Bathtub
Newlywed programmers went to a store to select a bathtub and found that due to the complex shapes of the bathtub bottoms, it was difficult to determine the water level in each when the same volume of water was added. They took photos of the bathtubs from various angles and later used computer modeling at home. They quickly created triangulations of the bathtub surfaces, and the only task left was to calculate the water height for a given volume.
All the triangulated surfaces are simply connected and consist only of triangles whose projections onto the XY plane do not intersect and are not degenerate into line segments. Additionally, the bathtub bottom does not have local maxima, and horizontal sections can only occur at the maximum depth. For simplicity, the newlyweds did not define external vertical boundaries, assuming the given surface is enclosed by vertical walls, with the top edge at zero depth.
Input
The first line contains two natural numbers separated by at least one space: n (1 ≤ n ≤ 200) - the number of vertices in the triangulation, and m (1 ≤ m ≤ 400) - the number of triangles. Each of the next n lines provides the vertices of the triangulation, with 3 real numbers per line representing coordinates in meters, where each coordinate ranges from 0 to 10, and the third coordinate indicates the depth at that point. Each of the following m lines describes a triangle, with 3 natural numbers per line, each number representing the index of a triangulation vertex. The last line contains one natural number - the volume of water poured, measured in liters. The water is always poured such that the height of the rise does not exceed the maximum depth of the bathtub.
Output
Output one real number, rounded to three decimal places in fixed-point format, representing the height of the water rise relative to the deepest point of the bathtub.