Snuke Panic (1D)

AtCoder

IDabc266_d

Time2000ms

Memory256MB

Difficulty—

Takahashi is trying to catch many Snuke. There are five pits at coordinates $0$, $1$, $2$, $3$, and $4$ on a number line, connected to Snuke's nest. Now, $N$ Snuke will appear from the pits. It is known that the $i$\-th Snuke will appear from the pit at coordinate $X_i$ at time $T_i$, and its size is $A_i$. Takahashi is at coordinate $0$ at time $0$ and can move on the line at a speed of at most $1$. He can catch a Snuke appearing from a pit if and only if he is at the coordinate of that pit exactly when it appears. The time it takes to catch a Snuke is negligible. Find the maximum sum of the sizes of Snuke that Takahashi can catch by moving optimally. ## Constraints * $1 \leq N \leq 10^5$ * $0 < T_1 < T_2 < \ldots < T_N \leq 10^5$ * $0 \leq X_i \leq 4$ * $1 \leq A_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $T_1$ $X_1$ $A_1$ $T_2$ $X_2$ $A_2$ $\vdots$ $T_N$ $X_N$ $A_N$ [samples]

Samples

Input #1

Output #1

101

The optimal strategy is as follows.

*   Wait at coordinate $0$ to catch the first Snuke at time $1$.
*   Go to coordinate $4$ to catch the third Snuke at time $5$.

It is impossible to catch both the first and second Snuke, so this is the best he can.

Input #2

Output #2

0

Takahashi cannot catch any Snuke.

Input #3

10
1 4 602436426
2 1 623690081
3 3 262703497
4 4 628894325
5 3 450968417
6 1 161735902
7 1 707723857
8 2 802329211
9 0 317063340
10 2 125660016

Output #3

2978279323

API Response (JSON)

{
  "problem": {
    "name": "Snuke Panic (1D)",
    "description": {
      "content": "Takahashi is trying to catch many Snuke. There are five pits at coordinates $0$, $1$, $2$, $3$, and $4$ on a number line, connected to Snuke's nest. Now, $N$ Snuke will appear from the pits. It is kno",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc266_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi is trying to catch many Snuke.\nThere are five pits at coordinates $0$, $1$, $2$, $3$, and $4$ on a number line, connected to Snuke's nest.\nNow, $N$ Snuke will appear from the pits. It is kno...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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