Consecutive Sum Representation

Given a positive integer n, determine the number of ways to represent n as a sum of consecutive positive integers. In other words, find the number of sequences of consecutive positive integers whose sum equals n.

Any sequence of k consecutive positive integers starting with a can be written as:

\(n = a + (a+1) + \cdots + (a+k-1) = k \cdot a + \frac{k(k-1)}{2}\)

Your task is to compute the number of such representations. Note that the representation with a single number (i.e. n itself) is also counted.

inputFormat

The input consists of a single positive integer n read from the standard input.

outputFormat

Output a single integer representing the number of ways to write n as a sum of one or more consecutive positive integers. Print the result to the standard output.

15

4