Collect Resources

There is a rectangular field with two types of resources viz, resource A and resource B. At each cell in the field, both of the resources can be present. There are two types of factories which can collect resource A and B. If resource A is collected in a factory then resource B is lost and vice versa. Now, these two factories are located perpendicular to each other i.e the factory collecting resource A is at the top ( north) of the rectangular field and the factory collecting resource B is to the left ( west) of the rectangular field. The resources have to be brought to the factory on a straight path without taking any turns. This implies that if there is any south-north conveyor belt in the cell, but the cell north of it contains an east-west conveyor belt, then all resources transported on the south-north conveyor belt will be lost.

You have to design a conveyor belt system that maximizes the total amount of minerals mined, i.e the sum of the amount of resource A transported to the top and the sum of the amount of resource B transported to the left. You are given a 2-D matrix A and B of the same size denoting the amount of resource of the corresponding type in that cell.

Since the answer can be large, return it modulo 10⁹ + 7.

1 <= |A| = |B| <= 10³

1 <= |A[0]| = |B[0]| <=10³

0 <= A[i][j], B[i][j] <= 10⁹

The first line contains a matrix that specifies the availability of the resource A in each of the cells. 

The second line contains a matrix that specifies the availability of the resource B in each of the cells.

Return a single integer which specifies the maximum amount of resources that can be processed by the factories.

Input 1:

   A = [
         [7, 8, 9]
         [4, 5, 6]
         [1, 2, 3]
       ]


B = [
         [1, 2, 3]
         [4, 5, 6]
         [7, 8, 9]
       ]

Input 2:

   A = [
         [1, 0, 1]
       ]


B = [
         [2, 1, 0]
       ]

Output 1:

  63

Output 2:

  4

Explanation 1:

  The first row can be sent to the top to collect resource A. The rest two rows will be sent to the left to collect resource B. 

Explanation 2:

  The first two columns can be sent to the left. The third column will be sent to the top.Total resource collected - 2 + 1 + 1 = 4