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Shortest representation in generalised Roman numerals

Given a positive integer, find its shortest representation in generalised Roman numerals. Since there is more than one way to generalise, only the definition shown below applies to this challenge.

## Definition
The digits used are the same as for standard Roman numerals, with the same values:

```text
I: 1
V: 5
X: 10
L: 50
C: 100
D: 500
M: 1000
```

A number is represented as a string of digits. To determine the value of the number:

- Find the first occurrence of the largest digit present. Call this the pivotal digit
- This pivotal digit will be preceded by a prefix of zero or more digits, and will be followed by a suffix of zero or more digits
- The value of the number is the value of the pivotal digit, minus the value of the prefix, plus the value of the suffix.

The value of the prefix and the suffix are calculated in the same way.

## Input
- A positive integer
- The input will never be zero

## Output
- A string of Roman numeral digits (letters from `IVXLCDM`)
- This must be the shortest string that represents the input
- If there is more than one shortest representation, you may output any of them, but you must output only one of them

## Examples

### Evaluating a string
The representation `VIXIX` is evaluated as follows:
- `X` is the largest digit, so the pivotal digit is the first X
- The prefix is `VI` and the suffix is `IX`
- The value is `pivot - prefix + suffix`, or `X - VI + IX`
- Applying the same approach to `VI` gives `V + I`, or 6
- Applying the same approach to `IX` gives `X - I`, or 9
- So the value is `X - VI + IX`, or `10 - 6 + 9`, or `13`

### Processing an input integer
For input `4`, there are a variety of ways of representing this number:

- `VIIXI` (5 digits) is `X - (V + I + I) + I` or `10 - (5 + 1 + 1) + 1` 
- `IIII` (4 digits) is `I + I + I + I` or `1 + 1 + 1 + 1`
- `VIX` (3 digits) is `X - (V + I)` or `10 - (5 + 1)`
- `IV` (2 digits) is `V - I` or `5 - 1`

The shortest representation is `IV`, so this is the valid output.

### Multiple valid outputs
For input `3`, both `III` and `IIV` are the shortest possible representation, so both are valid outputs.

## Test cases
Test cases are in the format `integer : ["valid", "output", "strings"]`.

*Note that you must only output one valid string, not all of the them.*

```text





            TODO: test cases






```

> Explanations are optional, but I'm more likely to upvote answers that have one.