3D Geometry

An axis-aligned tetrahedron (triangular pyramid) $DABC$ is a convex polyhedron in three dimensions with these vertices:

• $D: (x_1, y_1, z_1)$
• $A: (x_2, y_1, z_1)$
• $B: (x_1, y_2, z_1)$
• $C: (x_1, y_1, z_2)$

An axis-aligned cube $PQRSDEFG$ is also a convex polyhedron, with these vertices:

• $P: (x_3, y_3, z_3)$
• $Q: (x_3, y_3, z_4)$
• $R: (x_3, y_4, z_3)$
• $S: (x_3, y_4, z_4)$
• $D: (x_4, y_3, z_3)$
• $E: (x_4, y_3, z_4)$
• $F: (x_4, y_4, z_3)$
• $G: (x_4, y_4, z_4)$

Given the tetrahedron $DABC$ and the cube $PQRSDEFG$, find the volume of their intersection.

The input contains several test cases and ends at end-of-file. Each test case has 4 lines. The $i$-th line contains three integers $x_i$, $y_i$, and $z_i$.

For each test case, print the volume as a real number. Your answer is accepted if its absolute or relative error does not exceed $10^{-6}$.

• $-500 \le x_i, y_i, z_i \le 500$ for each $1 \le i \le 4$
• $x_1 \neq x_2$, $y_1 \neq y_2$, $z_1 \neq z_2$
• $x_3 \neq x_4$, $y_3 \neq y_4$, $z_3 \neq z_4$
• The number of test cases does not exceed $10^5$.