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Hunan Normal University
College of Information Science and Engineering
Triangle
Time Limit: 1000ms, Special Time Limit:2500ms, Memory Limit:65536KB
Total submit users: 29, Accepted users: 28
Problem 10533 : No special judgement
Problem description
  A lattice point is an ordered pair (x, y) where x and y are both integers. Given the coordinates of the vertices of a triangle (which happen to be lattice points), you are to count the number of lattice points which lie completely inside of the triangle (points on the edges or vertices of the triangle do not count).

Input
  The input test file will contain multiple test cases. Each input test case consists of six integers x1, y1, x2, y2, x3, and y3, where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of vertices of the triangle. All triangles in the input will be non-degenerate (will have positive area), and −15000 x1, y1, x2, y2, x3, y3 15000. The end-of-file is marked by a test case with x1y1 = x2 = y2 = x3 = y3 = 0 and should not be processed.

Output
  For each input case, the program should print the number of internal lattice points on a single line.

Sample Input
0 0 1 0 0 1
0 0 5 0 0 5
0 0 0 0 0 0
Sample Output
0
6
Problem Source
  jiyanmoyu

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