L is fighting Kira which can be dangerous as Kira has the Death Note. Watari has to decide a successor for L in case L dies. Watari gives a point $(x,y,z)$ in cartesian plane to Mello and Near and they have to play a game such that they take turns. In one turn, the player can change one of the coordinates (say $w$) to$[w/2], [w/3], [w/5]$.(w > 0) So $(8,9,10)$ can be reduced to $(4,9,10)$ or $(2,9,10)$ or $(1,9,10)$ or $(8,9,3)$ and so on. The person who changes the point to origin wins the game. Watari wants Near to win but he forgot the z coordinate so he randomly selects $z$ between $0$ and $12345$ ( both inclusive ). So the point is $L$(2^{60}, 2^{61}, z), where z is between 0 and 12345 (both inclusive). Given that Near starts play calculate the probability that Near will win the game if both players play optimally.

If the answer is of the form u/v where u and v are co prime you have to input u+v as the answer.