I am stuck on the problem of finding volume of the figure given by $0 \leq z \leq 2, x^{2} + y^{2} \leq 2, x^{2} + y^{2} + z \leq 2x$. I have tried three different coordinates but the problem is $2x$ in the last relation. Thanks ahead for help!

**Add.** Sorry that I didn't mention this before. But I want a full solution without "brute-force" computation. I did try many different tricks, so if any of those works, it means that I do not know how to work out the details.