






import numpy as np

def        _lowerCamelCase		(  __A      :							Union[str, Any]	) ->   Union[str, Any]:
    _UpperCAmelCase					,	_UpperCAmelCase			: List[Any]     					=			a.shape
    _UpperCAmelCase			: Optional[int]     					=			min(__A						,						__A	)
    _UpperCAmelCase			: int     					=			np.eye(__A	)
    _UpperCAmelCase			: List[str]     					=			a.copy()

    for k in range(t - 1	):
        # select a column of modified matrix A':
        _UpperCAmelCase			: Tuple     					=			r[k:, [k]]
        # construct first basis vector
        _UpperCAmelCase			: Optional[Any]     					=			np.zeros_like(__A	)
        _UpperCAmelCase			: Union[str, Any]     					=			1.0
        # determine scaling factor
        _UpperCAmelCase			: List[Any]     					=			np.linalg.norm(__A	)
        # construct vector v for Householder reflection
        _UpperCAmelCase			: List[str]     					=			x + np.sign(x[0]	) * alpha * ea
        v /= np.linalg.norm(__A	)

        # construct the Householder matrix
        _UpperCAmelCase			: str     					=			np.eye(m - k	) - 2.0 * v @ v.T
        # pad with ones and zeros as necessary
        _UpperCAmelCase			: str     					=			np.block([[np.eye(__A	), np.zeros((k, m - k)	)], [np.zeros((m - k, k)	), q_k]]	)

        _UpperCAmelCase			: str     					=			q @ q_k.T
        _UpperCAmelCase			: List[str]     					=			q_k @ r

    return q, r


if __name__ == "__main__":
  import doctest

  doctest.testmod()












def        _lowerCamelCase		(  __A      :							list	) ->   list:
    _UpperCAmelCase			: Dict     					=			1.3
    _UpperCAmelCase			: Any     					=			len(__A	)
    _UpperCAmelCase			: List[Any]     					=			False

    while not completed:
        # Update the gap value for a next comb
        _UpperCAmelCase			: Optional[Any]     					=			int(gap / shrink_factor	)
        if gap <= 1:
            _UpperCAmelCase			: Any     					=			True

        _UpperCAmelCase			: Optional[Any]     					=			0
        while index + gap < len(__A	):
            if data[index] > data[index + gap]:
                # Swap values
                _UpperCAmelCase					,	_UpperCAmelCase			: Union[str, Any]     					=			data[index + gap], data[index]
                _UpperCAmelCase			: Any     					=			False
            index += 1

    return data


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  SCREAMING_SNAKE_CASE								=  input('Enter numbers separated by a comma:\n').strip()
  SCREAMING_SNAKE_CASE								=  [int(item) for item in user_input.split(',')]
  print(comb_sort(unsorted))




