Mahmoud and Zomhan play a game where they alternatively write numbers on a board. In each turn, a player takes the old number $N$ written on the board and replaces it either by the number $T$ of divisors of $n$ or by the difference $N-T$. For example if $N=22$ is written on the blackboard then $T=4$ with the divisors 1, 2, 11, 22 of $N=22$, and the next player may write $T=4$ or $N-T=18$ on the blackboard.
Mahmoud is the first player to play, and whichever player is the first player to write the number $0$ is the winner of the game. Given that the initial number on the board is $1036$, determine which player has a winning strategy.