Problem 53064. Amazing circle of numbers 1 to n

Archin

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For given natural number n, create amazing circle of numbers 1 to n without a repeat.
This circle is that the sum of any two adjacent numbers is a perfect square.
For example, if n = 32,
So, output is
                          [1 8 28 21 4 32 17 19 30 6 3 13 12 24 25 11 5 31 18 7 29 20 16 9 27 22 14 2 23 26 10 15]
If the condition is satisfied, it is the correct answer regardless of the order of the vectors.
If there is no amazing circle vector, return empty vector [].