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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?
The only line of input contains three space-separated positive integers , , . They are bounded as follows: , .
Your program should output exactly one integer: the number of sky-scrapers in the Finity City.
For the input data:
3 4 13
the correct result is:
Task author: Jakub Pawlewicz.