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a C7 problem with a C1 hardness

Source: Iranian Third Round 2020 Combinatorics exam Problem2

November 18, 2020
combinatoricscirclemoduloidentical

Problem Statement

For each nn find the number of ways one can put the numbers {1,2,3,...,n}\{1,2,3,...,n\} numbers on the circle, such that if for any 44 numbers a,b,c,da,b,c,d where n∣a+b−c−dn|a+b-c-d. The segments joining a,ba,b and c,dc,d do not meet inside the circle. (Two ways are said to be identical , if one can be obtained from rotaiting the other)
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