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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