Sum

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

a + (a + 1) + (a + 2) + ... + (b - 1) + b = s

Input

A single integer s (1 ≤ s ≤ 10^12).

Output

The first line should display a single integer k, representing the number of pairs a and b found. The following k 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