There is an infinite grid in the Cartesian plane composed of isosceles triangles, with the following design: A single triangle in this grid is a triangle with vertices on intersections of grid lines that has not other triangles inside it. Given two points P and Q in the Cartesian plane you must determine how many single triangles are intersected by the segment P Q. A segment intersects a polygon if and only if there exists one point of the segment that lies inside the polygon (excluding its boundary). Note that the segment P Q in the example intersects exactly six single triangles. Input The problem input consists of several cases, each one defined in a line that contains six integer values B,H,x1,y1,x2 andy2 (1≤B≤200, 2≤H≤200, −1000≤x1,y1,x2,y2 ≤1000),where: • B is the length of the base of all isosceles single triangles of the grid. • H is the height of all isosceles single triangles of the grid. • (x1,y1) is the point P, that defines the first extreme of the segment. • (x2,y2) is the point Q, that defines the second extreme of the segment. You can suppose that neither P nor Q lie in the boundary of any single triangle, and that P ̸= Q. The end of the input is specified by a line with the string ‘0 0 0 0 0 0’. Output For each case in the input, print one line with the number of single triangles on the grid that are intersected by the segment PQ.
2/2 Sample Input 100 120 -20 -100 160 160 10 8 5 5 5 4 10 8 5 5 10 5 10 8 5 5 10 10 000000 Sample Output 6 1 2 3