Alex and Bella play the following game. They first choose a positive integer N, and take turns writing numbers on a blackboard. Alex starts first, and writes the number 1. After that, if the number k is on the board, the next player may write down either k+1 or 2k, if the new number is not greater than N, and then erase k. The player who writes N on the blackboard wins. For how many integers N≤1000 does Bella have a winning strategy?

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