Sum#3354
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Sum

1 second
128 megabytes
Very easy

Vovochka, known for his love of creating math problems, recently devised this challenge: Given an integer , identify all positive integer pairs and such that a \leq b and

a + (a + 1) + (a + 2) + \ldots + (b - 1) + b = s

Input

A single integer (1 \leq s \leq 10^{12}).

Output

The first line should display a single integer , representing the number of pairs and found. The following lines should each contain two integers, where the first is not greater than the second, representing the pair. List the pairs in ascending order based on the first integer.

Examples

Example 1

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