I need help to find a proof for the following inquality.
Assuming that $ 0 \leq c_i \leq 1 $ and $ 0 \leq d_i \leq 1 $, show that $$ \prod_{i=1}^N (c_i + d_i - c_i d_i) \geq \prod_{i=1}^N c_i + \prod_{i=1}^N d_i - \prod_{i=1}^N c_i d_i $$
This seems to have some relation with Weierstrass inequalities. This also looks like the outcome of using Jensen's inequality for composition of functions. However, the latter is not applicable as $ \prod_i c_i d_i $ is not convex. Any help will be appreciated.