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