Max (Sum - Max)

AtCoder

IDabc348_g

Time2000ms

Memory256MB

Difficulty—

You are given two integer sequences $A$ and $B$ of length $N$. For $k = 1, 2, \ldots, N$, solve the following problem: * Consider choosing $k$ distinct integers between $1$ and $N$, inclusive. Let $S$ be the set of chosen integers. Find the maximum value of $\displaystyle (\sum_{i \in S} A_i) - \max_{i \in S} B_i$. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $-10^9 \leq A_i \leq 10^9$ * $-2 \times 10^{14} \leq B_i \leq 2 \times 10^{14}$ ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $B_1$ $A_2$ $B_2$ $\vdots$ $A_N$ $B_N$ [samples]

Samples

Input #1

Output #1

3
5
6

The following choices are optimal.

*   $k = 1$: $S = {1}$
*   $k = 2$: $S = {1, 3}$
*   $k = 3$: $S = {1, 2, 3}$

Input #2

2
0 1
0 1

Output #2

\-1
-1

Input #3

Output #3

API Response (JSON)

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  "problem": {
    "name": "Max (Sum - Max)",
    "description": {
      "content": "You are given two integer sequences $A$ and $B$ of length $N$. For $k = 1, 2, \\ldots, N$, solve the following problem: *   Consider choosing $k$ distinct integers between $1$ and $N$, inclusive. Let ",
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    "platform": "AtCoder",
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      "memory_limit": 262144
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    "difficulty": "None",
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    "sync_url": null,
    "sign": "abc348_g"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given two integer sequences $A$ and $B$ of length $N$. For $k = 1, 2, \\ldots, N$, solve the following problem:\n\n*   Consider choosing $k$ distinct integers between $1$ and $N$, inclusive. Let ...",
      "is_translate": false,
      "language": "English"
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Full JSON Raw Segments