code: 
  """simple docstring"""
  import numpy as np
  
  
  
  
  
  def 				lowerCamelCase_		(UpperCamelCase__	:	Any							):
      _UpperCAmelCase							:						str       							=					a.shape
      _UpperCAmelCase							:						Union[str, Any]       							=					min(SCREAMING_SNAKE_CASE__  , SCREAMING_SNAKE_CASE__							)
      _UpperCAmelCase							:						List[Any]       							=					np.eye(SCREAMING_SNAKE_CASE__							)
      _UpperCAmelCase							:						Union[str, Any]       							=					a.copy()
  
      for k in range(t - 1							):
          # select a column of modified matrix A':
          _UpperCAmelCase							:						Union[str, Any]       							=					r[k:, [k]]
          # construct first basis vector
          _UpperCAmelCase							:						str       							=					np.zeros_like(SCREAMING_SNAKE_CASE__							)
          _UpperCAmelCase							:						List[str]       							=					1.0
          # determine scaling factor
          _UpperCAmelCase							:						int       							=					np.linalg.norm(SCREAMING_SNAKE_CASE__							)
          # construct vector v for Householder reflection
          _UpperCAmelCase							:						Optional[int]       							=					x + np.sign(x[0]							) * alpha * ea
          v /= np.linalg.norm(SCREAMING_SNAKE_CASE__							)
  
          # construct the Householder matrix
          _UpperCAmelCase							:						Tuple       							=					np.eye(m - k							) - 2.0 * v @ v.T
          # pad with ones and zeros as necessary
          _UpperCAmelCase							:						int       							=					np.block([[np.eye(SCREAMING_SNAKE_CASE__							), np.zeros((k, m - k)							)], [np.zeros((m - k, k)							), q_k]]							)
  
          _UpperCAmelCase							:						int       							=					q @ q_k.T
          _UpperCAmelCase							:						Dict       							=					q_k @ r
  
      return q, r
  
  
  if __name__ == "__main__":
    import doctest
  
    doctest.testmod()
  
  
  
style_context: 
  
  
  
  """simple docstring"""
  def 				lowerCamelCase_		(UpperCamelCase__	:	List[Any]  , UpperCamelCase__	:	int							):
      sequence.append(UpperCamelCase__							)
  
      _UpperCAmelCase							:						str       							=					0
      while sequence[index] != target:
          index += 1
  
      sequence.pop()
  
      if index == len(UpperCamelCase__							):
          return None
  
      return index
  
  
  if __name__ == "__main__":
    _lowerCAmelCase					:Dict  =      input('Enter numbers separated by comma:\n').strip()
    _lowerCAmelCase					:List[Any]  =      [int(item) for item in user_input.split(',')]
  
    _lowerCAmelCase					:int  =      input('Enter a single number to be found in the list:\n')
    _lowerCAmelCase					:List[Any]  =      int(target_input)
    _lowerCAmelCase					:Optional[int]  =      sentinel_linear_search(sequence, target)
    if result is not None:
      print(f"{target} found at positions: {result}")
    else:
      print('Not found')
  
  
  