The field is covered in NN patches of grass (1≤N≤10001≤N≤1000), conveniently numbered 1…N1…N, that each have a distinct quality value. If Bessie eats grass of quality QQ, she gains QQ units of energy. Each patch is connected to up to 10 neighboring patches via bi-directional paths, and it takes Bessie EE units of energy to move between adjacent patches (1≤E≤1,000,0001≤E≤1,000,000). Bessie can choose to start grazing in any patch she wishes, and she wants to stop grazing once she has accumulated a maximum amount of energy.
Unfortunately, Bessie is a picky bovine, and once she eats grass of a certain quality, she’ll never eat grass at or below that quality level again! She is still happy to walk through patches without eating their grass; in fact, she might find it beneficial to walk through a patch of high-quality grass without eating it, only to return later for a tasty snack.
Please help determine the maximum amount of energy Bessie can accumulate.
SAMPLE INPUT:
5 2
4 1 2
1 3 1 3 4
6 2 2 5
5 2 2 5
2 2 3 4
SAMPLE OUTPUT:
7
Bessie starts at patch 4 gaining 5 units of energy from the grass there. She then takes the path to patch 5 losing 2 units of energy during her travel. She refuses to eat the lower quality grass at patch 5 and travels to patch 3 again losing 2 units of energy. Finally she eats the grass at patch 3 gaining 6 units of energy for a total of 7 energy.
Note tha the sample case above is different from test case 1 when you submit.