Problem Description

There is a chocolate with $ H $ rows and $ W $ columns. Each cell is either black chocolate or white chocolate. Black chocolates and white chocolates do not share an edge (i.e., the chocolate forms a checkerboard pattern). Each cell has a defined chocolate concentration. An example of the chocolate is shown below (the numbers represent the concentrations):

My sister decided to cut out a rectangular region from this chocolate and melt it to make chocolate cream. She is particular about the taste of the chocolate and wants the total concentration of black chocolates and white chocolates used in the chocolate cream to be equal (if either type is not used, the total concentration is considered to be $ 0 $).

My sister wants to know the maximum number of chocolate cells she can use in a cutting method that satisfies this condition.

Input Format

The input is given from the standard input in the following format:

$ H $ $ W $ $ C_{1,1} $ $ C_{1,2} $ .. $ C_{1,W} $ $ C_{2,1} $ $ C_{2,2} $ .. $ C_{2,W} $ : $ C_{H,1} $ $ C_{H,2} $ .. $ C_{H,W} $

• The first line contains the number of rows $H\ (1\ ≦\ H\ ≦\ 100)$ and the number of columns $W\ (1\ ≦\ W\ ≦\ 100)$ of the chocolate, separated by spaces.
• The next $ H $ lines provide information about the concentrations. Each line contains $ W $ non-negative integers separated by spaces. The $ j $ -th integer on the $ i $ -th line $C_{i,j}\ (0\ ≦\ C_{i,j}\ ≦\ 99)$ represents the concentration of the cell in the $ i $ -th row and $ j $ -th column, starting from the top-left corner.

Output Format

If there exists a cutting method that satisfies the condition, output the maximum number of cells used. If no such method exists, output 0. Include a newline at the end of the output.

Sample Input and Output

Sample Input #1

3 4
4 6 2 5
3 5 6 7
2 5 5 6

Sample Output #1

6

Sample Input #2

2 2
4 0
7 3

Sample Output #2

4

Sample Input #3

2 3
0 0 0
1 2 3

Sample Output #3

3

Sample Input #4

3 3
1 2 3
6 5 4
7 8 9

Sample Output #4

0

Sample Input #5

1 5
0 1 2 3 4

Sample Output #5

1

Notes/Hints

Sample Explanation 1

By cutting out a rectangular region of $ 2 $ rows and $ 3 $ columns as shown in the figure below, the number of cells is $ 6 $ and the total concentration is $ 17 $ each, satisfying the condition. 

Sample Explanation 2

Note that concentrations of $ 0 $ can be included.

Sample Explanation 4

In this example, no cutting method satisfies the condition.

Sample Explanation 5

Note that there can be cases where only one type of chocolate (either black or white) is cut out and the condition is satisfied.

见题面 Input 部分

见题面 Output 部分