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

# Triangle	 	P3,n=n(n+1)/2	 	1, 3, 6, 10, 15, ...
# Square	 	P4,n=n^2	 		1, 4, 9, 16, 25, ...
# Pentagonal	P5,n=n(3n−1)/2	 	1, 5, 12, 22, 35, ...
# Hexagonal	 	P6,n=n(2n−1)	 	1, 6, 15, 28, 45, ...
# Heptagonal	P7,n=n(5n−3)/2	 	1, 7, 18, 34, 55, ...
# Octagonal	 	P8,n=n(3n−2)	 	1, 8, 21, 40, 65, ...
# 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 (P3,127=8128), square (P4,91=8281), and pentagonal (P5,44=2882), 
# is represented by a different number in the set.
# This is the only set of 4-digit numbers with this property.
# Find the sum of the only ordered set of six cyclic 4-digit numbers for which each polygonal type: 
# triangle, square, pentagonal, hexagonal, heptagonal, and octagonal, 
# is represented by a different number in the set.