Problem:
Max Score: $600$ Points

Problem Statement

Sigma and his brother Sugim are in the $H \times W$ grid. They wants to buy some souvenirs.

Their start position is upper-left cell, and the goal position is lower-right cell.

Some cells has a souvenir shop. At $i$-th row and $j$-th column, there is $a_{i, j}$ souvenirs.

In one move, they can go left, right, down, and up cell.

But they have little time, so they can move only $H+W-2$ times.

They wanted to buy souvenirs as many as possible, but they had no computer, so they couldn't get the maximal numbers of souvenirs.

Write a program and calculate the maximum souvenirs they can get, and help them.

Input

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

$H \ W$
$a_{1, 1} \ a_{1, 2} \ \cdots \ a_{1, W}$
$a_{2, 1} \ a_{2, 2} \ \cdots \ a_{2, W}$
$\vdots \ \ \ \ \ \ \ \ \ \ \vdots \ \ \ \ \ \ \ \ \ \ \vdots$
$a_{H, 1} \ a_{H, 2} \ \cdots \ a_{H, W}$

Output

Print the maximum number of souvenirs they can get.

Constraints

$1 \le H, W \le 200$

$0 \le a_{i, j} \le 10^5$

Subtasks

Subtask 1 [ 50 points ]

The testcase in the subtask satisfies $1 \le H \le 2$.

Subtask 2 [ 80 points ]

The testcase in the subtask satisfies $1 \le H \le 3$.

Subtask 3 [ 120 points ]

The testcase in the subtask satisfies $1 \le H, W \le 7$.

Subtask 4 [ 150 points ]

The testcase in the subtask satisfies $1 \le H, W \le 30$.

Subtask 5 [ 200 points ]

There are no additional constraints.

Sample Input 1

3 3
1 0 5
2 2 3
4 2 4

Sample Output 1

21

The cell at $i$-th row and $j$-th column is denoted $(i, j)$.

In this case, one of the optimal solution is this:

Sigma moves $(1, 1) -> (1, 2) -> (1, 3) -> (2, 3) -> (3, 3)$.

Sugim moves $(1, 1) -> (2, 1) -> (3, 1) -> (3, 2) -> (3, 3)$.

Then, they can get $21$ souvernirs.

Sample Input 2

6 6
1 2 3 4 5 6
8 6 9 1 2 0
3 1 4 1 5 9
2 6 5 3 5 8
1 4 1 4 2 1
2 7 1 8 2 8

Sample Output 2

97

Writer : square1001

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define REP(i,n,s) for (int i = (s); i < (n); i++)
#define SIZE 201
using namespace std;
typedef long long int LL;

int H, W, A[SIZE][SIZE];
int cache[SIZE][SIZE][SIZE];

LL calc(int x1, int y1, int x2, int y2) {
	if (cache[x1][y1][x2] > -1) return cache[x1][y1][x2];
	if (x1 == H || y1 == W || x2 == H || y2 == W) {
		return 0;
	}
	if (x1 == H-1 && y1 == W-1 && x2 == H-1 && y2 == W-1) {
		return A[H-1][W-1];
	}
	LL res = 0;
	if (x1 == x2) {
		res += A[x1][y1];
		res += max(
			max(
				calc(x1+1, y1, x2+1, y2),
				calc(x1+1, y1, x2, y2+1)
			), calc (x1, y1+1, x2, y2+1));
	} else {
		res += A[x1][y1] + A[x2][y2];
		res += max(
			max(
				calc(x1+1, y1, x2+1, y2),
				calc(x1+1, y1, x2, y2+1)
			), max(
				calc(x1, y1+1, x2+1, y2),
				calc(x1, y1+1, x2, y2+1)));
	}
	cache[x1][y1][x2] = res;
	return res;
}

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);

	cin >> H >> W;
	REP(i, H, 0) {
		REP(j, W, 0) {
			cin >> A[i][j];
		}
	}
	memset(cache, -1, sizeof(cache));
	cout << calc(0, 0, 0, 0) << endl;
}