Sports Event Applause Count

During a sports event, two classes cheer for their athletes on the field. Class A claps every \(x\) seconds and Class B claps every \(y\) seconds. Each clap lasts exactly 1 second. If the event lasts for \(n\) seconds, determine the total number of seconds in which there is applause.

Note: If both classes clap during the same second, that second is counted only once.

The mathematical formula to compute the answer is:

\[ \text{Total Seconds} = \left\lfloor \frac{n}{x} \right\rfloor + \left\lfloor \frac{n}{y} \right\rfloor - \left\lfloor \frac{n}{\mathrm{lcm}(x,y)} \right\rfloor. \]

For example, when \(x=2\), \(y=3\), and \(n=10\):

• Class A claps at seconds: 2, 4, 6, 8, 10.
• Class B claps at seconds: 3, 6, 9.

The union of these seconds is \({2,3,4,6,8,9,10}\), so the answer is 7.

inputFormat

The input consists of three positive integers \(x\), \(y\), and \(n\) separated by spaces, where:

• \(x\) is the interval (in seconds) at which Class A claps.
• \(y\) is the interval (in seconds) at which Class B claps.
• \(n\) is the total duration of the event in seconds.

outputFormat

Output a single integer which represents the total number of seconds in which there was applause.

sample

2 3 10

7