## Shift the digits [tag:code-golf] [tag:integer] [tag:arithmetic] [tag:restricted-time]
Given a single positive integer (say **x**), find the smallest positive integer, after being multiplied by **x**, produces a result equivalent to shifting the **positive integer**. Under a formula, it basically means `n * x = n shifted. Find n (n > 0)`.

Here's an example of shifting:
```
123456789 -> 912345678
abcdefghi -> iabcdefgh (letters = any 0~9 digit)
123       -> 312
```
## Rules

* Preceding zeros count after shifting. If the number is `10` and is multiplied by `0.1` (`0.1` isn't a valid input), the result is `1`, which isn't equal to `01` (`10` after shifting).
* Your code has to run on [Try It Online](https://tio.run/#) without timing out.
* If your number only has one digit, the shifted result is your number:
```
1 -> 1
4 -> 4
9 -> 9
```