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