The painted points#297
A triangle was constructed on a grid paper so that its vertices are at lattice points (grid intersections). All lattice points that are strictly inside the triangle were then painted, excluding the triangle's vertices and all points that lie on the triangle's sides.
Count the number of such painted points.
Each line contains six integers: the coordinates x_1, y_1, x_2, y_2, x_3, y_3 of the triangle's vertices (-15000 \le x_1, y_1, x_2, y_2, x_3, y_3 \le 15000). All input data is correct and describes a non-degenerate triangle. The last line contains all six numbers equal to zero. This line should not be processed and marks the end of input.
For each test case, output the number of painted points in a separate line.
Example 1