The IOI 2002 awards ceremony will be held in the YONG-IN Hall. After the excitement of the World Cup, people are in high spirits. To make the ceremony more attractive, it has been suggested to build an I-shaped podium in the YONG-IN Hall to represent Informatics. Considering that the competition sponsors may have placed many display stands in the YONG-IN Hall, they may be unwilling to move them. As the gold medalist of IOI 2002, you have naturally become the person they turn to for help.
The YONG-IN Hall is a rectangular grid area. Each sponsor's display stand occupies a certain number of unit cells. The I-shaped podium will be built upright and parallel to the edges of the YONG-IN Hall. An I-shaped podium is formed by three rectangles connected together, where both sides of the top and bottom rectangles must extend beyond the middle rectangle; otherwise, it would be misinterpreted as letters such as T, L, or J. For example:
These are two valid I-shaped podiums, while the following three cases are invalid:
The right side of the bottom rectangle does not extend beyond the middle rectangle, which would be misinterpreted as J
Rectangles are not connected, invalid
A 90-degree rotated podium is invalid, which would be misinterpreted as H
You are expected to write a program to find the I-shaped podium with the largest area that does not cover any display stands.
Input
The first line of the input contains two positive integers $n$ and $m$ ($1 \le n, m \le 200$), representing the number of rows and columns of the rectangular grid area of the YONG-IN Hall, respectively. The following $n$ lines each contain $m$ numbers, either $0$ or $1$. Each number describes a unit cell, where $1$ indicates that the unit cell contains a display stand, and $0$ indicates that the unit cell does not contain a display stand.
Output
The output contains only one integer, representing the area of the largest I-shaped podium. If no valid I-shaped podium exists, output $0$.
Examples
Input 1
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
Output 1
15