NMC 2007 Problem 3

The number $10^{2007}$ is written on a blackboard, Anne and Berit play a game where the player in turn makes one of two operations:

(i) replace a number $x$ on the blackboard by two integer numbers a and $b$ greater than 1 such that $x=a b$;

(ii) erase one or both of two equal numbers on the blackboard.

The player who is not able to make her turn loses the game. Who has a winning strategy?