P7160 "dWoi R1" Sixth Monokuma's Son.

The problem first defines a matrix ring as follows: given a matrix $A$, which is initially all white, select a submatrix $A_1$ in it and paint it black, then select a submatrix $A_2$ inside $A_1$ and paint it white, and a matrix ring is formed. Note that a matrix ring must have selected parts on all four sides (top, bottom, left, and right), and the whole matrix ring is not a rectangular matrix. Assume `+` is black and `-` is white. The following is a matrix ring: ``` ---+++++-- ---++--+-- ---+++++-- ---+++++-- ---------- ``` The following are not matrix rings: ``` ------- ------ ---+++- --+++- ---+-+- --+++- ------- --+++- ``` Therefore, a matrix ring has four sides: top, bottom, left, and right. For each direction, the number of painted-black layers is the thickness in that direction. For example, in the first valid figure, the thicknesses of the top and right sides are $1$, and the thicknesses of the left and bottom sides are $2$. **Note that a complete matrix is not a matrix ring.** --- Next is the actual background story: After Saihara got the clue "Gokuhara found some small bugs", he took action immediately. First, he used Iruma's ~~relic~~, the thing that looked like a flamethrower, to suck in some air. Then, he planned to use Kibo's mechanical eye to inspect it.

Kibo's mechanical eye can scan an $n \times m$ area. At row $i$ and column $j$, it detects an abnormality value of $a_{i,j}$. Because Kibo is severely tortured by external forces, he can only lock onto one matrix ring to inspect. Kibo wants to ask you for help: he wants you to lock onto a matrix ring such that the sum of abnormality values of all positions in the matrix ring is maximized, **the thicknesses of the top and bottom sides are $1$, and the top row is the first row of the whole area, while the bottom row is the last row of the whole area**. As for the left and right thicknesses, Kibo has no further constraints.

The first line contains two integers $n, m$, representing the size of the whole area. Then $n$ lines follow, each containing $m$ integers $a_{i,j}$, representing the abnormality value at each position.

Output one integer in one line, representing the answer. If it is impossible to choose a matrix ring that satisfies the requirements, output $-1$.

#### Sample Explanation Explanation for Sample 1: You can choose a matrix ring of the following form (but in fact the two solutions are the same, because the sum of all numbers in the first column is $0$): ``` ++++ -+++ ++-+ -+-+ ++-+ -+-+ ++++ -+++ ``` Here, `+` means selected, and `-` means not selected. For Sample 3, the provider is @[cmll02](https://www.luogu.com.cn/user/171487). Thanks for the contribution. #### Constraints and Notes **This problem uses bundled testdata.** - Subtask 1 (5 pts): $n \le 2$ or $m \le 2$. - Subtask 2 (5 pts): $a_{i,j} > 0$. - Subtask 3 (40 pts): $m \le 1000$. - Subtask 4 (50 pts): No special constraints. For $100\%$ of the testdata, $1 \le n \le 10$, $1 \le m \le 10^5$, $|a_{i,j}| \le 100$. Translated by ChatGPT 5