Triangular Grid 

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 $\overline{{PQ}}$. 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 $\overline{{PQ}}$ 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 and y₂ ( 1 $\leq$ B $\leq$ 200,   2 $\leq$ H $\leq$ 200,   -1000 $\leq$ x₁, y₁, x₂, y₂ $\leq$ 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 $\neq$ 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 $\overline{{PQ}}$.

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
0 0 0 0 0 0

Sample Output 

6
1
2
3