Chessboard Puzzle
Description
Farmer John has invented a game, Chessboard Puzzle, which perplexes lots of puzzle fanatics. The game is quite simple. Given a chessboard in such a way that every grid is presented by a specified integer, you are obliged to color every grid in white or black. For each pair of grids subjected to following restraints:
- they are neighbor, in detail, sharing common edge;
- they are colored differently.
add the product of the two specified integers to the score. And your goal is to maximum the total score. Could you write a program to tell John the maximum score?
Input
The input describes one puzzle which begins with two integer n, m(1 ≤ n, m ≤16). Then n lines follow. Each contains m integers. The j-th number on i-th row corresponds to the grid(i,j). The absolute value of each number is less than 1000.
Output
Print the maximum score in a line.
5 5
-136 -712 -286 -622 564
6 -899 623 -152 -519
904 982 593 799 93
-815 122 -307 572 -359
921 757 -888 351 935
5852863Source
POJ Founder Monthly Contest – 2008.01.31, Qi-feng CHEN