Distinct pebbles are placed on a $1001 \times 1001$ board consisting of $1001^2$ unit tiles, such that every unit tile consists of at most one pebble. The pebble set of a unit tile is the set of all pebbles situated in the same row or column with said unit tile. Determine the minimum amount of pebbles that must be placed on the board so that no two distinct tiles have the same pebble set.

HIDE: Where's the Algebra Problem? It's already posted here.