Let H be the hemisphere $x^2 + y^2 + z^2 = 19$, $z \ge 0$, and suppose $f$ is a continuous function with $f(3, 3, 1) = 5$, $f(3, -3, 1) = 9$, $f(-3, 3, 1) = 13$, and $f(-3, -3, 1) = 14$. By dividing H into four patches, estimate the value below. (Round your answer to the nearest whole number.)
$\iint_H f(x, y, z) \,dS$