





import os
import string
import sys


lowercase      :       Tuple									=  1 << 8

lowercase      :       Dict									=  {
    """tab""": ord("""\t"""),
    """newline""": ord("""\r"""),
    """esc""": 2_7,
    """up""": 6_5 + ARROW_KEY_FLAG,
    """down""": 6_6 + ARROW_KEY_FLAG,
    """right""": 6_7 + ARROW_KEY_FLAG,
    """left""": 6_8 + ARROW_KEY_FLAG,
    """mod_int""": 9_1,
    """undefined""": sys.maxsize,
    """interrupt""": 3,
    """insert""": 5_0,
    """delete""": 5_1,
    """pg_up""": 5_3,
    """pg_down""": 5_4,
}

lowercase      :       Optional[int]									=  KEYMAP["""up"""]
lowercase      :       List[str]									=  KEYMAP["""left"""]

if sys.platform == "win32":
    lowercase      :       Dict									=  []
    lowercase      :       Optional[int]									=  {
        b"""\xe0H""": KEYMAP["""up"""] - ARROW_KEY_FLAG,
        b"""\x00H""": KEYMAP["""up"""] - ARROW_KEY_FLAG,
        b"""\xe0P""": KEYMAP["""down"""] - ARROW_KEY_FLAG,
        b"""\x00P""": KEYMAP["""down"""] - ARROW_KEY_FLAG,
        b"""\xe0M""": KEYMAP["""right"""] - ARROW_KEY_FLAG,
        b"""\x00M""": KEYMAP["""right"""] - ARROW_KEY_FLAG,
        b"""\xe0K""": KEYMAP["""left"""] - ARROW_KEY_FLAG,
        b"""\x00K""": KEYMAP["""left"""] - ARROW_KEY_FLAG,
    }

for i in range(1_0):
    lowercase      :       List[str]									=  ord(str(i))



def A_	(		)  ->		int:
       if os.name == "nt":
              import msvcrt

              a__						:	Optional[int] =				'mbcs'
              # Flush the keyboard buffer
              while msvcrt.kbhit():
                     msvcrt.getch()
              if len(A__				) == 0:
                     # Read the keystroke
                     a__						:	int =				msvcrt.getch()

                     # If it is a prefix char, get second part
                     if ch in (b"\x00", b"\xe0"):
                            a__						:	Dict =				ch + msvcrt.getch()
                            # Translate actual Win chars to bullet char types
                            try:
                                   a__						:	Optional[Any] =				chr(WIN_KEYMAP[cha]				)
                                   WIN_CH_BUFFER.append(chr(KEYMAP['mod_int']				)				)
                                   WIN_CH_BUFFER.append(A__				)
                                   if ord(A__				) in (
                                       KEYMAP["insert"] - 1 << 9,
                                       KEYMAP["delete"] - 1 << 9,
                                       KEYMAP["pg_up"] - 1 << 9,
                                       KEYMAP["pg_down"] - 1 << 9,
                                   ):
                                          WIN_CH_BUFFER.append(chr(126				)				)
                                   a__						:	List[Any] =				chr(KEYMAP['esc']				)
                            except KeyError:
                                   a__						:	Tuple =				cha[1]
                     else:
                            a__						:	Union[str, Any] =				ch.decode(A__				)
              else:
                     a__						:	Any =				WIN_CH_BUFFER.pop(0				)
       elif os.name == "posix":
              import termios
              import tty

              a__						:	List[Any] =				sys.stdin.fileno()
              a__						:	Any =				termios.tcgetattr(A__				)
              try:
                     tty.setraw(A__				)
                     a__						:	Optional[int] =				sys.stdin.read(1				)
              finally:
                     termios.tcsetattr(A__		,      termios.TCSADRAIN		,      A__				)
       return ch



def A_	(		)  ->		List[Any]:
       a__						:	Union[str, Any] =				get_raw_chars()
       if ord(A__				) in [KEYMAP["interrupt"], KEYMAP["newline"]]:
              return char

       elif ord(A__				) == KEYMAP["esc"]:
              a__						:	Any =				get_raw_chars()
              if ord(A__				) == KEYMAP["mod_int"]:
                     a__						:	Dict =				get_raw_chars()
                     if ord(A__				) >= KEYMAP["arrow_begin"] - ARROW_KEY_FLAG and ord(A__				) <= KEYMAP["arrow_end"] - ARROW_KEY_FLAG:
                            return chr(ord(A__				) + ARROW_KEY_FLAG				)
                     else:
                            return KEYMAP["undefined"]
              else:
                     return get_raw_chars()

       else:
              if char in string.printable:
                     return char
              else:
                     return KEYMAP["undefined"]







def        lowercase_							(A : Union[str, Any]		,					A : List[str]		,					A : int		,					A : Optional[int]      ):
       global f  # a global dp table for knapsack
       if f[i][j] < 0:
              if j < wt[i - 1]:
                     snake_case__							:	Union[str, Any]   	=	mf_knapsack(i - 1		,					A		,					A		,					A      )
              else:
                     snake_case__							:	Any   	=	max(
                         mf_knapsack(i - 1		,					A		,					A		,					A      )		,					mf_knapsack(i - 1		,					A		,					A		,					j - wt[i - 1]      ) + val[i - 1]		,					)
              snake_case__							:	Optional[int]   	=	val
       return f[i][j]
def        lowercase_							(A : Optional[int]		,					A : Union[str, Any]		,					A : str		,					A : Dict      ):
       snake_case__							:	int   	=	[[0] * (w + 1) for _ in range(n + 1      )]

       for i in range(1		,					n + 1      ):
              for w_ in range(1		,					w + 1      ):
                     if wt[i - 1] <= w_:
                            snake_case__							:	Union[str, Any]   	=	max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]		,					dp[i - 1][w_]      )
                     else:
                            snake_case__							:	str   	=	dp[i - 1][w_]

       return dp[n][w_], dp
def        lowercase_							(A : int		,					A : list		,					A : list      ):
       if not (isinstance(A		,					(list, tuple)      ) and isinstance(A		,					(list, tuple)      )):
              raise ValueError(
                  'Both the weights and values vectors must be either lists or tuples'      )

       snake_case__							:	Dict   	=	len(A      )
       if num_items != len(A      ):
              snake_case__							:	str   	=	(
                  'The number of weights must be the same as the number of values.\n'
                  F'''But got {num_items} weights and {len(A      )} values'''
              )
              raise ValueError(A      )
       for i in range(A      ):
              if not isinstance(wt[i]		,					A      ):
                     snake_case__							:	Optional[int]   	=	(
                         'All weights must be integers but got weight of '
                         F'''type {type(wt[i]      )} at index {i}'''
                     )
                     raise TypeError(A      )

       snake_case__	,				snake_case__							:	Optional[int]   	=	knapsack(A		,					A		,					A		,					A      )
       snake_case__							:	set   	=	set()
       _construct_solution(A		,					A		,					A		,					A		,					A      )

       return optimal_val, example_optional_set
def        lowercase_							(A : list		,					A : list		,					A : int		,					A : int		,					A : set      ):
       # for the current item i at a maximum weight j to be part of an optimal subset,
       # the optimal value at (i, j) must be greater than the optimal value at (i-1, j).
       # where i - 1 means considering only the previous items at the given maximum weight
       if i > 0 and j > 0:
              if dp[i - 1][j] == dp[i][j]:
                     _construct_solution(A		,					A		,					i - 1		,					A		,					A      )
              else:
                     optimal_set.add(A      )
                     _construct_solution(A		,					A		,					i - 1		,					j - wt[i - 1]		,					A      )


if __name__ == "__main__":
 a_   :Any        =      [3, 2, 4, 4]
 a_   :List[Any]        =      [4, 3, 2, 3]
 a_   :Union[str, Any]        =      4
 a_   :List[str]        =      6
 a_   :Union[str, Any]        =      [[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
 a_  ,						a_   :List[Any]        =      knapsack(w, wt, val, n)
 print(optimal_solution)
 print(mf_knapsack(n, wt, val, w))  # switched the n and w

 # testing the dynamic programming problem with example
 # the optimal subset for the above example are items 3 and 4
 a_  ,						a_   :Any        =      knapsack_with_example_solution(w, wt, val)
 assert optimal_solution == 8
 assert optimal_subset == {3, 4}
 print("optimal_value = ", optimal_solution)
 print("An optimal subset corresponding to the optimal value", optimal_subset)






