Perfect square digi-numbers (Inspired by Chan Tin Ping)

We call a positive integer $N$ perfect square digi-number if it's digits and number itself are perfect square numbers. For example, 49 is perfect square digi-number since $\begin{aligned}49= 7^2 \quad\text{where} \quad 4=2^2\quad \text{and} \quad 9=3^2\end{aligned}$ How many such integers are there between 10 to 10000 inclusive ?

Note:

$\bullet$ Integers ending with only zeros are not counted as perfect square digi-number. For example , 100.

$\bullet$ The digits can be distinct or identical . Enter your answer including 49 as well.