You are given an integer N and asked to partition it into a sum of natural numbers so that the sum of the inverses of these natural numbers would be equal to one; that is, to find K natural numbers n_1, ... n_K such that
, и .
The only input line contains the integer N (1 ≤ N ≤ 1000000000).
If the required partition does not exist, the only output line should contain the text Epic fail, otherwise the first output line should contain the number of addends and the second line the addends themselves, in any order. If there are several solutions, output any one of them.