Flowers

AtCoder

IDdp_q

Time2000ms

Memory256MB

Difficulty—

There are $N$ flowers arranged in a row. For each $i$ ($1 \leq i \leq N$), the height and the beauty of the $i$\-th flower from the left is $h_i$ and $a_i$, respectively. Here, $h_1, h_2, \ldots, h_N$ are all distinct. Taro is pulling out some flowers so that the following condition is met: * The heights of the remaining flowers are monotonically increasing from left to right. Find the maximum possible sum of the beauties of the remaining flowers. ## Constraints * All values in input are integers. * $1 \leq N \leq 2 × 10^5$ * $1 \leq h_i \leq N$ * $h_1, h_2, \ldots, h_N$ are all distinct. * $1 \leq a_i \leq 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $h_1$ $h_2$ $\ldots$ $h_N$ $a_1$ $a_2$ $\ldots$ $a_N$ [samples]

Samples

Input #1

4
3 1 4 2
10 20 30 40

Output #1

60

We should keep the second and fourth flowers from the left. Then, the heights would be $1, 2$ from left to right, which is monotonically increasing, and the sum of the beauties would be $20 + 40 = 60$.

Input #2

1
1
10

Output #2

10

The condition is met already at the beginning.

Input #3

5
1 2 3 4 5
1000000000 1000000000 1000000000 1000000000 1000000000

Output #3

5000000000

The answer may not fit into a 32-bit integer type.

Input #4

9
4 2 5 8 3 6 1 7 9
6 8 8 4 6 3 5 7 5

Output #4

31

We should keep the second, third, sixth, eighth and ninth flowers from the left.

API Response (JSON)

{
  "problem": {
    "name": "Flowers",
    "description": {
      "content": "There are $N$ flowers arranged in a row. For each $i$ ($1 \\leq i \\leq N$), the height and the beauty of the $i$\\-th flower from the left is $h_i$ and $a_i$, respectively. Here, $h_1, h_2, \\ldots, h_N$",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "dp_q"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ flowers arranged in a row. For each $i$ ($1 \\leq i \\leq N$), the height and the beauty of the $i$\\-th flower from the left is $h_i$ and $a_i$, respectively. Here, $h_1, h_2, \\ldots, h_N$...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments