1393. Maximal orders of permutations

A permutation of n elements is a one-to-one function (injection) p: {1,2,…,n} -> {1,2,…,n}. An order of permutation p is the minimal k >= 1, such that for all i=1,2,…,n we have:

, i.e. p composed with itself k times becomes identity function. For example, the order of the permutation of 3 elements p(1)=3, p(2)=2, p(3)=1 is 2, because p(p(1))=1, p(p(2))=2, p(p(3))=3.

For a given n let us consider permutations of n-elements having the the largest order possible. For example, the maximal order of a permutation of 5 elements is 6. An example of a permutation of 5 elements whose order is 6 is p(1)=4, p(2)=5, p(3)=2, p(4)=1, p(5)=3.

Among all permutations of n elements having the maximal order, we would like to find the earliest one (in a lexycographic order). Being more precise, we say a permutation p of n elements is earlier than a permutation r of n elements, if there is i, such that p(j) = r(j) for all j < i and p(i) < r(i). The earliest permutation of 5 elements having an order 6 is p(1)=2,p(2)=1,p(3)=4,p(4)=5,p(5)=3.

Task

Write a programme that:

reads from the standard input a set of integers n1,n2,…,nd,

for each number ni (for i=1,2,…,d) determines the earliest permutation of ni elements havaing the maximal order,

writes the determined permutations to the standard output.