Testing Eggs I

You are given $2$ identical eggs and access to an $n-$ floor building. The goal is to determine the highest floor from which an egg will not break when dropped out of a window from that floor. Call this floor the $\textit{critical floor}$ . There is exactly one critical floor in the building. If an egg is dropped and does not break, it's undamaged and can be dropped again. Broken eggs can't be dropped again. If an egg breaks on floor $n$ , it also breaks for all floors $m > n$ ; similarly, if an egg doesn't break on floor $n$ , it also doesn't break for any floor $m < n$ . What is the maximum value of $n$ such that the critical floor can be identified in at most $d$ drops? Report the answer when $d = 10$ .

Answer format: enter an integer.