Fox Ciel has a board with n rows and n columns, there is one integer in each cell.It's known that n is an odd number, so let's introduce . Fox Ciel can do the following operation many times: she choose a sub-board with size x rows and x columns, then all numbers in it will be multiplied by -1.Return the maximal sum of numbers in the board that she can get by these operations.

Input The first line contains an integer n, (1 \le n \le 33, and n is an odd integer) - the size of the board.Each of the next n lines contains n integers - the numbers in the board. Each number doesn't exceed 1000 by its absolute value.

Output Output a single integer: the maximal sum of numbers in the board that can be accomplished.

In the first test, we can apply this operation twice: first on the top left 2 \times 2 sub-board, then on the bottom right 2 \times 2 sub-board. Then all numbers will become positive.