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.

Constraints

$1\le N\le 10$

$1\le X,Y\le {10}^4$

Input Specification

The first and only line contains three space-separated integers, $X$, $Y$, and $N$.

Output Specification

Output the desired beauty to exactly six decimal places.

Sample Input

5 5 5

Sample Output

1.800000