Four Eggs, Eight Drops

You hold 4 identical eggs and stand in a building of $n$ floors. There is one critical floor $c \in {0,1,\dots,n}$: an egg dropped from any floor above $c$ breaks, an egg dropped from floor $c$ or lower survives undamaged and can be dropped again ($c = 0$ means an egg breaks even from floor 1). A broken egg is gone.

You may drop at most 8 times in total, and whatever the results, you must end up knowing $c$ with certainty.

What is the largest $n$ you can handle? Answer format: enter an integer.