Dream Team

AtCoder

IDabc247_g

Time2000ms

Memory256MB

Difficulty—

There are $N$ competitive programmers. The $i$\-th competitive programmer belongs to University $A_i$, is good at Subject $B_i$, and has a power of $C_i$. Consider a team consisting of some of the $N$ people. Let us call such a team a **dream team** if both of the following conditions are satisfied: * Any two people belonging to the team belong to different universities. * Any two people belonging to the team are good at different subjects. Let $k$ be the maximum possible number of members of a dream team. For each $i=1,2,\ldots,k$, solve the following question. Question: find the maximum sum of power of people belonging to a dream team consisting of $i$ people. ## Constraints * $1 \leq N \leq 3\times 10^4$ * $1 \leq A_i,B_i \leq 150$ * $1 \leq C_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $B_1$ $C_1$ $A_2$ $B_2$ $C_2$ $\vdots$ $A_N$ $B_N$ $C_N$ [samples]

Samples

Input #1

Output #1

2
100
11

*   The sum of power of members of a dream team consisting of exactly $1$ person is $100$, when the team consists of the $1$\-st competitive programmer.
*   The sum of power of members of a dream team consisting of exactly $2$ people is $11$, when the team consists of the $2$\-nd and the $3$\-rd competitive programmers.
*   It is impossible to form a dream team consisting of exactly $3$ people.

Input #2

10
1 4 142135623
2 6 457513110
3 1 622776601
5 1 961524227
2 2 360679774
2 4 494897427
3 7 416573867
5 2 915026221
1 7 320508075
5 3 851648071

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Dream Team",
    "description": {
      "content": "There are $N$ competitive programmers.   The $i$\\-th competitive programmer belongs to University $A_i$, is good at Subject $B_i$, and has a power of $C_i$. Consider a team consisting of some of the $",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc247_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ competitive programmers.  \nThe $i$\\-th competitive programmer belongs to University $A_i$, is good at Subject $B_i$, and has a power of $C_i$.\nConsider a team consisting of some of the $...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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