'''simple docstring'''

def      UpperCamelCase_						(					snake_case_       :       int      )					->     int:






 '''simple docstring'''

 __lowerCAmelCase											=						[1]

 __lowerCAmelCase							,       __lowerCAmelCase							,       __lowerCAmelCase											=						0, 0, 0
 __lowerCAmelCase											=						ugly_nums[ia] * 2
 __lowerCAmelCase											=						ugly_nums[ia] * 3
 __lowerCAmelCase											=						ugly_nums[ia] * 5

 for _ in range(1						,		snake_case_      ):
  __lowerCAmelCase											=						min(snake_case_						,		snake_case_						,		snake_case_      )
  ugly_nums.append(snake_case_      )
  if next_num == next_a:
   ia += 1
   __lowerCAmelCase											=						ugly_nums[ia] * 2
  if next_num == next_a:
   ia += 1
   __lowerCAmelCase											=						ugly_nums[ia] * 3
  if next_num == next_a:
   ia += 1
   __lowerCAmelCase											=						ugly_nums[ia] * 5
 return ugly_nums[-1]


if __name__ == "__main__":
 from doctest import testmod

 testmod(verbose=True)
 print(f'{ugly_numbers(200) = }')







'''simple docstring'''

def      UpperCamelCase_						(					snake_case_       :       list[int]						,		snake_case_       :       list[int]      )					->     tuple[float, float]:






 '''simple docstring'''

 if not len(snake_case_      ) == len(snake_case_      ) == 3:
  raise ValueError("""Please enter a valid equation."""      )
 if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
  raise ValueError("""Both a & b of two equations can't be zero."""      )

 # Extract the coefficients
 __lowerCAmelCase							,       __lowerCAmelCase							,       __lowerCAmelCase											=						equationa
 __lowerCAmelCase							,       __lowerCAmelCase							,       __lowerCAmelCase											=						equationa

 # Calculate the determinants of the matrices
 __lowerCAmelCase											=						aa * ba - aa * ba
 __lowerCAmelCase											=						ca * ba - ca * ba
 __lowerCAmelCase											=						aa * ca - aa * ca

 # Check if the system of linear equations has a solution (using Cramer's rule)
 if determinant == 0:
  if determinant_x == determinant_y == 0:
   raise ValueError("""Infinite solutions. (Consistent system)"""      )
  else:
   raise ValueError("""No solution. (Inconsistent system)"""      )
 else:
  if determinant_x == determinant_y == 0:
   # Trivial solution (Inconsistent system)
   return (0.0, 0.0)
  else:
   __lowerCAmelCase											=						determinant_x / determinant
   __lowerCAmelCase											=						determinant_y / determinant
   # Non-Trivial Solution (Consistent system)
   return (x, y)






