_{This problem is a programming version of Problem 61 from projecteuler.net}

Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are all figurate (polygonal) numbers and are generated by the following formulae:

The ordered set of three 4-digit numbers: 8128, 2882, 8281, has three interesting properties.

• The set is cyclic, in that the last two digits of each number is the first two digits of the next number (including the last number with the first).

• Each polygonal type: triangle , square , and pentagonal , is represented by a different number in the set.

• This is the only set of 4-digit numbers with this property.

You are given a set of numbers find the sum of numbers from sets that respect the above property. If there are multiple such numbers print their sums in sorted order.