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Problem B
Bounding Box

The Archeologists of the Current Millenium (ACM) now and then discover ancient artifacts located at vertices of regular polygons. (Recall that an n-sided regular polygon is a polygon where all n sides have the same lengths, and the n internal angles where two sides meet are all equal.)

The moving sand dunes of the desert render the excavations difficult and thus once three vertices of a polygon are discovered there is a need to cover the entire polygon with protective fabric.

Input

Input contains multiple test cases, at most 50.

Each case describes one polygon. It starts with an integer 3n50, the number of vertices in the polygon, followed by three pairs of real numbers giving the x and y coordinates of three vertices of the polygon. The coordinates have absolute value at most 1000 and at most 5 digits after the decimal point.

The input ends with a dummy case having n=0, this case should not be processed.

Output

For each test case, output one line giving the smallest area of a rectangle which can cover all the vertices of the polygon and whose sides are parallel to the x and y axes. You may assume that this area is at most 100000. Your answers should have an absolute or relative error of at most 109.

Sample Input 1 Sample Output 1
4
10.00000 0.00000
0.00000 -10.00000
-10.00000 0.00000
6
22.23086 0.42320
-4.87328 11.92822
1.76914 27.57680
23
156.71567 -13.63236
139.03195 -22.04236
137.96925 -11.70517
0
400.0000000000
1056.1719423660
397.6729693617
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