The Billionaire's Home Decorating Project

Apparently, it wasn't enough for that guy to merely let you use the toilet and get 8 acres of land; now he's hired you to paint a wall of his mansion, and he'll pay you a hefty sum of money if you do the job well. If you don't do the job well, then he won't pay you a hefty sum of money. He sets the plan of the wall on the table for you to see:

"I have created a ten cells wide by ten cells high grid on this wall," the billionaire explains. "I want you to paint some of the cells in the grid using my black paint. You may not paint two cells which share an edge, nor may the painted cells divide the grid; all the unpainted cells must form a single contiguous region. The only other rule is that any arrow in an unpainted cell must provide an accurate count of the number of painted cells in that row or column in the direction of the arrow. You are allowed to paint a cell with an arrow in it; if you do, that arrow's information becomes useless. If you can fulfill these conditions, I shall pay you a hefty sum of money."

As much as you hate the stench of paint freshly applied to a wall, you really want that hefty sum of money. How must you paint the cells?