SP10113 REGPOLYG - 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? **Input** Each test case consists of three lines. Line _i_ consists of two floating point values _x_ $ _{i} $ and _y_ $ _{i} $ (−10 $ ^{4} $ x $ _{1} $ , _y_ $ _{1} $ 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. **Output** For each test case, print one line with the minimum number of vertices that _R_ must have. **Sample Input** ```

-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
```
  
  
**Sample Output**

 ```
3
4
```
- - - - - -

> _Problemsetter: Adrian Kuegel_
                            

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