G. Minimum volume tetrahedron
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

There is the angle $$$OABC$$$ in the 3D Cartesian space with the vertex $$$O(0,0,0)$$$ and points $$$A(a_1,a_2,a_3)$$$, $$$B(b_1,b_2,b_3)$$$, $$$C(c_1,c_2,c_3)$$$ on the edges.

Point $$$P(p_1,p_2,p_3)$$$ is placed strictly inside angle $$$OABC$$$ (i.e. the vector $$$OP$$$ has positive elements in basis $$$OA$$$, $$$OB$$$, $$$OC$$$). Draw the plane through point $$$P$$$ to make the tetrahedron with the minimum possible volume formed by the plane and the angle.

Input

Four lines contains the coordinates of points $$$A$$$, $$$B$$$, $$$C$$$, $$$P$$$ separated by spaces. Coordinates are positive integer numbers that don t exceed $$$10^3$$$. Vectors $$$OA$$$, $$$OB$$$ and $$$OC$$$ are linearly independent.

Output

Output the minimum volume of tetrahedron cut by plane from the given angle with absolute or relative precision $$$10^{-6}$$$.

Example
Input
1 2 3
2 3 1
2 5 3
2 4 3
Output
2.53125