Convert to Roman Numeral! Your task is to convert a given positive integer from Arabic numeral to Roman numeral.

Things get difficult when you count to 4000.

The romans did this by adding a line above a symbol to multiply that symbol by 1 000. However, overlines aren't exactly displayable in ASCII. Also, there are double overlines to multiply a symbol by 1 000 000, and then triple overline to multiply a symbol by 1 000 000 000, etc...

Therefore, I decided to use parentheses to replace overlines.

The symbols can be individually placed in parentheses. For example, both (VI) and (V)(I) are valid representations of 6 000. (V)M is also a valid representation of 6000.

(I) is a valid way to represent 1 000.

Testcases

Input: 1
Output: I
Input: 2
Output: II
Input: 3
Output: III
Input: 4
Output: IV
Input: 15
Output: XV
Input: 40
Output: XL
Input: 60
Output: LX
Input: 67
Output: LXVII
Input: 400
Output: CD
Input: 666
Output: DCLXVI
Input: 3000
Output: MMM
Input: 3999
Output: MMMCMXCIX
Input: 4000
Output: M(V)
Input: 4999
Output: M(V)CMXCIX
Input: 6000
Output: (VI)
Input: 6000000
Output: ((VI))
Input: 6006000
Output: ((VI)VI)
Input: 6666666666
Output: (((VI)DCLXVI)DCLXVI)DCLXVI


Scoring

This is code-golf. Shortest code in bytes win.
Mathematica, 67 bytes

Fold["("&lt;&gt;#&lt;&gt;")"&lt;&gt;#2&amp;,RomanNumeral[#~IntegerDigits~1000]/."N"-&gt;""]&amp;


Avoids all trouble with M by converting the input to base 1000 and converting each digit separately with RomanNumeral. Then we fold them up by inserting (...) from the left.

Unfortunately, Mathematica represents zeros as N so we need to get rid of those.