AtCoder Magics

AtCoder

IDabc354_c

Time2000ms

Memory256MB

Difficulty—

Takahashi has $N$ cards from the card game "AtCoder Magics." The $i$\-th card will be called card $i$. Each card has two parameters: strength and cost. Card $i$ has a strength of $A_i$ and a cost of $C_i$. He does not like weak cards, so he will discard them. Specifically, he will repeat the following operation until it can no longer be performed: * Choose two cards $x$ and $y$ such that $A_x > A_y$ and $C_x < C_y$. Discard card $y$. It can be proved that the set of remaining cards when the operations can no longer be performed is uniquely determined. Find this set of cards. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $1 \leq A_i, C_i \leq 10^9$ * $A_1, A_2, \dots ,A_N$ are all distinct. * $C_1, C_2, \dots ,C_N$ are all distinct. * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $C_1$ $A_2$ $C_2$ $\vdots$ $A_N$ $C_N$ [samples]

Samples

Input #1

Output #1

2
2 3

Focusing on cards $1$ and $3$, we have $A_1 < A_3$ and $C_1 > C_3$, so card $1$ can be discarded.
No further operations can be performed. At this point, cards $2$ and $3$ remain, so print them.

Input #2

Output #2

5
1 2 3 4 5

In this case, no cards can be discarded.

Input #3

Output #3

4
2 3 5 6

API Response (JSON)

{
  "problem": {
    "name": "AtCoder Magics",
    "description": {
      "content": "Takahashi has $N$ cards from the card game \"AtCoder Magics.\" The $i$\\-th card will be called card $i$. Each card has two parameters: strength and cost. Card $i$ has a strength of $A_i$ and a cost of $",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc354_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi has $N$ cards from the card game \"AtCoder Magics.\" The $i$\\-th card will be called card $i$. Each card has two parameters: strength and cost. Card $i$ has a strength of $A_i$ and a cost of $...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments