  We prove that there exists no a priori bound on the Euler characteristic of a
closed symplectic 4-manifold coming solely from the genus of a compatible
Lefschetz pencil on it, nor is there a similar bound for Stein fillings of a
contact 3-manifold coming from the genus of a compatible open book --- except
possibly for a few low genera cases. To obtain our results, we produce the
first examples of factorizations of a boundary parallel Dehn twist as
arbitrarily long products of positive Dehn twists along non-separating curves
on a fixed surface with boundary. This solves an open problem posed by Auroux,
Smith and Wajnryb, and a more general variant of it raised by Korkmaz, Ozbagci
and Stipsicz, independently.
