Define a heterosquare to be a square grid containing consecutive positive integers starting from 1 such that the sums of the integers in each row, column, and long diagonal are all different. Furthermore, define an anti-magic square to be a heterosquare whose sums form a consecutive sequence of integers.
If there exists a anti-magic square, then there are possible values for the sum of its two diagonal sums. Find the value of
Note: A diagonal sum is the sum of the numbers along a long diagonal of the square. For example, the two diagonal sums of the following square are and
This problem is related to Open Problem #2 of the Brilliant.org Open Problems Group.