A positive integer $a$ consists of four digits, three of which are equal to each other. The square of $a$ consists of seven digits, all of which are different. The number $b$ arises by reading number $a$ from right to left. It turns out that $b$ is greater than $a$. In addition, it turns out that $b^2$ is exactly equal to $a^2$ read from right to left.
Find all possibilities for $a$.