CF487C.Prefix Product Sequence

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Consider a sequence \[a_{1},a_{2},... ,a_{n}\] . Define its prefix product sequence .

Now given $n$ , find a permutation of \[1,2,...,n\] , such that its prefix product sequence is a permutation of \[0,1,...,n-1\] .

The only input line contains an integer $n$ ( $1<=n<=10^{5}$ ).

Consider a sequence \[a_{1},a_{2},... ,a_{n}\] . Define its prefix product sequence .

Now given $n$ , find a permutation of \[1,2,...,n\] , such that its prefix product sequence is a permutation of \[0,1,...,n-1\] .

For the second sample, there are no valid sequences.