Sum#6088

Sum

0.5 seconds
256 megabytes
Very easy

It is well known that Mark likes creating mathematical tasks very much. Recently he has invented the following one: for given find all positive integers and , that A \le B and

A + (A + 1) + (A + 2) + \ldots + (B - 1) + B = S

Input

One integer (1 \le S \le 10^{12}).

Output

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

Examples

Example 1

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