Two Sided Random Interval With degree of freedom

Random Variables $X_1,....X_n$ are independent identical normal distrobuted variables with unknown variance $\sigma^2$.

The sample variance is $S^2=\Sigma_{i=1}^n(X_i-\bar{X})^2/(n-1)$ use the result that $\frac{(n-1)S^2}{\sigma^2}\approx \chi^2_v$ to construct a $100(1-\alpha)%$ two sided random interval (L,U) for $\sigma^2$ where L and U are functions of $S^2$ such that $Pr(L>\sigma^2)=Pr(U<\sigma^2)=\frac{\alpha}{2}$.

State the degrees of freedom of v and express L and U as a function of $S^2$.

Thanks for any help.