CF321D.Ciel and Flipboard

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.

Fox Ciel 有一个 $n$ 行 $n$ 列的方格板，每个格子中有一个整数。

已知 $n$ 是奇数，因此我们定义 $x = \frac{n+1}{2}$。Fox Ciel 可以执行以下操作任意多次：她选择一个大小为 $x$ 行 $x$ 列的子方格板，并将其中所有数字乘以 $-1$。

返回通过这些操作所能得到的方格板上数字之和的最大值。

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.

第一行包含一个整数 $n$（$1 \leq n \leq 33$，且 $n$ 为奇数）—— 表示棋盘的大小。

接下来的 $n$ 行，每行包含 $n$ 个整数 —— 表示棋盘中的数字。每个数字的绝对值不超过 $1000$。

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

输出一个整数：棋盘上所能达到的最大数字之和。

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.

在第一个测试用例中，我们可以执行该操作两次：第一次作用于左上角的 $2 \times 2$ 子棋盘，第二次作用于右下角的 $2 \times 2$ 子棋盘。之后，所有数字都将变为正数。