Shuai often plays a matrix game with his classmates: for a given ~n \times m~ matrix, each element ~a_{i,j}~ in the matrix is a non-negative integer. The rules of the game are as follows:

1. Each step, one must remove one element from each row each time, for a total of ~n~ numbers removed. After ~m~ times, all elements of the matrix are removed;

2. Each element removed each time can only be the beginning or end of a line;

3. Each removal has a score value, which is the sum of the scores of the number removed in the rows. These scores are the value of the element to be removed times ~2^i~, where ~i~ represents the ~i~-th removal (starting from ~1~);

4. The total score at the end of the game is the sum of the scores obtained from the ~m~ times' removal.

Shuai would like to ask you to help write a program, for any matrix, you can find the maximum score after the game.

Input Specification

• Line ~1~ contains two integers ~n~ and ~m~.
• Lines ~2 \ldots n+1~ contain the ~n \times m~ matrix, where each line has ~m~ non-negative integers separated by a single space each.

Output Specification

One intger, the maximum score.

Sample Input 1

2 3 
1 2 3
3 4 2

Sample Output 1

82

Explanation of Sample 1

• The first time: the first element is taken from the first line, and the last element is taken from the second line. This time the score is ~1\times 2^1+2\times 2^1=6~
• The second time: take the first element of both lines, this time the score is ~2\times 2^2+3\times 2^2=20~
• Third time: score is ~3\times 2^3+4\times 2^3=56~. The total score is ~6+20+56=82~.

Sample Input 2

1 4 
4 5 0 5

Sample Output 2

122

Sample Input 3

2 10 
96 56 54 46 86 12 23 88 80 43 
16 95 18 29 30 53 88 83 64 67

Sample Output 3

316994

Constraints

~60\%~ of the data satisfy ~1 \leq n, m \leq 30~, answer does not exceed ~10^{16}~.

~100\%~ of the data satisfy ~1 \leq n, m \leq 80~, ~0 \leq a_{i,j} \leq 1\,000~.