






def     a_   (__A = 50      )				->						int:



					"""simple docstring"""
					__a					:						Optional[int]      =					[1] * (length + 1)

					for row_length in range(length + 1      ):
										for tile_length in range(2				,       5      ):
															for tile_start in range(row_length - tile_length + 1      ):
																				ways_number[row_length] += ways_number[
																				    row_length - tile_start - tile_length
																				]

					return ways_number[length]


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













def     a_   (__A      )				->						Dict:



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







def     a_   (__A      )				->						Union[str, Any]:



					"""simple docstring"""
					if not head or not head.next:
										return True

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

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

					# 3. Comparison
					while stack:
										if stack.pop() != cur.val:
															return False
										__a					:						List[str]      =					cur.next

					return True







def     a_   (__A      )				->						List[str]:



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





