Calvin's favorite number $N$ has the following properties:

- $N$ has 8 distinct digits.
- The digits of $N$ are strictly decreasing from left to right.
- $N$ is divisible by 180.

What are the first three digits of Calvin's favorite number?

This problem is posed by Muhammad A.

**Details and assumptions**

The first three digits of $1023$ are $102$. Ignore any leading zeroes.

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