F. The Farthest Point
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

An ant is on one of the vertices, say the starting vertex, of a rectangular cuboid (a hexahedron with all of its faces being rectangular). The surface of the cuboid constitutes the entire world of the ant.

We'd like to know which point on the surface of the cuboid is the farthest for the ant from the starting vertex. You may think that the opposite vertex, that is, the opposite end of the interior diagonal from the starting vertex, is the farthest. The opposite vertex is, however, not necessarily the farthest.

For example, on the surface of a cuboid of size $$$1\times 1\times 2$$$, the distance from a vertex to the opposite vertex is the square root of $$$8$$$. The distance to the farthest point is, however, the square root of $$$65/8$$$ (Figure F-1).

Figure F-1: Rectangular cuboid of size $$$1\times 1\times 2$$$, and its net

You are given the size of the rectangular cuboid. Write a program which calculates the distance from the starting vertex to the farthest point.

Input

The input consists of a single test case of the following format.

$$$a$$$ $$$b$$$ $$$c$$$

The three integers $$$a$$$, $$$b$$$, and $$$c$$$ mean that the size of the rectangular cuboid is $$$a\times b\times c.$$$ All of them are between 1 and 100, inclusive.

Output

Output a line containing the distance from the starting vertex to the farthest point. The relative error of the output must be less than or equal to $$$10^{-9}$$$.

Examples
Input
1 1 2
Output
2.850438562747845
Input
10 10 10
Output
22.360679774997898
Input
100 2 3
Output
101.0503923792481
Input
2 3 5
Output
7.093659140387279
Input
84 41 51
Output
124.58275515757813