Square A B C D has sides of length 1 . Points E and F are on \overline{B C} and \overline{C D}, respectively, so that \triangle A E F is equilateral. A square with vertex B has sides that are parallel to those of A B C D and a vertex on \overline{A E}. The length of a side of this smaller square is \frac{a-\sqrt{b}}{c}, where a, b, and c are positive integers and b is not divisible by the square of any prime. Find a+b+c.