The Digits ABCABD

Number Theory Level 3

How many possible 6 digit numbers are there of the form $N=\overline{abcabd}$ where $a \neq 0, d \neq 0$ , $d = c + 1$ and $N$ is a perfect square?

Details and assumptions

The condition of $a \neq 0$ follows because we have a 6 digit number.
The condition of $d \neq 0$ follows because $0 \neq 9 + 1$ .