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문제

There are $n$ points in three-dimensional space. Consider the convex hull of these $n$ points.

You are given $q$ queries. Each query defines a plane in three-dimensional space. For each given plane, find the area of section of the convex hull produced by this plane.

입력

The first line of input contains two integers $n$ and $q$, the number of points and the number of queries ($1 \le n, q \le 1000$).

Each of the next $n$ lines contains three integers $x$, $y$ and $z$: the coordinates of one of the points.

The next $q$ lines describe queries. Each of them contains four integers $a$, $b$, $c$ and $d$ which specify the plane given by the equation $a x + b y + c z + d = 0$.

It is guaranteed that the absolute values of $x$, $y$, $z$, $a$, $b$, $c$ and $d$ are not greater than $2000$.

출력

For each query, print the answer with absolute error at most $10^{-3}$.

예제 입력 1

6 1
0 0 1
1 0 1
0 1 1
0 0 -1
1 0 -1
0 1 -1
0 0 1 0

예제 출력 1

0.500