The sum of p (p > 0) consecutive integers can often be equal to the sum of next q consecutive positive integers. For example:

• 9 + 10 + 11 + 12 = 13 + 14 + 15, here p = 4 and q = 3
• 4 + 5 + 6 + 7 + 8 = 9 + 10 + 11, here p = 5 and q = 3.

Given the value of q, how many possible values of p are there?

Input

Contains at most 1500 lines. Each line contains a positive integer less than 1014, which denotes the value of q. Input is terminated by a line containing a single zero. This line should not be processed.

Output

For each input line print one line that contains an integer, which denotes the total number of possible values of p.