


def 				__lowercase  (					__lowerCAmelCase				:							Union[str, Any]  ):







							if not head:
														return True
							# split the list to two parts
							a__ ,   a__			 =	head.next, head
							while fast and fast.next:
														a__			 =	fast.next.next
														a__			 =	slow.next
							a__			 =	slow.next
							a__			 =	None  # Don't forget here! But forget still works!
							# reverse the second part
							a__			 =	None
							while second:
														a__			 =	second.next
														a__			 =	node
														a__			 =	second
														a__			 =	nxt
							# compare two parts
							# second part has the same or one less node
							while node:
														if node.val != head.val:
																					return False
														a__			 =	node.next
														a__			 =	head.next
							return True






def 				__lowercase  (					__lowerCAmelCase				:							Union[str, Any]  ):







							if not head or not head.next:
														return True

							# 1. Get the midpoint (slow)
							a__			 =	a__			 =	a__			 =	head
							while fast and fast.next:
														a__ ,   a__			 =	fast.next.next, slow.next

							# 2. Push the second half into the stack
							a__			 =	[slow.val]
							while slow.next:
														a__			 =	slow.next
														stack.append(slow.val  )

							# 3. Comparison
							while stack:
														if stack.pop() != cur.val:
																					return False
														a__			 =	cur.next

							return True






def 				__lowercase  (					__lowerCAmelCase				:							Tuple  ):







							if not head or not head.next:
														return True
							a__			 =	{}
							a__			 =	0
							while head:
														if head.val in d:
																					d[head.val].append(SCREAMING_SNAKE_CASE_  )
														else:
																					a__			 =	[pos]
														a__			 =	head.next
														pos += 1
							a__			 =	pos - 1
							a__			 =	0
							for v in d.values():
														if len(SCREAMING_SNAKE_CASE_  ) % 2 != 0:
																					middle += 1
														else:
																					a__			 =	0
																					for i in range(0   ,       len(SCREAMING_SNAKE_CASE_  )  ):
																												if v[i] + v[len(SCREAMING_SNAKE_CASE_  ) - 1 - step] != checksum:
																																			return False
																												step += 1
														if middle > 1:
																					return False
							return True











def      A__       (    SCREAMING_SNAKE_CASE_   :      int = 2_00_00_00						)  ->  int:






   """simple docstring"""







   _UpperCAmelCase           =   [0 for i in range(n + 1						)]
   _UpperCAmelCase           =   1
   _UpperCAmelCase           =   1

   for i in range(2				,	int(n**0.5						) + 1						):
      if primality_list[i] == 0:
         for j in range(i * i				,	n + 1				,	SCREAMING_SNAKE_CASE_						):
            _UpperCAmelCase           =   1
   _UpperCAmelCase           =   0
   for i in range(SCREAMING_SNAKE_CASE_						):
      if primality_list[i] == 0:
         sum_of_primes += i
   return sum_of_primes


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