Let S be a square of side length 1 . Two points are chosen independently at random on the sides of S. The probability that the straight-line distance between the points is at least \dfrac{1}{2} is \dfrac{a-b \pi}{c}, where a, b, and c are positive integers and \operatorname{gcd}(a, b, c)=1. What is a+b+c ?
Answer Choices
A. 59
B. 60
C. 61
D. 62
E. 63