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Problems

Jelly-Oxygen Beans

Jelly-Oxygen Beans

Do you think that eating candies is easy? This is not the case when they are oxygen candies actually. As you like everything sweet, you've just bought a fresh pack of \textbf{N} jelly beans. But usual jelly beans are, of course, not an option. As a part of your desire to taste everything in your life, you've bought special jelly-oxygen beans, rare and exclusive candies. Now it came to eating, and you decided to solve the jelly-oxygen beans eating problem in a mathematical way. \includegraphics{https://static.e-olymp.com/content/fa/fa36e5d50c7e048b74f942dd78208200aa533ea6.jpg} \includegraphics{https://static.e-olymp.com/content/29/2997696d35db62b4892007e26b2ee4ba10c0580b.jpg} Suppose you want to eat \textbf{N} jelly-oxygen beans during the next \textbf{M} (\textbf{1} ≤ \textbf{M} ≤ \textbf{N}) days, eating the same number of jelly-oxygen beans each day. It might be impossible, however, if \textbf{M} doesn't divide \textbf{N}. In this case, you want to eat \textbf{N}/\textbf{M }jelly-oxygen beans each day. The remaining \textbf{N mod M} jelly-oxygen beans should be divided into \textbf{M} equal smaller parts. If this is possible, you'll eat exactly one of these parts each day. How many possible choices of \textbf{M} do you have? \InputFile The only line contains an integer number \textbf{N} (\textbf{1} ≤ \textbf{N} ≤ \textbf{10^12}). \OutputFile Print the number of possible values of \textbf{M}. \Note The possible values of \textbf{M} in the example are \textbf{1} (eat all candies on the only day), \textbf{2} (divide a candy into two equal parts and eat two undivided candies and one of the parts each day), \textbf{4} (divide a candy into four equal parts and eat one undivided candy and one of the parts each day) and \textbf{5} (eat one candy each day). Note that \textbf{M} can't be equal to \textbf{3}, as you can't divide \textbf{N mod M }=\textbf{ 2} candies into \textbf{M} = \textbf{3} equal parts.
Time limit 2 seconds
Memory limit 256 MiB
Input example #1
5
Output example #1
4
Author Gennady Korotkevich
Source Gennady Korotkevich Contest 1, Petrozavodsk Training Camp, Day 1, Friday, August 23, 2013