One day Petya got a set of wooden cubes as a present from his mom. Petya immediately built a whole city from these cubes.

The base of the city is an n×n square, divided into unit squares. The square's sides are parallel to the coordinate axes, the square's opposite corners have coordinates (0,0) and (n,n). On each of the unit squares Petya built a tower of wooden cubes. The side of a wooden cube also has a unit length.

After that Petya went an infinitely large distance away from his masterpiece and looked at it in the direction of vector v=(v_x,v_y,0). Petya wonders, how many distinct cubes are visible from this position. Help him, find this number.

Each cube includes the border. We think that a cube is visible if there is a ray emanating from some point p, belonging to the cube, in the direction of vector -v, that doesn't contain any points, belonging to other cubes.

The first line contains three integers n, v_x and v_y (1≤n≤10³, |v_x|,|v_y|≤|10⁴|, |v_x|+|v_y|>0).

Next n lines contain n integers each: the j-th integer in the i-th line a_ij (0≤a_ij≤10⁹, 1≤i,j≤n) represents the height of the cube tower that stands on the unit square with opposite corners at points (i-1,j-1) and (i,j).

Print a single integer − the number of visible cubes.

Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.