Someone suggested the idea of handing out a sticker with the BSUIR Open logo to each participant. To do this, a rectangular sheet of self-adhesive paper measuring $$$n \times m$$$ was found at the university. In total, $$$k$$$ participants will come to the competition, so you need to cut out exactly $$$k$$$ logos in the form of a square of the same size. Now it remains to determine the maximum size of each logo sticker.
Unfortunately, the organizers have no free hands for this task, so you are asked to help determine the maximum size of the logo (the length of the side of the square).
Apparently stickers will be next year...
The first line contains three integers $$$n$$$, $$$m$$$ and $$$k$$$ — the width, the height of the sheet of paper and the number of participants respectively.
$$$$$$ 1 \le n, m \le 10^3 $$$$$$ $$$$$$ 1 \le k \le 10^9 $$$$$$
In a single line print a single real number — the maximum logo size.
Your answer will be counted if the relative or absolute error does not exceed $$$10^{-6}$$$. Formally, if $$$a$$$ — is your answer, and $$$b$$$ — is the jury's answer, then it will be counted if $$$\frac{|a - b|}{max(b, 1)} \le 10^{-6}$$$.
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