# Problem I

Skyline

In this problem, we assume that all buildings have a trapezoid shape when viewed from a distance. That is, vertical walls but a roof that may slope. Given the coordinates of the buildings, calculate how large part of each building that is visible to you (i.e. not covered by other buildings).

## Input

The first line contains an integer, $N$ ($2 \le N \le 100$), the number of buildings in the city. Then follow $N$ lines each describing a building. Each such line contains $4$ integers, $x_1$, $y_1$, $x_2$, and $y_2$ ($0 \le x_1 < x_2 \le 10 000, 0 \le y_1, y_2 \le 10 000$). The buildings are given in distance order, the first building being the one closest to you, and so on.

## Output

For each building, output a line containing a floating point number between $0$ and $1$, the relative visible part of the building. The absolute error for each building must be within $10^{-6}$.

Sample Input 1 | Sample Output 1 |
---|---|

4 2 3 7 5 4 6 9 2 11 4 15 4 13 2 20 2 |
1.00000000 0.38083333 1.00000000 0.71428571 |

Sample Input 2 | Sample Output 2 |
---|---|

5 200 1200 400 700 1200 1400 1700 900 5000 300 7000 900 8200 400 8900 1300 0 1000 10000 800 |
1.00000000 1.00000000 1.00000000 1.00000000 0.73667852 |