Tower

AtCoder

IDdp_x

Time2000ms

Memory256MB

Difficulty—

There are $N$ blocks, numbered $1, 2, \ldots, N$. For each $i$ ($1 \leq i \leq N$), Block $i$ has a weight of $w_i$, a solidness of $s_i$ and a value of $v_i$. Taro has decided to build a tower by choosing some of the $N$ blocks and stacking them vertically in some order. Here, the tower must satisfy the following condition: * For each Block $i$ contained in the tower, the sum of the weights of the blocks stacked above it is not greater than $s_i$. Find the maximum possible sum of the values of the blocks contained in the tower. ## Constraints * All values in input are integers. * $1 \leq N \leq 10^3$ * $1 \leq w_i, s_i \leq 10^4$ * $1 \leq v_i \leq 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $w_1$ $s_1$ $v_1$ $w_2$ $s_2$ $v_2$ $:$ $w_N$ $s_N$ $v_N$ [samples]

Samples

Input #1

Output #1

50

If Blocks $2, 1$ are stacked in this order from top to bottom, this tower will satisfy the condition, with the total value of $30 + 20 = 50$.

Input #2

Output #2

40

Blocks $1, 2, 3, 4$ should be stacked in this order from top to bottom.

Input #3

5
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000
1 10000 1000000000

Output #3

5000000000

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

Input #4

Output #4

22

We should, for example, stack Blocks $5, 6, 8, 4$ in this order from top to bottom.

API Response (JSON)

{
  "problem": {
    "name": "Tower",
    "description": {
      "content": "There are $N$ blocks, numbered $1, 2, \\ldots, N$. For each $i$ ($1 \\leq i \\leq N$), Block $i$ has a weight of $w_i$, a solidness of $s_i$ and a value of $v_i$. Taro has decided to build a tower by cho",
      "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_x"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ blocks, numbered $1, 2, \\ldots, N$. For each $i$ ($1 \\leq i \\leq N$), Block $i$ has a weight of $w_i$, a solidness of $s_i$ and a value of $v_i$.\nTaro has decided to build a tower by cho...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments