from typing import Optional, List, Dict, Set

class Heap:
    def __init__( self ) -> None:
        self.fro : List[ List[ int ] ] = []
        self.to  : List[ List[ int ] ] = []

    def boundcheck( self, obj_id: int, index: int ) -> bool:
        return obj_id >= 0 and \
               obj_id < len( self.to ) and \
               index < len( self.to[ obj_id ] )

    def read( self, obj_id: int, index: int ) -> Optional[int]:
        if not self.boundcheck( obj_id, index ):
            return None
        return self.to[ obj_id ][ index ]

    def write( self, obj_id: int, index: int, value: int ) -> bool:
        if not self.boundcheck( obj_id, index ):
            return False
        self.to[ obj_id ][ index ] = value
        return True

    def collect( self ) -> None:
        refmap : Dict[ int, int ] = {}
        self.fro = self.to
        self.to = []
        self.copy( 0, refmap )

    def copy( self, now: int, refmap: Dict[ int, int ] ) -> int:
        if now < 0:
            return now
        if now in refmap:
            return refmap[ now ]

        refmap[ now ] = len( self.to )
        copy : List[ int ] = []
        self.to.append( copy )

        for val in self.fro[ now ]:
            copy.append( self.copy( val, refmap ) )
        return refmap[ now ]

    def make( self, size: int ) -> int:
        self.to.append( [ 0 for _ in range( size ) ] )
        return len( self.to ) - 1

import run_tests