Open-Pit Mining

Open-pit mining takes rock or minerals out of the ground through a pit dug at the surface. Miners use it when a commercially useful deposit sits near the surface. The mining company ACM wants the largest profit it can get this way, and it has asked you for a program that reads a description of a piece of land and reports that profit.

One piece of land is modelled as a set of blocks of material. Block $i$ has a value $v_i$, and digging it out of the land costs $c_i$. Some blocks bury other blocks. If block $j$ and block $k$ obstruct block $i$, then block $j$ and block $k$ must both be dug up before block $i$ can be dug up. A block can be dug up only once no block obstructs it.

The profit of a set of dug blocks is the sum of their values minus the sum of their costs. ACM may stop digging at any point, and digging no block at all gives a profit of 0.

The first line contains an integer $N$ ($1 \le N \le 200$), the number of blocks. The blocks are numbered 1 through $N$.

The next $N$ lines describe the blocks. The $i$-th of those lines describes block $i$ and starts with the value $v_i$ and the cost $c_i$ of block $i$ ($0 \le v_i, c_i \le 200$). A third integer $m_i$ then gives the number of blocks that block $i$ obstructs ($0 \le m_i \le N - 1$). After it come the labels of those blocks, $m_i$ integers separated by spaces. The labels are distinct, lie between 1 and $N$, and never include $i$.

Some digging order gets every block out. The sum of $m_i$ over all blocks $i$ is at most 500.

Print a single integer, the maximum profit ACM can achieve from the given piece of land.