Count the grid

Count the grid | JXNUOJ 

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describe ：

Lattice points are ordered pairs (x, y), among x and y Are integers. . Given the coordinates of the vertices of the triangle （ It happens to be a grid point ）, You want to calculate the number of grid points completely inside the triangle （ Points on triangle edges or vertices are not counted ）.
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 form , among (x1, y1)、(x2, y2) and (x3, y3) Is the coordinates of the vertex of the triangle . All triangles in the input will be non degenerate （ Will have a positive area ）, also -15000 ≤ x1, y1, x2, y2, x3, y3 ≤ 15000. End of file by x1 = Test case tags for y1 = x2 = y2 = x3 = y3 = 0 And should not deal with .

Output ：
For each input case , The program shall print the number of internal grid points on one line .