<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 A rectangular ceiling PQRS measures 6m by 4m and is to be completely covered using 12 rectangular tiles, each measuring 1m by 2m. A beam TU is positioned so that PT = SU = 2m, and no tile can cross the beam. Calculate the total number of possible arrangements of tiles. Express your answer as a single integer. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
180
A rectangular ceiling PQRS measures 6m by 4m and is to be completely covered using 12 rectangular tiles, each measuring 1m by 2m. A beam TU is positioned so that PT = SU = 2m, and no tile can cross the beam. Calculate the total number of possible arrangements of tiles. Express your answer as a single integer.
test