Bill is working in a secret laboratory. He is developing missiles for
national security projects. Bill is the head of the aerodynamics department.

One surprising fact of aerodynamics is called Whitcomb area rule.
An object flying at high-subsonic speeds develops local
supersonic airflows and the resulting shock waves create the effect called wave drag.
Wave drag does not depend on the exact form of the object, but rather
on its cross-sectional profile.
Consider a coordinate system with OZ axis
pointing in the direction of object's motion. Denote the area of
a section of the object by a plane z = z_{0} as S(z_{0}).
Cross-sectional profile of the object is a function S that maps z_{0} to
S(z_{0}). There is a perfect aerodynamic shape called Sears-Haack body.
The closer cross-sectional profile of an object to the cross-sectional
profile of Sears-Haack body, the less wave drag it introduces.
That is an essence of Whitcomb area rule.
Bill's department makes a lot of computer simulations to study missile's aerodynamic properties
before it is even built. To approximate missile's cross-sectional profile one
takes samples of S(z_{0}) for integer arguments z_{0} from z_{min}
to z_{max}.
Your task is to find the area S(z_{0}) for each integer
z_{0} from z_{min} to z_{max}, inclusive, given the description of the missile.
The description of the missile
is given to you as a set of points. The missile is the minimal convex
solid containing all the given points. It is guaranteed that there are
four points that do not belong to the same plane.

Input file format

The first line of the input file contains three integer numbers:
n, z_{min} and z_{max}.
The following n lines contain three integer numbers each: x, y, and z coordinates
of the given points. All coordinates do not exceed 100 by their absolute values.
No two points coincide. There are four points that do not belong to the same plane.

Output file format

For each integer z_{0} from z_{min} to z_{max}, inclusive, output one floating
point number: the area S(z_{0}).
The area must be precise to
at least 5 digits after decimal point.