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 $2\dots n+1$ 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

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

$100\mathrm{\%}$ of the data satisfy $1\le n,m\le 80$, $0\le a_{i,j}\le 1000$.