3. A pair of four-digit numbers in the form $\overline{a b c d}$ and $\overline{c d a b}$ (where $a, b, c, d$ can be the same digits) are called a "brother number pair". The pairs ( $\overline{a b c d}, \overline{c d a b}$ ) and ( $\overline{c d a b} ， \overline{a b c d}$ ) are considered the same brother number pair, such as $(1091,9110)$ and $(9110,1091)$. Among all "brother number pairs", the number of pairs where the sum of the two numbers is a perfect square is $\qquad$ pairs.
$41$