Maximum OR Minimum

Alice and Bob are ready to play a new game. Both the players take alternate turns. Alice starts first. There are $N$ **binary** numbers written on a blackboard. - Alice, in her turn, erases any $2$ numbers from the blackboard and writes the [bitwise OR](https://en.wikipedia.org/wiki/Bitwise_operation#OR) of those $2$ numbers on the blackboard. - Bob, in his turn, erases any $2$ numbers from