1.2. Inside a rectangular parallelepiped $A B C D A^{\prime} B^{\prime} C^{\prime} D^{\prime}$, there are two spheres such that the first one touches all three faces containing $A$, and the second one touches all three faces containing $C^{\prime}$. Additionally, the spheres touch each other. The radii of the spheres are 10 and 11, respectively. The lengths of the edges $A B$ and $A D$ are 25 and 26. Find the length of the edge $A A^{\prime}$.