<|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
 Fill the $3 \times 3$ grid with the numbers $1, 2, \cdots, 9$ so that within each row, the numbers are in increasing order from left to right, and within each column, the numbers are in decreasing order from top to bottom. How many different ways can this be done? 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
42
Fill the $3 \times 3$ grid with the numbers $1, 2, \cdots, 9$ so that within each row, the numbers are in increasing order from left to right, and within each column, the numbers are in decreasing order from top to bottom. How many different ways can this be done? Express your answer as a single integer.
test