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.

Input

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 $(*i*, *j*)$.

Output

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.