative'  )
					if area < 0:
										raise ValueError('Area can not be negative'  )
					if force == 0:
										_snake_case													=			(REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (
										    240 * (distance) ** 4
										)
										return {"force": force}
					elif area == 0:
										_snake_case													=			(240 * force * (distance) ** 4) / (
										    REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2
										)
										return {"area": area}
					elif distance == 0:
										_snake_case													=			(
										    (REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (240 * force)
										) ** (1 / 4)
										return {"distance": distance}
					raise ValueError('One and only one argument must be 0'  )


# Run doctest
if __name__ == "__main__":
					import doctest

					doctest.testmod()










def   lowerCamelCase__       (       UpperCamelCase__     :    list[list[int]]    ,      UpperCamelCase__     :    int    ,      UpperCamelCase__     :    int    ,      UpperCamelCase__     :    list[int]  )     ->	bool:



					'''simple docstring'''




					if graph[path[curr_ind - 1]][next_ver] == 0:
										return False

					# 2. Validate that next vertex is not already in path
					return not any(vertex == next_ver for vertex in path  )





def   lowerCamelCase__       (       UpperCamelCase__     :    list[list[int]]    ,      UpperCamelCase__     :    list[int]    ,      UpperCamelCase__     :    int  )     ->	bool:



					'''simple docstring'''




					if curr_ind == len(UpperCamelCase__  ):
										# return whether path exists between current and starting vertices
										return graph[path[curr_ind - 1]][path[0]] == 1

					# Recursive Step
					for next_ver in range(0    ,      len(UpperCamelCase__  )  ):
										if valid_connection(UpperCamelCase__    ,      UpperCamelCase__    ,      UpperCamelCase__    ,      UpperCamelCase__  ):
															# Insert current vertex  into path as next transition
															_snake_case													=			next_ver
															# Validate created path
															if util_hamilton_cycle(UpperCamelCase__    ,      UpperCamelCase__    ,      curr_ind + 1  ):
																				return True
															# Backtrack
															_snake_case													=			-1
					return False





def   lowerCamelCase__       (       UpperCamelCase__     :    list[list[int]]    ,      UpperCamelCase__     :    int = 0  )     ->	list[int]:



					'''simple docstring'''




					_snake_case													=			[-1] * (len(UpperCamelCase__  ) + 1)
					# initialize start and end of path with starting index
					_snake_case													=			_snake_case													=			start_index
					# evaluate and if we find answer return path either return empty array
					return path if util_hamilton_cycle(UpperCamelCase__    ,      UpperCamelCase__    ,      1  ) else []



