Pyramid Alignment

AtCoder

IDabc428_f

Time2000ms

Memory256MB

Difficulty—

There are $N$ intervals on a number line, numbered from $1$ to $N$. The left endpoint of interval $i$ is at coordinate $0$, and the right endpoint is at coordinate $W_i$. Here, $W_1 < W_2 < \dots < W_N$. You are given $Q$ queries; process them in the order they are given. Each query is one of the following three types: * Type $1$ (`1 v`): Let $l$ be the coordinate of the current **left endpoint** of interval $v$. Translate each of the intervals numbered $v$ or less so that its **left endpoint** is at coordinate $l$. * Type $2$ (`2 v`): Let $r$ be the coordinate of the current **right endpoint** of interval $v$. Translate each of the intervals numbered $v$ or less so that its **right endpoint** is at coordinate $r$. * Type $3$ (`3 x`): Output the current number of intervals that contain coordinate $x+\frac{1}{2}$. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $1 \leq Q \leq 2 \times 10^5$ * $1 \leq W_i \leq 10^9$ ($1 \leq i \leq N$) * $W_1 < W_2 < \dots < W_N$ * For $v$ given in queries of types $1$ and $2$, $1 \leq v \leq N$. * For $x$ given in queries of type $3$, $0 \leq x \leq 10^9$. * At least one query of type $3$ is given. * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $W_1$ $\dots$ $W_N$ $Q$ $\textrm{query}_1$ $\textrm{query}_2$ $\vdots$ $\textrm{query}_Q$ $\textrm{query}_j$ represents the $j$\-th query. Each query is given in one of the following formats: $1$ $v$ $2$ $v$ $3$ $x$ [samples]

Samples

Input #1

Output #1

4
1

Initially, the intervals in order of their numbers are $[0, 2], [0, 4], [0, 6], [0, 10]$.

*   For the $1$st query, the coordinate of the **right endpoint** of interval $3$ before the operation is $6$, so the intervals after the operation are $[4, 6], [2, 6], [0, 6], [0, 10]$ in order of their numbers.
*   For the $2$nd query, the coordinate of the **left endpoint** of interval $2$ before the operation is $2$, so the intervals after the operation are $[2, 4], [2, 6], [0, 6], [0, 10]$ in order of their numbers.
*   For the $3$rd query, the intervals that contain coordinate $2 + \frac{1}{2}$ are intervals $1,2,3,4$, which is four intervals, so output $4$.
*   For the $4$th query, the coordinate of the **right endpoint** of interval $4$ before the operation is $10$, so the intervals after the operation are $[8, 10], [6, 10], [4, 10], [0, 10]$ in order of their numbers.
*   For the $5$th query, the intervals that contain coordinate $1 + \frac{1}{2}$ is only interval $4$, which is one interval, so output $1$.

API Response (JSON)

{
  "problem": {
    "name": "Pyramid Alignment",
    "description": {
      "content": "There are $N$ intervals on a number line, numbered from $1$ to $N$. The left endpoint of interval $i$ is at coordinate $0$, and the right endpoint is at coordinate $W_i$. Here, $W_1 < W_2 < \\dots < W_",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc428_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ intervals on a number line, numbered from $1$ to $N$.\nThe left endpoint of interval $i$ is at coordinate $0$, and the right endpoint is at coordinate $W_i$. Here, $W_1 < W_2 < \\dots < W_...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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