quantum mechanics - Bohr-Sommerfeld quantization from the WKB approximation

How can one prove the Bohr-Sommerfeld quantization formula

$$ \oint p~dq ~=~2\pi n \hbar $$

from the WKB ansatz solution $$\Psi(x)~=~e^{iS(x)/ \hbar}$$ for the Schroedinger equation?

With $S$ the action of the particle defined by Hamilton-Jacobi equation

$$ \frac{\partial S}{\partial t}+ \frac{(\nabla S)^{2} }{2m}+V(x)~=~0 .$$