what would be best for the body?

[Da CaVeman]

I'm in my senior yr of college and as some of you know, pulling all nighters to study are pretty common. I usually pull one once every 2 weeks or so avg. for exams...
My question is, would you go to the gym the day ur studying and/or the day after ur studying considering ur losing out on a night's sleep? Also, what would you eat throughout the night? At around 4 a.m, is ur metabolism still up and running hard since ur body is still active or would you still have to eat like u were going to bed...?? I would assume the latter...

This is my avg. typical all nighter.
typical day, wake up 9 a.m school and stuff until 9 p.m
normal dinner 9 (post workout)
maintain water intake
piece of chicken breast 12ish
grilled chicken salad and salsa 3 a.m
Red Bull (sugar free) 4 a.m
Snack (cottage cheese and banana) 6 a.m
continue study until about 9 a.m
Turkey sausage, chicken breast, 4 egg whites and protein drink 9:30 a.m
Red Bull (sugar free) 10:00 A.M
Exam 10:30-12:30 a.m
Class 12:30-2:30 pm
Steak/vegetables Burrito and protein drink 3:00 pm
hibernate 3:00 pm until I wake up which is usually 6 hrs later eat a meal and go to sleep at about midnight to start the next day at 10

I know this is harsh on the body but I once pulled an all nighter and didn't sleep until the next night but I remained active throughout the day and went to the gym...Oddly enough, that was one of my most intense workouts...

I try my best to keep my performance both in school and gym high but sometimes ur pushed to sacrifice one over the other...People still think I'm crazy for sipping on my protein drink while studying for an exam...