You are asked to guess an integer between $1$ and $N$ inclusive.

Each time you make a guess, you are told either

**(a)** you are too high,

**(b)** you are too low, or

**(c)** you got it!

You are allowed to guess too high twice and too low twice, but if you have a $3^\text{rd}$ guess that is too high or a $3^\text{rd}$ guess that is too low, you are out.

What is the maximum $N$ for which you are guaranteed to accomplish this?

$$

**Clarification**: For example, if you were allowed to guess too high once and too low once, you could guarantee to guess the right answer if $N=5$, but not for $N>5$. So, in this case, the answer would be $5$.

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