The beauty of a rectangle is the ratio between the length of the longer side and the length of the shorter side.
Given a rectangle with side lengths ~X~ and ~Y~, repeat the following process until you have ~N~ rectangles:
Select one rectangle Cut it into two rectangles
After doing this, all rectangles must have the same area.
The beauty of a set of rectangles is the maximum beauty present among all rectangles in the set. Compute the minimum possible beauty of the set assuming optimal cuts.
~1 \le N \le 10~
~1 \le X, Y \le 10^4~
The first and only line contains three space-separated integers, ~X~, ~Y~, and ~N~.
Output the desired beauty to exactly six decimal places.
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