Description:
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 $$x = \frac{n+1}{2}$$. 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 Format:
The first line contains an integer n, (1 ≤ n ≤ 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 Format:
Output a single integer: the maximal sum of numbers in the board that can be accomplished.
Note:
In the first test, we can apply this operation twice: first on the top left 2 × 2 sub-board, then on the bottom right 2 × 2 sub-board. Then all numbers will become positive.