



'''simple docstring'''


from __future__ import annotations

from bisect import bisect_left
from functools import total_ordering
from heapq import merge







@total_ordering
class 	UpperCAmelCase	(		__a):


 '''simple docstring'''




 def __lt__(   self							,  lowerCAmelCase_) ->      Tuple:



      """simple docstring"""







      return self[-1] < other[-1]




 def __eq__(   self							,  lowerCAmelCase_) ->      Optional[Any]:



      """simple docstring"""







      return self[-1] == other[-1]






def  UpperCAmelCase_       (		lowercase__       ):


     '''simple docstring'''







     a_       		=[]
     # sort into stacks
     for element in collection:
          a_       		=Stack([element]       )
          a_       		=bisect_left(lowercase__       ,	lowercase__       )
          if i != len(lowercase__       ):
               stacks[i].append(lowercase__       )
          else:
               stacks.append(lowercase__       )

    # use a heap-based merge to merge stack efficiently
     a_       		=merge(*(reversed(lowercase__       ) for stack in stacks)       )
     return collection


if __name__ == "__main__":
  lowercase							       =			input('''Enter numbers separated by a comma:\n''').strip()
  lowercase							       =			[int(item) for item in user_input.split(''',''')]
  print(patience_sort(unsorted))







'''simple docstring'''


from typing import Any

import numpy as np






def  UpperCAmelCase_       (		lowercase__       ):


     '''simple docstring'''







     return np.array_equal(lowercase__       ,	matrix.conjugate().T       )






def  UpperCAmelCase_       (		lowercase__       ,	lowercase__       ):


     '''simple docstring'''







     a_       		=v.conjugate().T
     a_       		=v_star.dot(lowercase__       )
     assert isinstance(lowercase__       ,	np.ndarray       )
     return (v_star_dot.dot(lowercase__       )) / (v_star.dot(lowercase__       ))






def  UpperCAmelCase_       (		):


     '''simple docstring'''







     a_       		=np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]       )
     a_       		=np.array([[1], [2], [3]]       )
     assert is_hermitian(lowercase__       ), F"""{a} is not hermitian."""
     print(rayleigh_quotient(lowercase__       ,	lowercase__       )       )

     a_       		=np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]       )
     assert is_hermitian(lowercase__       ), F"""{a} is not hermitian."""
     assert rayleigh_quotient(lowercase__       ,	lowercase__       ) == float(3       )


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  tests()


