Monday Mutant 79: Streampunk (all 3's)

Shade in some cells black such that the black cells are all connected to each other through their edges, and no 2x2 cell area within the grid contains all black cells. Numbers in a cell indicate the sizes of the orthogonally contiguous groups formed by black cells sharing a corner or an edge with that cell. For example, "3" means that the cell shares a corner or an edge with three black cells, and they form a single group, whereas "1 3" means the cell shares a corner with four black cells which form a group of three cells and a single separate cell. Cells with numbers cannot be black. A 3 or a clue with a 3 in it has been placed in every white cell that could legally contain one.