Monday Mutant 21: Polyominous / Battleships

Ten ships (as indicated below the grid: one four-cell ship, two three-cell ships, three two-cell ships, and four one-cell ships) are hidden in the grid. The ships may be rotated from the orientations shown (without changing the numbers), but may not overlap or occupy cells which share a corner or an edge. A number to the right of a row or below a column indicates how many cells in that row or column are occupied by ships. The numbers on these ships also function as clues in a Polyominous puzzle. None of the numbers already present in the grid are part of the ships. Locate the ships and solve the Polyominous puzzle.
Today's Monday Mutant was inspired by the ever-so-inspirational Thomas Snyder.