



"""simple docstring"""





from __future__ import annotations
def      a__			(   lowerCAmelCase__			,    lowerCAmelCase__   ):
      UpperCAmelCase_    				=							[]
      UpperCAmelCase_    				=							[]
      UpperCAmelCase_    				=							0
      UpperCAmelCase_    				=							sum(lowerCAmelCase__   )
      create_state_space_tree(lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__   )
      return result
def      a__			(   lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    ):
      if sum(lowerCAmelCase__   ) > max_sum or (remaining_nums_sum + sum(lowerCAmelCase__   )) < max_sum:
            return
      if sum(lowerCAmelCase__   ) == max_sum:
            result.append(lowerCAmelCase__   )
            return
      for index in range(lowerCAmelCase__			,    len(lowerCAmelCase__   )   ):
            create_state_space_tree(
                lowerCAmelCase__			,    lowerCAmelCase__			,    index + 1			,    [*path, nums[index]]			,    lowerCAmelCase__			,    remaining_nums_sum - nums[index]			,    )
lowerCamelCase            =		[3, 34, 4, 12, 5, 2]
lowerCamelCase            =		9
lowerCamelCase            =		generate_sum_of_subsets_soln(nums, max_sum)


print(*result)









"""simple docstring"""





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

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

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

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

      return True


def      a__			(   lowerCAmelCase__   ):
      if not head or not head.next:
            return True
      UpperCAmelCase_    				=							{}
      UpperCAmelCase_    				=							0
      while head:
            if head.val in d:
                  d[head.val].append(lowerCAmelCase__   )
            else:
                  UpperCAmelCase_    				=							[pos]
            UpperCAmelCase_    				=							head.next
            pos += 1
      UpperCAmelCase_    				=							pos - 1
      UpperCAmelCase_    				=							0
      for v in d.values():
            if len(lowerCAmelCase__   ) % 2 != 0:
                  middle += 1
            else:
                  UpperCAmelCase_    				=							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




