There is an infinite grid in the Cartesian plane composed of isosceles triangles, with the following design: \includegraphics{https://static.e-olymp.com/content/ec/ecc7cfe11eac8975f5c185511ecb69e541ed3957.jpg} A single triangle in this grid is a triangle with vertices on intersections of grid lines that has not other triangles inside it. \includegraphics{http://uva.onlinejudge.org/external/116/11662img2.png} Given two points \textbf{P} and \textbf{Q} in the Cartesian plane you must determine how many single triangles are intersected by the segment . A segment intersects a polygon if and only if there exists one point of the segment that lies inside the polygon (excluding its boundary). \includegraphics{http://uva.onlinejudge.org/external/116/11662img2.png} Note that the segment in the example intersects exactly six single triangles. \InputFile The problem input consists of several cases, each one defined in a line that contains six integer values \textbf{B}, \textbf{H}, \textbf{x_1}, \textbf{y_1}, \textbf{x_2} and \textbf{y_2} (\textbf{1} ≤ \textbf{B} ≤ \textbf{200}, \textbf{2} ≤ \textbf{H} ≤ \textbf{200}, \textbf{-1000} ≤ \textbf{x_1}, \textbf{y_1}, \textbf{x_2}, \textbf{y_2} ≤ \textbf{1000}), where: \begin{itemize} \item \textbf{B} is the length of the base of all isosceles single triangles of the grid. \item \textbf{H} is the height of all isosceles single triangles of the grid. \item (\textbf{x_1}, \textbf{y_1}) is the point \textbf{P}, that defines the first extreme of the segment. \item (\textbf{x_2}, \textbf{y_2}) is the point \textbf{Q}, that defines the second extreme of the segment. \end{itemize} You can suppose that neither \textbf{P} nor \textbf{Q} lie in the boundary of any single triangle, and that \textbf{P} ≠ \textbf{Q}. The end of the input is specified by a line with the string "\textbf{0 0 0 0 0 0}". \OutputFile \includegraphics{http://uva.onlinejudge.org/external/116/11662img2.png} For each case in the input, print one line with the number of single triangles on the grid that are intersected by the segment.