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.