Find the largest integer $N$ whose decimal representation has the following properties:
- The rightmost digit in the decimal representation is not $0$.
- There exists a digit $d$ in the decimal representation which is not the leftmost digit, so that crossing out this digit $d$ yields the decimal representation of an integer divisor of $N$.
Example:
The integer $121$ is not divisible by $10$, and crossing out the digit $2$ yields the divisor $11$ of $121$.