






'''simple docstring'''
from __future__ import annotations

import sys
from collections import deque
from typing import Generic, TypeVar

a_					= TypeVar('T')






class      __SCREAMING_SNAKE_CASE      (			Generic[T]				):
 snake_case_  							=							42  # Cache store of keys
 snake_case_  							=							42  # References of the keys in cache
 snake_case_  							=							10  # Maximum capacity of cache




 def __init__(      self	:							Dict					,      __lowercase	:							int      )	->						None:
       SCREAMING_SNAKE_CASE__     :				Any									=deque()
       SCREAMING_SNAKE_CASE__     :				str									=set()
       if not n:
             SCREAMING_SNAKE_CASE__     :				Optional[Any]									=sys.maxsize
       elif n < 0:
             raise ValueError('''n should be an integer greater than 0.'''      )
       else:
             SCREAMING_SNAKE_CASE__     :				Optional[Any]									=n




 def      __magic_name__	(      self	:							List[str]					,      __lowercase	:							T      )	->						None:
       if x not in self.key_reference:
             if len(self.dq_store      ) == LRUCache._MAX_CAPACITY:
                   SCREAMING_SNAKE_CASE__     :				int									=self.dq_store.pop()
                   self.key_reference.remove(__lowercase      )
       else:
             self.dq_store.remove(__lowercase      )

       self.dq_store.appendleft(__lowercase      )
       self.key_reference.add(__lowercase      )




 def      __magic_name__	(      self	:							Union[str, Any]      )	->						None:
       for k in self.dq_store:
             print(__lowercase      )




 def __repr__(      self	:							List[Any]      )	->						str:
       return F"LRUCache({self._MAX_CAPACITY}) => {list(self.dq_store      )}"


if __name__ == "__main__":
      import doctest

      doctest.testmod()

      a_					= LRUCache(4)
      lru_cache.refer('A')
      lru_cache.refer(2)
      lru_cache.refer(3)
      lru_cache.refer('A')
      lru_cache.refer(4)
      lru_cache.refer(5)
      lru_cache.display()

      print(lru_cache)
      assert str(lru_cache) == "LRUCache(4) => [5, 4, 'A', 3]"







'''simple docstring'''
from __future__ import annotations

from collections.abc import Callable

a_					= list[list[float | int]]





def  _a(  UpperCamelCase__				:						Matrix,	UpperCamelCase__				:						Matrix							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__     :				int									=len(UpperCamelCase__							)
      SCREAMING_SNAKE_CASE__     :				Matrix									=[[0 for _ in range(size + 1							)] for _ in range(UpperCamelCase__							)]
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				float

      for row in range(UpperCamelCase__							):
            for col in range(UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Tuple									=matrix[row][col]

            SCREAMING_SNAKE_CASE__     :				Optional[int]									=vector[row][0]

      SCREAMING_SNAKE_CASE__     :				Any									=0
      SCREAMING_SNAKE_CASE__     :				Union[str, Any]									=0
      while row < size and col < size:
            # pivoting
            SCREAMING_SNAKE_CASE__     :				Any									=max((abs(augmented[rowa][col]							), rowa) for rowa in range(UpperCamelCase__,	UpperCamelCase__							)							)[
                1
            ]
            if augmented[pivot_row][col] == 0:
                  col += 1
                  continue
            else:
                  SCREAMING_SNAKE_CASE__		,	SCREAMING_SNAKE_CASE__     :				Optional[Any]									=augmented[pivot_row], augmented[row]

            for rowa in range(row + 1,	UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Union[str, Any]									=augmented[rowa][col] / augmented[row][col]
                  SCREAMING_SNAKE_CASE__     :				Tuple									=0
                  for cola in range(col + 1,	size + 1							):
                        augmented[rowa][cola] -= augmented[row][cola] * ratio

            row += 1
            col += 1

      # back substitution
      for col in range(1,	UpperCamelCase__							):
            for row in range(UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Optional[Any]									=augmented[row][col] / augmented[col][col]
                  for cola in range(UpperCamelCase__,	size + 1							):
                        augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
      return [
          [round(augmented[row][size] / augmented[row][row],	1_0							)] for row in range(UpperCamelCase__							)
      ]





def  _a(  UpperCamelCase__				:						list[int]							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__     :				int									=len(UpperCamelCase__							)
      SCREAMING_SNAKE_CASE__     :				Matrix									=[[0 for _ in range(UpperCamelCase__							)] for _ in range(UpperCamelCase__							)]
      SCREAMING_SNAKE_CASE__     :				Matrix									=[[0] for _ in range(UpperCamelCase__							)]
      SCREAMING_SNAKE_CASE__     :				Matrix
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int

      for x_val, y_val in enumerate(UpperCamelCase__							):
            for col in range(UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Optional[int]									=(x_val + 1) ** (size - col - 1)
            SCREAMING_SNAKE_CASE__     :				Dict									=y_val

      SCREAMING_SNAKE_CASE__     :				Optional[int]									=solve(UpperCamelCase__,	UpperCamelCase__							)

      def interpolated_func(UpperCamelCase__				:						int							) -> int:
            return sum(
                round(coeffs[x_val][0]							) * (var ** (size - x_val - 1))
                for x_val in range(UpperCamelCase__							)							)

      return interpolated_func





def  _a(  UpperCamelCase__				:						int							):




      '''simple docstring'''






      return (
          1
          - variable
          + variable**2
          - variable**3
          + variable**4
          - variable**5
          + variable**6
          - variable**7
          + variable**8
          - variable**9
          + variable**1_0
      )





def  _a(  UpperCamelCase__				:						Callable[[int], int] = question_function,	UpperCamelCase__				:						int = 1_0							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__     :				list[int]									=[func(UpperCamelCase__							) for x_val in range(1,	order + 1							)]

      SCREAMING_SNAKE_CASE__     :				list[Callable[[int], int]]									=[
          interpolate(data_points[:max_coeff]							) for max_coeff in range(1,	order + 1							)
      ]

      SCREAMING_SNAKE_CASE__     :				int									=0
      SCREAMING_SNAKE_CASE__     :				Callable[[int], int]
      SCREAMING_SNAKE_CASE__     :				int

      for poly in polynomials:
            SCREAMING_SNAKE_CASE__     :				Any									=1
            while func(UpperCamelCase__							) == poly(UpperCamelCase__							):
                  x_val += 1

            ret += poly(UpperCamelCase__							)

      return ret


if __name__ == "__main__":
  print(F'''{solution() = }''')