_{This problem is a programming version of Problem 166 from projecteuler.net}

A grid is filled with digits .

It can be seen that in the grid

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

the sum of each row and each column has the value . Moreover the sum of each diagonal is also .

In how many ways can you fill a grid with the digits so that each row, each column, and both diagonals have the same sum?