Let ABCDE be a nonconvex pentagon with internal angles ∠A=∠E=90∘ and ∠B=∠D=45∘. Suppose that DE<AB, AE=20, BC=142, and points B, C, and D lie on the same side of line AE. Suppose further that AB is an integer with AB<2026 and the area of pentagon ABCDE is an integer multiple of 16. Find the number of possible values of AB.
