Forest

Bruce Force is standing in the forest. He wonders which tree trunk is the farthest away that is not blocked from his view by other tree trunks.

Bruce has drawn a map of the trees in the forest. On the map his current position is the origin of a Cartesian coordinate system. Tree $i$ is drawn as a circle with center $(x_i, y_i)$ and radius $r_i$. A tree trunk is considered visible if and only if there is a line segment on the map from the origin $(0, 0)$ to some point on the border of that tree's circle such that the segment does not intersect or touch any other circle.

The input contains several test cases. The first line of each test case contains an integer $n$ ($1 \le n \le 1000$), the number of trees on the map. Each of the following $n$ lines contains three integers $x_i$, $y_i$, $r_i$ ($-10000 \le x_i, y_i \le 10000$, $1 \le r_i \le 1000$), where $(x_i, y_i)$ is the center of the circle representing tree trunk $i$ and $r_i$ is its radius.

No two circles intersect: for any two circles, the distance between their centers is strictly greater than the sum of their radii. No circle contains the origin.

The last test case is followed by a line containing a single $0$.

For each test case, print one line with the maximum Euclidean distance from the origin to a visible tree. The distance to a tree is measured to the point of that tree closest to the origin (that is, $\sqrt{x_i^2 + y_i^2} - r_i$), regardless of whether that particular point is itself visible.

Round the answer to exactly 3 digits after the decimal point.