# Problem 482: The incenter of a triangle
ABC is an integer sided triangle with incenter I and perimeter p. The
segments IA, IB and IC have integral length as well. Let L = p + |IA| +
|IB| + |IC|. Let S(P) = ∑L for all such triangles where p ≤ P. For
example, S(103) = 3619. Find S(107).