Regular Convex Polygon

A regular convex polygon is a polygon where each side has the same length, and all interior angles are equal and less than 180 degrees. A square, for example, is a regular convex polygon. You are given three points which are vertices of a regular convex polygon R; can you determine the minimum number of vertices that R must have?

Each test case consists of three lines. Line i consists of two floating point values x_i and y_i (-10⁴ <=x_i,y_i<=10⁴) where (x_i,y_i) are the coordinates of a vertex of R. The coordinates are given with a precision of 10^-6, i.e., they differ from the exact coordinates by at most 10^-6. You may assume that for each test case the Euclidean distance between any two given points is at least 1, and R has at most 1000 vertices. The input will finish with a line containing the word END.

For each test case, print one line with the minimum number of vertices that R must have.

-1385.736326 -146.954822
430.000292 -2041.361203
1162.736034 478.316025
0.000000 4147.000000
-4147.000000 0.000000
0.000000 -4147.000000
END

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SWERC 2011