TUYMAADA 2013 Problem 1

$100$ heaps of stones lie on a table. Two players make moves in turn. At each move, a player can remove any non-zero number of stones from the table, so that at least one heap is left untouched. The player that cannot move loses. Determine, for each initial position, which of the players, the first or the second, has a winning strategy.

K. KokhasEDIT. It is indeed confirmed by the sender that empty heaps are still heaps, so the third post contains the right guess of an interpretation.