P9491 ZHY's Sets

## 赛后时限改为 1s。 ZHY 又一次在赛时看错题了。 [](T341514)

The time limit was changed to 1 s after the contest. ZHY once again misread the problem during the contest. [](T341514) For two sets $A,B$ each of size $x$, satisfying $A\cap B=\varnothing$ (the empty set), ZHY defines $f(A,B)$ as follows: - Let $C=A\cup B$. Sort the elements in $C$ in increasing order. - $f(A,B)=\displaystyle \sum_{i=1}^x C_i$. Now, ZHY has $n$ sets $S_1,S_2,\cdots,S_n$, each of size $m$. He wants to know the value of $\displaystyle \sum_{i=1}^n\sum_{j=i + 1}^n f(S_i,S_j)$. However, ZHY is not satisfied with this. So he performs $q$ modification operations. In each operation, one set is given again. After each modification, output the answer once, i.e., $\displaystyle \sum_{i=1}^n\sum_{j=i + 1}^n f(S_i,S_j)$. It is guaranteed that at any time, all elements within any set are pairwise distinct, and the intersection of any two sets is empty.

The first line contains three integers $n,m,q$. Lines $2$ to $n+1$ each contain $m$ integers describing the sets $S_1,S_2,\cdots,S_n$. The $m$ numbers on line $i+1$ are the $m$ integers in set $S_i$. Then follow $q$ lines. In each line, the first integer is $x$, indicating the index of the set to be modified. The following $m$ numbers are the $m$ integers in the new $S_x$.

The first line contains one integer, the initial answer. Then output $q$ lines, each containing one integer, the answer after each modification.

**This problem uses bundled testdata.** | $\mathrm{Subtask} \kern{2pt} \mathrm{id}$ | $n$ | $m$ | $q$ | Score | | :-----: | :-----: | :-----: | :-----: | :-----: | | $0$ | $\le 100$ | $\le 10$ | $\le 10$ | $7$ | | $1$ | $\le 100$ | $\le 100$ | $\le 100$ | $11$ | | $2$ | $\le 10^3$ | $\le 100$ | $\le 10^3$ | $7$ | | $3$ | $\le 10^4$ | $\le 100$ | $=0$ | $15$ | | $4$ | $\le 10^4$ | $\le 100$ | $\le 10^3$ | $27$ | | $5$ | $\le 10^4$ | $\le 100$ | $\le 10^4$ | $33$ | For all data, $0 \le n, q \le 10^4$, $1 \le m \le 100$, $1 \le S_{i,j} \le 10^9$. It is guaranteed that at any time, for $\forall i\in [1,n],\kern{2pt}j \in [1,m],\kern{2pt}i' \in[1,n],\kern{2pt}j'\in [1,m]$, if $i \ne i'$ or $j \ne j'$, then $S_{i,j} \ne S_{i',j'}。$ Translated by ChatGPT 5