Four small spheres each with radius 6 are cach interually tangent to a large sphere with radius 17. The four small spheres form a ring with each of the four spheres externally tangent to its two neighboring small
spheres. A sixth intermediately sized sphere is intemally tangent to the large sphere and externally tangent
to each of the four small spheres. Its radius is , where m and n are relatively prime positive integers.
Find mn + n.​