C. Prefix Product Sequencetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputConsider a sequence [a1, a2, ... , an]. 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].InputThe only input line contains an integer n (1 ≤ n ≤ 105).OutputIn the first output line, print "YES" if such sequence exists, or print "NO" if no such sequence exists.If any solution exists, you should output n more lines. i-th line contains only an integer ai. The elements of the sequence should be different positive integers no larger than n.If there are multiple solutions, you are allowed to print any of them.ExamplesInput7OutputYES1436527Input6OutputNONoteFor the second sample, there are no valid sequences.
Input7
OutputYES1436527
['constructive algorithms', 'math', 'number theory', '*2300']