Roger, having now been bested twice in two dimensions, decides to move to three dimensions.

Roger has assembled a large block of stone, which has conveniently been subdivided into unit cubes that are either normal stones and paper. He challenges Victor to find a sub-block with a square base such that the entire sub-block contains no paper. The goal is to maximize the surface area of the components of the block perpendicular to one of the coordinate planes.

Constraints

$1\le A,B,C\le 150$

Input Specification

The first line contains three integers, $A$, $B$, and $C$.

$AB$ lines follow, each containing $C$ characters. Character $z$ on line $1+yA+x-A$ corresponds to the cube that is located at $(x,y,z)$, implying that all cubes lie in points $(x,y,z)$ where $1\le x\le A$, $1\le y\le B$, and $1\le z\le C$. Each character is either N for normal stone or P for paper.

Output Specification

Output the maximum possible surface area of a valid block. In particular, the block must have dimensions $a\times a\times b$ for some positive $a$ and $b$, and the answer to output should be $4ab$. The orientation of the valid block need not be such that the square base is parallel to the $xy$-plane.

Sample Input

3 2 5
PNNNN
PNNNN
NPPNP
PNNNP
NNNNP
PPNNP

Sample Output

24