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A permutation of elements is a one-to-one function (injection) . An order of permutation is the minimal , such that for all we have:
i.e. composed with itself times becomes identity function. For example, the order of the permutation of elements is , because .
For a given let us consider permutations of -elements having the the largest order possible. For example, the maximal order of a permutation of elements is . An example of a permutation of elements whose order is is .
Among all permutations of elements having the maximal order, we would like to find the earliest one (in a lexicographical order). Being more precise, we say a permutation of elements is earlier than a permutation of elements, if there exists , such that for all and . The earliest permutation of elements having an order is .
Write a programme that:
There is one positive integer in the first line of the standard input, . In the following lines there are positive integers , one per line, .
Your programme should write lines to the standard output. The 'th line should contain a sequence of integers separated by spaces, forming the least permutation of elements having the maximal order, i.e. the sequence , where denotes this permutation.
For the input data:
2 5 14
the correct result is:
2 1 4 5 3 2 3 1 5 6 7 4 9 10 11 12 13 14 8
Task author: Jakub Pawlewicz.