P8253 [NOI Online 2022 Senior] How to Sort Correctly

**After consideration by the administrators, we plan to store the community-provided testdata separately in the last Subtask. The score of these test points is 0, but failing any of them will be regarded as not passing this problem.** **In this problem, there is an issue where the test point numbers in the judging records are mixed up. This is caused by a naming conflict in the community testdata. However, we guarantee that their relative order is not messed up.** Community testdata provider: @QwQcOrZ。

There is an $m \times n$ array $a_{i,j}$. Define: $$f(i,j)=\min\limits_{k=1}^m(a_{k,i}+a_{k,j})+\max\limits_{k=1}^m(a_{k,i}+a_{k,j})$$ You need to compute $\sum\limits_{i=1}^n\sum\limits_{j=1}^nf(i,j)$。

The first line contains two positive integers $m, n$。 In the next $m$ lines, each line contains $n$ positive integers representing $a_{i,j}$。

Output one positive integer in one line, representing the answer。

**[Sample 1 Explanation]** Take $f(3,5)$ as an example: $$\begin{aligned}f(3,5)&=\max(a_{1,3}+a_{1,5},a_{2,3}+a_{2,5},a_{3,3}+a_{3,5})+\min(a_{1,3}+a_{1,5},a_{2,3}+a_{2,5},a_{3,3}+a_{3,5})\\&=\max(9,7,10)+\min(9,7,10)\\&=10+7\\&=17\end{aligned}$$ The table of $f(i,j)$ is given below. The entry in row $i$ and column $j$ represents $f(i,j)$: $$\begin{array}{|c|c|c|c|c|}\hline20&27&18&22&20\\\hline27&34&24&29&23\\\hline18&24&20&22&17\\\hline22&29&22&24&22\\\hline20&23&17&22&18\\\hline\end{array}$$ Their sum is the answer $564$。 **[Samples 2, 3, 4]** See `sort/sort*.in` and `sort/sort*.ans` in the contestant directory。 **[Constraints and Hints]** For all test points: $2\le m\le 4$，$1\le n\le 2\times {10}^5$，$1\le a_{i,j}\le 2\times 10^5$。 The specific limits for each test point are shown in the table below。 ::cute-table{tuack} | Test Point ID | $m =$ | $n \le$ | | :-: | :-: | :-: | | $1$ | $4$ | $3000$ | | $2$ | $2$ | $10^5$ | | $3 \sim 5$ | $3$ | ^ | | $6 \sim 7$ | $4$ | $5 \times 10^4$ | | $8 \sim 9$ | ^ | $10^5$ | | $10$ | ^ | $2 \times 10^5$ | Translated by ChatGPT 5