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 can guess as many times as you like, but are only allowed to guess too high 10 times and too low 3 times. That is, the \(4^\text{th}\) time you make a guess and are too low, or the \(11^\text{th}\) time you make a guess and are too high, you lose the game.

What is the maximum \(N\) for which you are guaranteed to be able 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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