Find all vanishing and non-vanishing components of mixed

Question

Find all [vanishing and non-vanishing] components of mixed curvature tensor. For metric

It means find all components of R^p_rmn.

Where p, r, m, and n varies from 0, 1, 2, 3.

ds² = e^N-M dr² + e^-(M+N)dt² + 2dxdy.

Where M and N are functions of variables x and y.

Formula for mixed curvature tensor is

R^p_rmn = _rn,mΓ^P - _rm,nΓ^P + _rnΓ^q _qmΓ^P- _rmΓ^q _qnΓ^P