The Mystic Circle
Arrange the numbers \(1 - 32\), inclusive, in a circle such that the sum of any two adjacent numbers in the circular chain is a perfect square.
When you crack the Mystic Circle, you will obtain \(32\) Square numbers which are the sums of adjacent numbers.
If the number of times the squares \(4, 9, 16, 25, 36, 49\) appear is given by \(A. B, C, D, E, F\) respectively, find \(1A + 2B + 3C + 4D + 5E + 6F\).