Flight of a Dream

Dima is taking part in an international paragliding olympiad. Every participant must complete the following task. Starting from a given point, fly $d$ kilometers south, then $d$ kilometers west, and then $d$ kilometers north. As a result of this flight, the participant must return to the starting point!

A participant is not allowed to come closer than one kilometer to the South Pole, because a tower with the olympiad jury stands there.

Each participant chooses the value of $d$ independently, subject only to the condition $d \ge 1$. Dima quickly realized that choosing $d$ is not so easy, and turned to you for help.

Treat the Earth as a sphere centered at $(0, 0, 0)$ with radius $6371$ kilometers. The North and South Poles have coordinates $(0, 0, 6371)$ and $(0, 0, -6371)$, respectively. The starting point has three-dimensional coordinates $(x, y, z)$, where $x$, $y$, and $z$ are integers, and the start lies on the surface of the Earth, that is, $x^2+y^2+z^2=6371^2$.

Help Dima choose a real number $d \ge 1$ such that, starting from the given point and flying $d$ kilometers south, then $d$ kilometers west, and then $d$ kilometers north, he returns to the starting point without passing close to the South Pole.

The single line of the input file contains three integers $x$, $y$, $z$, the coordinates of the start in the system described above.

The start lies on the surface of the Earth, and the distance from the starting point to the South Pole is at least 10 kilometers.

Print a single real number, the required $d$. The answer is considered correct if $d \ge 1$ and the distance between the starting point and the endpoint of the path is at most $10^{-6}$.

If several values of $d$ are possible, print any of them. At least one $d$ satisfying the conditions of the problem is guaranteed to exist.