A8867. Cubes

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 $v_{y}$ ( $1<=n<=10^{3}$ , $|v_{x}|,|v_{y}|<=|10^{4}|$ , $|v_{x}|+|v_{y}|>0$ ).

Next $n$ lines contain $n$ integers each: the $j$ -th integer in the $i$ -th line $a_{ij}$ $(0<=a_{ij}<=10^{9}$ , $1<=i,j<=n)$ 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 С++. It is preferred to use the cin, cout streams or the %I64d specifier.