Reachable Towns

AtCoder

IDacl1_a

Time2000ms

Memory256MB

Difficulty—

There are $N$ cities on a 2D plane. The coordinate of the $i$\-th city is $(x_i, y_i)$. Here $(x_1, x_2, \dots, x_N)$ and $(y_1, y_2, \dots, y_N)$ are both permuations of $(1, 2, \dots, N)$. For each $k = 1,2,\dots,N$, find the answer to the following question: Rng is in City $k$. Rng can perform the following move arbitrarily many times: * move to another city that has a smaller $x$\-coordinate and a smaller $y$\-coordinate, or a larger $x$\-coordinate and a larger $y$\-coordinate, than the city he is currently in. How many cities (including City $k$) are reachable from City $k$? ## Constraints * $1 \leq N \leq 200,000$ * $(x_1, x_2, \dots, x_N)$ is a permutation of $(1, 2, \dots, N)$. * $(y_1, y_2, \dots, y_N)$ is a permutation of $(1, 2, \dots, N)$. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $x_1$ $y_1$ $x_2$ $y_2$ $:$ $x_N$ $y_N$ [samples]

Samples

Input #1

Output #1

1
1
2
2

Rng can reach City $4$ from City $3$, or conversely City $3$ from City $4$.

Input #2

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Reachable Towns",
    "description": {
      "content": "There are $N$ cities on a 2D plane. The coordinate of the $i$\\-th city is $(x_i, y_i)$. Here $(x_1, x_2, \\dots, x_N)$ and $(y_1, y_2, \\dots, y_N)$ are both permuations of $(1, 2, \\dots, N)$. For each ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "acl1_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ cities on a 2D plane. The coordinate of the $i$\\-th city is $(x_i, y_i)$. Here $(x_1, x_2, \\dots, x_N)$ and $(y_1, y_2, \\dots, y_N)$ are both permuations of $(1, 2, \\dots, N)$.\nFor each ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments