You are given $2$ identical eggs and access to a building with n floors numbered from $1$ to n.

There exists some floor f where $0 \leq$ f $\leq$ n such that any egg dropped from a floor higher than f will break, and any egg dropped from floor f or below will not break.

In each move, you can take an unbroken egg and drop it from any chosen floor x where $1 \leq$ x $\leq$ n. If the egg breaks, you can no longer use it. If the egg does not break, you can reuse it in subsequent moves.

Return the minimum number of moves required to determine the value of f with certainty in the worst case.

Constraints:

• $1 \leq$ n $\leq 1000$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.