B. Working out （递推dp ）

B. Working out

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Summer is coming! It's time for Iahub and Iahubina to work out, as they both want to look hot at the beach. The gym where they go is a matrix a with n lines and m columns. Let number a[i][j] represents the calories burned by performing workout at the cell of gym in the i-th line and the j-th column.

Iahub starts with workout located at line 1 and column 1. He needs to finish with workout a[n][m]. After finishing workout a[i][j], he can go to workout a[i + 1][j] or a[i][j + 1]. Similarly, Iahubina starts with workout a[n][1] and she needs to finish with workout a[1][m]. After finishing workout from cell a[i][j], she goes to either a[i][j + 1] or a[i - 1][j].

There is one additional condition for their training. They have to meet in exactly one cell of gym. At that cell, none of them will work out. They will talk about fast exponentiation (pretty odd small talk) and then both of them will move to the next workout.

If a workout was done by either Iahub or Iahubina, it counts as total gain. Please plan a workout for Iahub and Iahubina such as total gain to be as big as possible. Note, that Iahub and Iahubina can perform workouts with different speed, so the number of cells that they use to reach meet cell may differs.

Input

The first line of the input contains two integers n and m (3 ≤ n, m ≤ 1000). Each of the next n lines contains m integers: j-th number from i-th line denotes element a[i][j] (0 ≤ a[i][j] ≤ 105).

Output

The output contains a single number — the maximum total gain possible.

Examples

input

3 3100 100 100100 1 100100 100 100

output

800

Note

Iahub will choose exercises a[1][1] → a[1][2] → a[2][2] → a[3][2] → a[3][3]. Iahubina will choose exercises a[3][1] → a[2][1] → a[2][2] → a[2][3] → a[1][3].

给出一个矩阵，一个人从左上角走到右下角，一个人从左下角走到右上角，两个人只会在一个点相交，问两个人经过路径上的数的和最大的情况下最大和是多少。

首先要保证只有一个格子重合,那么只可能是以下两种情况: 
1) A向右走,相遇后继续向右走,而B向上走,相遇后继续向上走 
2) A向下走,相遇后继续向下走,而B向右走,相遇后继续向右走

#include <stdio.h>#include <algorithm>using namespace std;#define maxn 1100int n,m;int dp[5][maxn][maxn];int a[maxn][maxn];int main(){    scanf("%d%d",&n, &m);    for( int i = 1; i <= n; i++)    {        for(int j = 1; j <= m; j++)            scanf("%d", &a[i][j]);    }    for( int i = 1; i <= n; i++)    {        for( int j = 1; j <= m; j++)        {             dp[1][i][j] = a[i][j];             dp[1][i][j] += max(dp[1][i][j-1],dp[1][i-1][j]);        }    }    for(int i = n; i >= 1; i--)    {        for(int j = 1; j <= m; j++)        {            dp[3][i][j] = a[i][j];            dp[3][i][j] += max(dp[3][i+1][j], dp[3][i][j-1]);        }    }    for( int i = 1; i <= n; i++)    {        for(int j = m; j >= 1; j--)        {            dp[4][i][j] = a[i][j];            dp[4][i][j] += max(dp[4][i-1][j],dp[4][i][j+1]);        }    }    for( int i = n; i >= 1; i--)    {        for(int j = m; j >= 1; j--)        {            dp[2][i][j] = a[i][j];            dp[2][i][j] += max(dp[2][i+1][j],dp[2][i][j+1]);        }    }    int ans = 0;    for(int i = 2; i < n; i++)    {        for(int j = 2; j < m; j++)        {            ans = max(dp[1][i-1][j] + dp[2][i+1][j] + dp[3][i][j-1] + dp[4][i][j+1],ans);            ans = max(dp[1][i][j-1] + dp[2][i][j+1] + dp[3][i+1][j] + dp[4][i-1][j],ans);        }    }    printf("%d\n",ans);}