A9723 | Vanya and Lanterns

Vanya walks late at night along a straight street of length $l$ , lit by $n$ lanterns. Consider the coordinate system with the beginning of the street corresponding to the point $0$ , and its end corresponding to the point $l$ . Then the $i$ -th lantern is at the point $a_{i}$ . The lantern lights all points of the street that are at the distance of at most $d$ from it, where $d$ is some positive number, common for all lanterns.

Vanya wonders: what is the minimum light radius $d$ should the lanterns have to light the whole street?

Vanya walks late at night along a straight street of length $l$ , lit by $n$ lanterns. Consider the coordinate system with the beginning of the street corresponding to the point $0$ , and its end corresponding to the point $l$ . Then the $i$ -th lantern is at the point $a_{i}$ . The lantern lights all points of the street that are at the distance of at most $d$ from it, where $d$ is some positive number, common for all lanterns.

Vanya wonders: what is the minimum light radius $d$ should the lanterns have to light the whole street?

Print the minimum light radius $d$ , needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed $10^{-9}$ .