Bela and Jenn play the following game on the set of integers $0, 1, \dots, n$ , where $n$ is a fixed integer greater than 4. They take turns playing, with Bela going first. At his first turn, Bela chooses any integer in the set. Thereafter, the player whose turn it is chooses an integer that is more than one unit away from all integers previously chosen by either player. A player unable to choose such a number loses. Using optimal strategy, which player will win the game?

Bela will win if and only if $n \equiv 0 (mod 4)$ or $n \equiv 1 (mod 4)$ .

Jenn will win if and only if $n \equiv 0 (mod 4)$ or $n \equiv 1 (mod 4)$ .

Bela will win if and only if $n$ is odd.

Jenn will win if and only if $n$ is odd.

Bela will always win.