Stacked Colored Paper

You glue $N$ sheets of colored paper onto the coordinate plane one sheet at a time, and no two sheets share a color. A sheet always lands on top of the plane and on top of every sheet that is already glued down. You cannot glue a sheet under the plane, and you cannot slide one between two sheets that are already there.

A sheet has one of two shapes.

1. A triangle with vertices $(x_1, y_1)$, $(x_2, y_2)$, $(x_3, y_3)$
2. A circle with center $(x, y)$ and radius $r$

Number the sheets from $1$ to $N$ and glue them in increasing order of number. The picture below shows one gluing process.

For every $i$, report how much of each glued sheet is visible at the moment sheets $1$ through $i$ are all in place.

The first line contains an integer $N$ ($1 \le N \le 200$).

Each of the next $N$ lines describes one sheet in gluing order. Line $i$ ($1 \le i \le N$) starts with an integer $t$ ($1 \le t \le 2$), the shape of sheet $i$.

If $t = 1$, sheet $i$ is a triangle, and six integers $x_1$, $y_1$, $x_2$, $y_2$, $x_3$, $y_3$ ($-100 \le x_1, y_1, x_2, y_2, x_3, y_3 \le 100$) follow on the same line, separated by spaces. The three vertices are never collinear.

If $t = 2$, sheet $i$ is a circle, and three integers follow on the same line, separated by spaces: the center coordinates $x$, $y$ ($-100 \le x, y \le 100$) and the radius $r$ ($1 \le r \le 100$).

Print $N$ lines. Line $i$ ($1 \le i \le N$) contains $i$ numbers separated by spaces: once sheets $1$ through $i$ have been glued down in order, the visible area of sheet $1$, the visible area of sheet $2$, and so on through the visible area of sheet $i$.

Round every area to six digits after the decimal point and print exactly six digits. An area of $2$ prints as 2.000000, and a sheet that is completely hidden prints as 0.000000.