All the numbers from $19$ to $93$ are written consecutively to form the number $N =19202122...........919293$. Find the largest power of $3$ that divides $N$.
The following hint has been provided.
The square of any integer is either divisible by $4$ or leaves a remainder $1$ divided by $4$. Thus, an integer which leaves a remainder $2$ or $3$ when divided by $4$ can never be a square. If a prime p divides a square number the $p^2$ also divides that number.