Earthquake

Memory limit: 32 MB

The Infinity City is located on an infinite quarterplane. There is an infinite number of sky-scrapers in the city, there is one sky-scraper located at every point with integer coordinates.

One unfortunate day there was an earthquake in the city. There was a huge tectonic crack along the line and all the sky-scrapers at positions satisfying the inequality simply disappeared. The city has now become a Finity City with only a finite number of sky-scrapers. But exactly how many?

Input

The only line of input contains three space-separated positive integers , , . They are bounded as follows: , .

Output

Your program should output exactly one integer: the number of sky-scrapers in the Finity City.

Example

For the input data:

3 4 13

the correct result is:

12

Task author: Jakub Pawlewicz.