<|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
 Given the set $M=\{a, b, -(a+b)\}$, where $a\in \mathbb{R}$ and $b\in \mathbb{R}$, and set $P=\{1, 0, -1\}$. If there is a mapping $f:x \to x$ that maps element $x$ in set $M$ to element $x$ in set $P$ (the image of $x$ under $f$ is still $x$), then the set $S$ formed by the points with coordinates $(a, b)$ has \_\_\_\_\_\_\_\_\_\_\_ subsets. 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
64
Given the set $M=\{a, b, -(a+b)\}$, where $a\in \mathbb{R}$ and $b\in \mathbb{R}$, and set $P=\{1, 0, -1\}$. If there is a mapping $f:x \to x$ that maps element $x$ in set $M$ to element $x$ in set $P$ (the image of $x$ under $f$ is still $x$), then the set $S$ formed by the points with coordinates $(a, b)$ has \_\_\_\_\_\_\_\_\_\_\_ subsets.
test