P8288 「DAOI R1」Fireworks

> Bow your head, and the whole city shines with lights. > > Look back, and meteors fly backward across the sky.

People used to set off fireworks, and each firework has its own beauty value. $\texttt{Iratis}$ wants to set off fireworks outdoors, but there are some relationships between fireworks: - Relationship 1: For a firework $x$, there is a corresponding firework $a_x$. If firework $x$ and firework $a_x$ are set off together, the beauty value of firework $x$ will decrease by $b_x$. - Relationship 2: Some fireworks belong to a series and must be set off at the same time. One of them is the main firework. **Each firework belongs to at most one series.** In particular, suppose there is a series $S_1$ (with main firework $p_1$). The firework corresponding to $p_1$ in Relationship 1 is a firework in series $S_2$. Meanwhile, the other fireworks in series $S_1$ form Relationship 1 with fireworks not in series $S_1$ or $S_2$. **Then for such a Relationship 1, it will not reduce the beauty value.** $\texttt{Iratis}$ has $n$ fireworks at home. He wants to choose some of them to set off, so that the **sum of the beauty values** of these fireworks is maximized.

The first line contains two integers $n,m$, which denote the number of fireworks and the number of Relationship 2 groups. The next $n$ lines each contain three integers $v_i,a_i,b_i$, which are the beauty value of this firework, the corresponding firework in Relationship 1, and the amount of beauty value reduced by Relationship 1. The last $m$ lines: each line first reads two numbers $p_i,k_i$, followed by $k_i$ numbers, meaning these $k_i$ fireworks form a series, and the firework with index $p_i$ is the main firework.

Output one line with one integer, representing the total sum of beauty values.

### Sample Explanation #### Sample 1 Explanation Set off fireworks $1,2,3$ together. The maximum beauty value is $2+2+2-1-1-1=3$. #### Sample 2 Explanation Set off fireworks $1,3,4$ together. Since $1,3$ are in the same series and $1$ is the main firework, Relationship 1 of firework $3$ does not take effect. So the total beauty value is $3 \times 3-2=7$. ### Constraints **This problem uses bundled testdata.** | Subtask | $m$ | Score | | :----------: | :----------: | :----------: | | $0$ | $=0$ | $30$ | | $1$ | No special restrictions | $70$ | For $100\%$ of the data, it holds that $0 \leq m \leq n \leq 5 \times 10^5$, $0 \leq b_i \leq v_i \leq 10^{12}$, $1 \leq a_i \leq n$, $a_i \neq i$. Translated by ChatGPT 5