"Sum"

It is well known that Mark likes creating mathematical tasks very much. Recently he has invented the following one: for given S find all positive integers А and В, that А ≤ В and

А + (А + 1) + (А + 2) + … + (В - 1) + В = S.

Input

Input contains one integer S (1 ≤ S ≤ 10^12).

Output

First line at output should contain one integer K – number of pairs that have been found. Each of following K lines should contain 2 integers, first not greater than second – corresponding pair. Pairs should be printed sorted ascending by first number.

Examples