
"""simple docstring"""



from __future__ import annotations

from typing import Any

class       lowerCAmelCase__				:







     def __init__(							self			:			Tuple    ,      _lowerCamelCase			:			int    ,      _lowerCamelCase			:			int    ,      _lowerCamelCase			:			float = 0			):
       _snake_case     ,					_snake_case					     =       row, column
       _snake_case					     =       [[default_value for c in range(_lowerCamelCase			)] for r in range(_lowerCamelCase			)]







     def __str__(							self			:			Optional[int]			):
       _snake_case					     =       f'''Matrix consist of {self.row} rows and {self.column} columns\n'''

       # Make string identifier
       _snake_case					     =       0
       for row_vector in self.array:
         for obj in row_vector:
           _snake_case					     =       max(_lowerCamelCase    ,      len(str(_lowerCamelCase			)			)			)
       _snake_case					     =       f'''%{max_element_length}s'''

       # Make string and return
       def single_line(_lowerCamelCase			:			list[float]			) -> str:
         nonlocal string_format_identifier
         _snake_case					     =       '''['''
         line += ", ".join(string_format_identifier % (obj,) for obj in row_vector			)
         line += "]"
         return line

       s += "\n".join(single_line(_lowerCamelCase			) for row_vector in self.array			)
       return s







     def __repr__(							self			:			Dict			):
       return str(self			)







     def      lowercase	(							self			:			Tuple    ,      _lowerCamelCase			:			tuple[int, int]			):
       if not (isinstance(_lowerCamelCase    ,      (list, tuple)			) and len(_lowerCamelCase			) == 2):
         return False
       elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
         return False
       else:
         return True







     def __getitem__(							self			:			Tuple    ,      _lowerCamelCase			:			tuple[int, int]			):
       assert self.validate_indicies(_lowerCamelCase			)
       return self.array[loc[0]][loc[1]]







     def __setitem__(							self			:			Tuple    ,      _lowerCamelCase			:			tuple[int, int]    ,      _lowerCamelCase			:			float			):
       assert self.validate_indicies(_lowerCamelCase			)
       _snake_case					     =       value







     def __add__(							self			:			Optional[int]    ,      _lowerCamelCase			:			Matrix			):
       assert isinstance(_lowerCamelCase    ,      _lowerCamelCase			)
       assert self.row == another.row and self.column == another.column

       # Add
       _snake_case					     =       Matrix(self.row    ,      self.column			)
       for r in range(self.row			):
         for c in range(self.column			):
           _snake_case					     =       self[r, c] + another[r, c]
       return result







     def __neg__(							self			:			Dict			):
       _snake_case					     =       Matrix(self.row    ,      self.column			)
       for r in range(self.row			):
         for c in range(self.column			):
           _snake_case					     =       -self[r, c]
       return result







     def __sub__(							self			:			Optional[Any]    ,      _lowerCamelCase			:			Matrix			):
       return self + (-another)







     def __mul__(							self			:			Optional[Any]    ,      _lowerCamelCase			:			int | float | Matrix			):

       if isinstance(_lowerCamelCase    ,      (int, float)			):  # Scalar multiplication
         _snake_case					     =       Matrix(self.row    ,      self.column			)
         for r in range(self.row			):
           for c in range(self.column			):
             _snake_case					     =       self[r, c] * another
         return result
       elif isinstance(_lowerCamelCase    ,      _lowerCamelCase			):  # Matrix multiplication
         assert self.column == another.row
         _snake_case					     =       Matrix(self.row    ,      another.column			)
         for r in range(self.row			):
           for c in range(another.column			):
             for i in range(self.column			):
               result[r, c] += self[r, i] * another[i, c]
         return result
       else:
         _snake_case					     =       f'''Unsupported type given for another ({type(_lowerCamelCase			)})'''
         raise TypeError(_lowerCamelCase			)







     def      lowercase	(							self			:			str			):
       _snake_case					     =       Matrix(self.column    ,      self.row			)
       for r in range(self.row			):
         for c in range(self.column			):
           _snake_case					     =       self[r, c]
       return result







     def      lowercase	(							self			:			str    ,      _lowerCamelCase			:			Matrix    ,      _lowerCamelCase			:			Matrix			):
       assert isinstance(_lowerCamelCase    ,      _lowerCamelCase			) and isinstance(_lowerCamelCase    ,      _lowerCamelCase			)
       assert self.row == self.column == u.row == v.row  # u, v should be column vector
       assert u.column == v.column == 1  # u, v should be column vector

       # Calculate
       _snake_case					     =       v.transpose()
       _snake_case					     =       (v_t * self * u)[0, 0] + 1
       if numerator_factor == 0:
         return None  # It's not invertable
       return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":
 def 					_UpperCAmelCase      ( )     ->					None:
   # a^(-1)
   _snake_case					     =       Matrix(3 ,					3 ,					0		)
   for i in range(3		):
     _snake_case					     =       1
   print(f'''a^(-1) is {ainv}'''		)
   # u, v
   _snake_case					     =       Matrix(3 ,					1 ,					0		)
   _snake_case     ,					_snake_case     ,					_snake_case					     =       1, 2, -3
   _snake_case					     =       Matrix(3 ,					1 ,					0		)
   _snake_case     ,					_snake_case     ,					_snake_case					     =       4, -2, 5
   print(f'''u is {u}'''		)
   print(f'''v is {v}'''		)
   print(f'''uv^T is {u * v.transpose()}'''		)
   # Sherman Morrison
   print(f'''(a + uv^T)^(-1) is {ainv.sherman_morrison(__lowerCamelCase ,					__lowerCamelCase		)}'''		)
 def 					_UpperCAmelCase      ( )     ->					None:
   import doctest

   doctest.testmod()

 testa()





"""simple docstring"""



from __future__ import annotations

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

@total_ordering
class       lowerCAmelCase__				(						A_	):







     def __lt__(							self			:			Any    ,      _lowerCamelCase			:			int			):
       return self[-1] < other[-1]







     def __eq__(							self			:			int    ,      _lowerCamelCase			:			Optional[Any]			):
       return self[-1] == other[-1]






def 					_UpperCAmelCase      ( __lowerCamelCase   :       list		)     ->					list:
  _snake_case					     =       []
  # sort into stacks
  for element in collection:
    _snake_case					     =       Stack([element]		)
    _snake_case					     =       bisect_left(__lowerCamelCase ,					__lowerCamelCase		)
    if i != len(__lowerCamelCase		):
      stacks[i].append(__lowerCamelCase		)
    else:
      stacks.append(__lowerCamelCase		)

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


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



