AREAS - Quad areas

Compass and Straightedge

Since you don't have any friends, you get to spend Saturday morning solving a geometry problem.

A convex quadrilateral can be divided into four non-overlapping triangles by connecting opposite vertices, as shown.

A divided convex quadrilateral

You must find the area of the largest of these four triangles.

You may find the shoelace formula helpful. It describes the area of a degree-n polygon with vertices: (x1, y1) (x2, y2) ... (xn, yn).

Input

The input is the four vertices, in order. Each vertex is on a line, and each line has the x- and y-coordinates separated by a space. All coordinates are integers from -500 to 500 inclusive.

The quadrilateral is guaranteed to be convex; i.e. the angle at each vertex is less than 180 degrees.

Output

Output a single number: the area of the largest triangle. This answer must be accurate to within 0.001.

Examples

Input:
0 0
0 1
1 1
1 0

Output
0.25
Input:
0 5
10 400
100 500
50 -5

Output
11588.288
Input:
-2 0
0 1
2 0
0 -1

Output
1

Added by:BYU Admin
Date:2015-11-05
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 MAWK BC NCSHARP COFFEE DART FORTH GOSU JS-MONKEY JULIA KTLN OCT PROLOG PYPY3 R RACKET SQLITE SWIFT UNLAMBDA

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