Consecutive Sum

There are cases where the sum of $p$ consecutive integers ($p > 0$) equals the sum of the $q$ consecutive positive integers that immediately follow them.

For example, $9+10+11+12 = 13+14+15$, so $p=4$ and $q=3$; and $4+5+6+7+8 = 9+10+11$, so $p=5$ and $q=3$.

Given $q$, write a program that counts how many values of $p$ satisfy this condition.

The input consists of several test cases. Each test case is a single line containing one integer $q$. $q$ is a positive integer less than $10^{14}$.

The last line of the input contains a single $0$, which is not processed. The number of test cases does not exceed $2{,}000$.

For each test case, print the number of values of $p$ that satisfy the condition, one per line.