Skyline

When you look at a city skyline from a distance, the buildings partly or wholly cover one another, which makes you wonder how much of each building you actually see.

In this problem we assume that, seen from a distance, every building has the shape of a trapezoid: the side walls are vertical, but the roof may slope.

Each building is a trapezoid standing on the ground:

• Left wall: the vertical segment from $(x_1, 0)$ to $(x_1, y_1)$
• Right wall: the vertical segment from $(x_2, 0)$ to $(x_2, y_2)$
• Roof: the segment from $(x_1, y_1)$ to $(x_2, y_2)$
• Base: the segment along the ground from $(x_1, 0)$ to $(x_2, 0)$

The buildings are given in order of distance, nearest first. Seen from the front, a nearer building hides everything behind it up to its own outline. For each building, compute the fraction of its area that stays visible (that is, not covered by any nearer building).

The first line contains the number of buildings $N$ ($2 \le N \le 100$).

Each of the next $N$ lines contains four integers $x_1$, $y_1$, $x_2$, $y_2$ describing one building ($0 \le x_1 < x_2 \le 10000$, $0 < y_1, y_2 \le 10000$).

The buildings are listed in order of distance: the first is the one closest to you, and so on.

For each building, print on its own line the visible fraction of that building (a value between 0 and 1), rounded to exactly 8 digits after the decimal point.

The test data guarantees that the exact value never lies on a rounding boundary, so any correct computation produces the same 8-digit result.

Figure 1: The layout of the first test case.