


'''simple docstring'''






def lowerCamelCase__      (						__lowerCamelCase	:							List[str]							):







			'''simple docstring'''




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





def lowerCamelCase__      (						__lowerCamelCase	:							Dict							):







			'''simple docstring'''




			if not head or not head.next:
						return True

			# 1. Get the midpoint (slow)
			_UpperCAmelCase       :       Any							   =head
			while fast and fast.next:
						_UpperCAmelCase       :       List[Any]							   =fast.next.next, slow.next

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

			# 3. Comparison
			while stack:
						if stack.pop() != cur.val:
									return False
						_UpperCAmelCase       :       Union[str, Any]							   =cur.next

			return True





def lowerCamelCase__      (						__lowerCamelCase	:							Any							):







			'''simple docstring'''




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





'''simple docstring'''






from __future__ import annotations

from random import choice





def lowerCamelCase__      (						__lowerCamelCase	:							Optional[int]							):







   '''simple docstring'''




   return choice(__lowerCamelCase							)





def lowerCamelCase__      (						__lowerCamelCase	:							list[int]	,   __lowerCamelCase	:							int							):







   '''simple docstring'''




   _UpperCAmelCase       :       int							   =random_pivot(__lowerCamelCase							)

   # partition based on pivot
   # linear time
   _UpperCAmelCase       :       str							   =[e for e in lst if e < pivot]
   _UpperCAmelCase       :       Dict							   =[e for e in lst if e > pivot]

   # if we get lucky, pivot might be the element we want.
   # we can easily see this:
   # small (elements smaller than k)
   # + pivot (kth element)
   # + big (elements larger than k)
   if len(__lowerCamelCase							) == k - 1:
      return pivot
   # pivot is in elements bigger than k
   elif len(__lowerCamelCase							) < k - 1:
      return kth_number(__lowerCamelCase	,   k - len(__lowerCamelCase							) - 1							)
   # pivot is in elements smaller than k
   else:
      return kth_number(__lowerCamelCase	,   __lowerCamelCase							)


if __name__ == "__main__":
 import doctest

 doctest.testmod()

