A list is created by writing all the positive integers from 1 to 3999 inclusively in Roman numerals in order.

Devise an algorithm that isolates all the perfect squares from the list and writes the corresponding square roots in Roman numerals.

Assume that:

• The algorithm will process a Roman Numeral directly without converting it to decimal when determining if it is a perfect square.
• The algorithm knows how to derive the square root of an integer.
• The algorithm is aware of the corresponding base ten value of all the six individual Roman numerals I, V, X, L, C, D, and M. For example, it knows that: X=10, C=100, D=500 and, so on.
• The algorithm knows the corresponding base ten value of a given Roman numeral representation. For example, it knows that: XVI = 10+5+1 =16