"""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      __magic_name__				(							lowercase							,			lowercase							,			lowercase ):

   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:
      SCREAMING_SNAKE_CASE_: Any     			=(REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (
          240 * (distance) ** 4
      )
      return {"force": force}
   elif area == 0:
      SCREAMING_SNAKE_CASE_: int     			=(240 * force * (distance) ** 4) / (
          REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2
      )
      return {"area": area}
   elif distance == 0:
      SCREAMING_SNAKE_CASE_: Tuple     			=(
          (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()








"""simple docstring"""
def      __magic_name__				(							lowercase ):
   if upper_limit < 0:
      raise ValueError("""Limit for the Catalan sequence must be ≥ 0""" )

   SCREAMING_SNAKE_CASE_: Tuple     			=[0] * (upper_limit + 1)

   # Base case: C(0) = C(1) = 1
   SCREAMING_SNAKE_CASE_: Any     			=1
   if upper_limit > 0:
      SCREAMING_SNAKE_CASE_: List[str]     			=1

   # Recurrence relation: C(i) = sum(C(j).C(i-j-1)), from j = 0 to i
   for i in range(2							,			upper_limit + 1 ):
      for j in range(lowercase ):
         catalan_list[i] += catalan_list[j] * catalan_list[i - j - 1]

   return catalan_list


if __name__ == "__main__":
   print("""\n********* Catalan Numbers Using Dynamic Programming ************\n""")
   print("""\n*** Enter -1 at any time to quit ***""")
   print("""\nEnter the upper limit (≥ 0) for the Catalan number sequence: """, end="""""")
   try:
      while True:
         _UpperCAmelCase     =			int(input().strip())
         if N < 0:
            print("""\n********* Goodbye!! ************""")
            break
         else:
            print(f"""The Catalan numbers from 0 through {N} are:""")
            print(catalan_numbers(N))
            print("""Try another upper limit for the sequence: """, end="""""")
   except (NameError, ValueError):
      print("""\n********* Invalid input, goodbye! ************\n""")

   import doctest

   doctest.testmod()



