$136

Time for another puzzle. And, like, way to go with the problem solving to-date! You're just encouraging me to keep this up.

This one is from my friend J. I cried quietly to myself when he first sent it to me, but I solved it in the end. I know you can too.

You have $136. You have to divide it up into some number of bags, in whole dollar increments, so that I can come along and ask brashly for any amount and you can give it to me by handing over one or more bags (without rearranging the amounts inside). What is the minimum number of bags you require?

I had to ask J a couple of follow-up questions; I'll repeat them here for your benefit:
Q: Do I know the amount in each bag?
A: Um. Yes. (duh)
Q: When you ask for an amount, can you ask only for whole dollar increments? (Like, $12.56 is not allowed, right?)
A: Correct.