While visiting a small town in some country, I lost my overcoat in a bus. When I reported the matter to the bus company I was asked the number of the bus. Though I did not remember the exact number of the bus, I did remember that the bus number had a certain peculiarity about it.

The number plate showed the bus number as a perfect square and also if the plate was turned upside down, the number would still be a perfect square.

I came to know from the bus company they had only five hundred buses numbered from 1 to 500. From this I was able to deduce the number.

Can you find out the bus number and the other one, too ?