Little Difference

Lidia likes playing with numbers. Today she has a positive integer $n$, and she wants to write it as a product of positive integers.

Lidia likes numbers that sit close together, so any two numbers used in a decomposition differ by at most 1, and the product of all numbers in the decomposition must equal $n$. Two decompositions are the same when they have the same number of elements and one is a permutation of the other.

Write a program that finds every decomposition Lidia can play with today.

The only line contains one integer $n$ ($1 \le n \le 10^{18}$).

If the number of decompositions is infinite, print $-1$ on the first line and nothing else.

Otherwise print the number of decompositions on the first line. Then print one decomposition per line. On each line print the number of elements $k$ of that decomposition first, then the $k$ elements in non-decreasing order, separated by single spaces.

Two different decompositions always have a different number of elements, so print the lines in increasing order of $k$.