Wedding Selfie

At his wedding, Daryl took a selfie with his bride. Both of them liked the photo enough to hang it on the wall of their new home. The photo has the shape of a convex polygon with $N$ vertices.

Daryl's brother Merle offered to hang it. Merle drove in $N$ nails, one at each vertex, but only the first nail was tightened properly. The other nails were loose and did not hold for long, so Daryl soon found the photo dangling from that single tight nail.

The photo turns freely around the tightened vertex. It settles once the area of the polygon to the right of the Y-axis equals the area to the left of the Y-axis. If several positions satisfy that, the photo settles in the position with the largest area below the X-axis. Find the coordinates of the vertices after the photo settles.

The first line contains the number of test cases $T$ ($1 \le T \le 100$). Each test case starts with a line holding the number of vertices $N$ ($3 \le N \le 100$). The next $N$ lines each contain two integers $X_i$ and $Y_i$ ($-1000 \le X_i, Y_i \le 1000$) separated by one space, the coordinates of the $i$-th vertex.

The vertices are given in counter clockwise order, and the first vertex is the one Merle tightened. The first vertex is always $(0, 0)$. No three consecutive vertices lie on one line. Every given polygon is convex, and all of its interior angles are smaller than $180$ degrees.

For each test case print a line with "Case n:", where $n$ is the test case number starting from $1$. Then print $N$ lines with the new coordinates of the vertices, in the same order as the input. Each line holds $X_i$ and $Y_i$ separated by one space, rounded to exactly six digits after the decimal point. Print 0.000000 instead of -0.000000. The settled position is uniquely determined.