

def 					__lowercase      (     _A			)     ->						list:
      if any(not isinstance(_A						,    _A			) or x < 0 for x in sequence			):
            raise TypeError("""Sequence must be list of non-negative integers"""			)
      for _ in range(len(_A			)			):
            for i, (rod_upper, rod_lower) in enumerate(zip(_A						,    sequence[1:]			)			):
                  if rod_upper > rod_lower:
                        sequence[i] -= rod_upper - rod_lower
                        sequence[i + 1] += rod_upper - rod_lower
      return sequence


if __name__ == "__main__":
  assert bead_sort([5, 4, 3, 2, 1]) == [1, 2, 3, 4, 5]
  assert bead_sort([7, 9, 4, 3, 5]) == [3, 4, 5, 7, 9]







from __future__ import annotations

import numpy as np






def 					__lowercase      (     _A			)     ->						tuple[np.ndarray, np.ndarray]:
      SCREAMING_SNAKE_CASE     ,	SCREAMING_SNAKE_CASE :      Dict       =   np.shape(_A			)
      if rows != columns:
            SCREAMING_SNAKE_CASE :      int       =   (
                """'table' has to be of square shaped array but got a """
                F"{rows}x{columns} array:\n{table}"
            )
            raise ValueError(_A			)

      SCREAMING_SNAKE_CASE :      Union[str, Any]       =   np.zeros((rows, columns)			)
      SCREAMING_SNAKE_CASE :      Optional[Any]       =   np.zeros((rows, columns)			)
      for i in range(_A			):
            for j in range(_A			):
                  SCREAMING_SNAKE_CASE :      Tuple       =   sum(lower[i][k] * upper[k][j] for k in range(_A			)			)
                  if upper[j][j] == 0:
                        raise ArithmeticError("""No LU decomposition exists"""			)
                  SCREAMING_SNAKE_CASE :      Union[str, Any]       =   (table[i][j] - total) / upper[j][j]
            SCREAMING_SNAKE_CASE :      Optional[Any]       =   1
            for j in range(_A						,    _A			):
                  SCREAMING_SNAKE_CASE :      List[str]       =   sum(lower[i][k] * upper[k][j] for k in range(_A			)			)
                  SCREAMING_SNAKE_CASE :      Optional[Any]       =   table[i][j] - total
      return lower, upper


if __name__ == "__main__":
  import doctest

  doctest.testmod()




