Now, there is a new play about lottery draw.
Give you a matrix with N * N integers, you can choose a A * B(0 <= A, B <= N) rectangle to box a part of the matrix, if the higher the sum of these integers in the rectangle are, the more you might win a prize in a lottery.
So, can you find the maximum sum in the matrix? You can also give up this time for getting 0.

Input until EOF.
Each test contains a integet N (4 <= N <= 100) and a N * N matrix, each integer will be in [-99, 99].

Print the maximum sum.