Expectation of the maximum fn

Expectation of the maximum fn

I am unable to compute the expectation and get the answer in the proper
format.Please help!
Let $\tilde{s}_i$ be independently and normally distributed each with mean
0. Let $\tilde{s}_i^+ = max(\tilde{s}_i,0)$ and $\tilde{s}_i^- =
max(-\tilde{s}_i,0)$. Also, $\tilde{S}^+ = \sum\limits_{i=1}^k
\tilde{s}_i^+$ and $\tilde{S}^- = \sum\limits_{i=1}^k \tilde{s}_i^-$ . I
need to show that
$$E(max(\tilde{S}^+,\tilde{S}^-))=\frac{1}{2}\sum\limits_{i=1}^k
E|\tilde{s}_i|+\frac{1}{2}E |\sum\limits_{i=1}^k \tilde{s}_i| =
\frac{1}{\sqrt{2\pi}}(\sum\limits_{i=1}^k
\sigma_i+\sqrt{\sum\limits_{i=1}^k \sigma_i^2}) .$$ where $\sigma_i$ is
the s.d. of $\tilde{s}_i$.