Cow Award!

Planning for the annual a-cow-demy award ceremony is underway. To make the ceremony more interesting, the organizers want to build the stage in the shape of an I (obviously to demonstrate that cows stride above their egos). However, many sponsors have created displays in the hall and, of course, they do not want to move these pre-existing displays. You have been asked to perform the task of selecting the location of this stage.

The awards hall has the shape of a rectangular grid with R (1 <= R <=
150) rows and C (1 <= C <= 150) columns. The I-shaped stage will
be placed rectilinearly. The stage will be in the shape of 3
rectangles stacked on top of each other. The width of the middle
rectangle must be less than the widths of both the top and bottom
rectangles.  The upper and lower rectangles must have at least one
segment farther right and one segment farther left than the middle
segment's span (otherwise, the stage might be mistaken for T, L or
J). The widths of the top and bottom may differ, as may the heights.

For example, the stage layouts below are valid (I represents part
of the stage, . represents empty space):

IIIII.      .IIIII
..II.. and  ..II..
IIIIII      IIIII.
IIIIII

The following stages are not valid:

IIII
.II.
III. (lower rectangle does not extend beyond the middle segment)

IIIII
.....
..I..
III.. (since it's not connected)

I..I
IIII
I..I (the top and bottom rectangles are not rectangles)

Your program should find the area of the largest 'I' that does not
overlap with any of the displays. Output 0 if no 'I' can be made.

PROBLEM NAME: award

INPUT FORMAT:

* Line 1: Two space-separated integers: R and C

* Lines 2..R+1: Line i+1 contains row i expressed as C space-separated
        integers. The jth integer is 1 if there is a display board in
        column j and 0 otherwise.

SAMPLE INPUT:

6 8
1 1 1 1 1 0 0 1
1 0 0 0 0 1 1 1
1 0 0 0 0 0 1 1
1 0 1 0 1 0 1 0
1 0 0 0 0 0 0 1
1 1 0 0 0 1 0 1

INPUT DETAILS:

The grid has 6 rows and 8 columns with a total of 23 pre-existing displays

OUTPUT FORMAT:

SAMPLE OUTPUT:

15

OUTPUT DETAILS:

The maximum sized I is denoted by the Is in the following diagram:
XXXXX..X
XIIIIXXX
XIIII.XX
X.XIX.X.
X.III..X
XXIIIX.X