





from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
UpperCamelCase_												=	2_99_79_24_58

# Symbols
UpperCamelCase_							,						UpperCamelCase_							,						UpperCamelCase_							,						UpperCamelCase_												=	symbols('ct x y z')






def 				_UpperCAmelCase			(    A     ):




   '''simple docstring'''

   if velocity > c:
      raise ValueError("Speed must not exceed light speed 299,792,458 [m/s]!"     )
   elif velocity < 1:
      # Usually the speed should be much higher than 1 (c order of magnitude)
      raise ValueError("Speed must be greater than or equal to 1!"     )

   return velocity / c






def 				_UpperCAmelCase			(    A     ):




   '''simple docstring'''

   return 1 / sqrt(1 - beta(SCREAMING_SNAKE_CASE_     ) ** 2     )






def 				_UpperCAmelCase			(    A     ):




   '''simple docstring'''

   return np.array(
       [
           [gamma(SCREAMING_SNAKE_CASE_     ), -gamma(SCREAMING_SNAKE_CASE_     ) * beta(SCREAMING_SNAKE_CASE_     ), 0, 0],
           [-gamma(SCREAMING_SNAKE_CASE_     ) * beta(SCREAMING_SNAKE_CASE_     ), gamma(SCREAMING_SNAKE_CASE_     ), 0, 0],
           [0, 0, 1, 0],
           [0, 0, 0, 1],
       ]     )






def 				_UpperCAmelCase			(    A				,							A = None     ):




   '''simple docstring'''

   if event is None:
      UpperCAmelCase__						=np.array([ct, x, y, z]     )  # Symbolic four vector
   else:
      event[0] *= c  # x0 is ct (speed of light * time)

   return transformation_matrix(SCREAMING_SNAKE_CASE_     ) @ event


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    # Example of symbolic vector:
    UpperCamelCase_												=	transform(29_97_92_45)
    print('Example of four vector: ')
    print(f"""ct\' = {four_vector[0]}""")
    print(f"""x\' = {four_vector[1]}""")
    print(f"""y\' = {four_vector[2]}""")
    print(f"""z\' = {four_vector[3]}""")

    # Substitute symbols with numerical values
    UpperCamelCase_												=	{ct: c, x: 1, y: 1, z: 1}
    UpperCamelCase_												=	[four_vector[i].subs(sub_dict) for i in range(4)]

    print(f"""\n{numerical_vector}""")










from __future__ import annotations
def      A__       (    SCREAMING_SNAKE_CASE_   :      int						)  ->  bool:






   """simple docstring"""







   _UpperCAmelCase           =   str(SCREAMING_SNAKE_CASE_						)
   return len(SCREAMING_SNAKE_CASE_						) == 9 and set(SCREAMING_SNAKE_CASE_						) == set('''123456789'''						)
def      A__       (    )  ->  int | None:






   """simple docstring"""







   for base_num in range(99_99				,	49_99				,	-1						):
      _UpperCAmelCase           =   10_00_02 * base_num
      if is_9_pandigital(SCREAMING_SNAKE_CASE_						):
         return candidate

   for base_num in range(3_33				,	99				,	-1						):
      _UpperCAmelCase           =   1_00_20_03 * base_num
      if is_9_pandigital(SCREAMING_SNAKE_CASE_						):
         return candidate

   return None


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