Generate Arrays

AtCoder

IDabc324_g

Time6000ms

Memory256MB

Difficulty—

Takahashi has a sequence of length $N$: $A=(A _ 1,A _ 2,\ldots,A _ N)$. $A$ is a permutation of $(1,2,\ldots,N)$. He is going to perform $Q$ operations to create $1+Q$ sequences. **He lets $A$ be the sequence numbered $0$**, and then begins the series of operations. The $i$\-th operation $(1\leq i\leq Q)$ is represented by a triple of integers $(t _ i,s _ i,x _ i)$ and corresponds to the following operation (see also the explanations in Sample Input/Output). * When $t _ i=1$, he removes the elements following the $x _ i$\-th element from the sequence numbered $s _ i$ $(0\leq s _ i\lt i)$, and creates a new sequence numbered $i$ with the removed elements, keeping their order. * When $t _ i=2$, he removes the elements greater than $x _ i$ from the sequence numbered $s _ i$ $(0\leq s _ i\lt i)$, and creates a new sequence numbered $i$ with the removed elements, keeping their order. For a sequence $X$ of length $L$, every element of $X$ is among "the elements following the $0$\-th element." Also, for any $l$ such that $L\leq l$, no element of $X$ is among "the elements following the $l$\-th element." For $i=1,2,\ldots,Q$, find the length of the sequence numbered $i$ **immediately after** the $i$\-th operation. ## Constraints * $1\leq N\leq2\times10^5$ * $1\leq A _ i\leq N\ (1\leq i\leq N)$ * $A _ i\neq A _ j\ (1\leq i\lt j\leq N)$ * $1\leq Q\leq2\times10^5$ * $t _ i=1,2\ (1\leq i\leq Q)$ * $0\leq s _ i\lt i\ (1\leq i\leq Q)$ * $0\leq x _ i\leq N\ (1\leq i\leq Q)$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $A _ 1$ $A _ 2$ $\ldots$ $A _ N$ $Q$ $t _ 1$ $s _ 1$ $x _ 1$ $t _ 2$ $s _ 2$ $x _ 2$ $\vdots$ $t _ Q$ $s _ Q$ $x _ Q$ [samples]

Samples

Input #1

10
1 8 7 4 5 6 3 2 9 10
5
2 0 4
1 1 2
2 0 2
2 2 5
1 0 1

Output #1

6
4
2
3
1

Initially, Takahashi has a sequence $A=(1,8,7,4,5,6,3,2,9,10)$ of length $10$. He lets $A=(1,8,7,4,5,6,3,2,9,10)$ be the sequence numbered $0$, and then begins the series of operations.
In the first operation, he removes elements greater than $4$ from the sequence numbered $0$, namely $8,7,5,6,9,10$, and creates a new sequence numbered $1$ with these elements. After this operation, the sequences numbered $0$ and $1$ are $(1,4,3,2)$ and $(8,7,5,6,9,10)$, respectively.
In the second operation, he removes the elements following the $2$\-nd element from the sequence numbered $1$, namely $5,6,9,10$, and creates a new sequence numbered $2$ with these elements. After this operation, the sequences numbered $0$, $1$, and $2$ are $(1,4,3,2)$, $(8,7)$, and $(5,6,9,10)$, respectively.
For the third and subsequent operations, the sequences numbered $0,1,2,\ldots,i$ after the $i$\-th operation are as follows:

*   $(1,2),(8,7),(5,6,9,10),(4,3)$
*   $(1,2),(8,7),(5),(4,3),(6,9,10)$
*   $(1),(8,7),(5),(4,3),(6,9,10),(2)$

The length of the sequence numbered $i$ after the $i$\-th operation for $i=1,2,\ldots,5$ is $6,4,2,3,1$. Print each of these in its own line.

Input #2

8
6 7 8 4 5 1 3 2
5
2 0 0
1 1 0
2 2 0
1 3 8
2 2 3

Output #2

8
8
8
0
0

The operations may create empty sequences.

Input #3

30
20 6 13 11 29 30 9 10 16 5 8 25 1 19 12 18 7 2 4 27 3 22 23 24 28 21 14 26 15 17
10
1 0 22
1 0 21
2 0 15
1 0 9
1 3 6
2 3 18
1 6 2
1 0 1
2 5 20
2 7 26

Output #3

API Response (JSON)

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      "content": "Takahashi has a sequence of length $N$: $A=(A _ 1,A _ 2,\\ldots,A _ N)$. $A$ is a permutation of $(1,2,\\ldots,N)$. He is going to perform $Q$ operations to create $1+Q$ sequences. **He lets $A$ be the ",
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      "memory_limit": 262144
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    "difficulty": "None",
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      "statement_type": "Markdown",
      "content": "Takahashi has a sequence of length $N$: $A=(A _ 1,A _ 2,\\ldots,A _ N)$. $A$ is a permutation of $(1,2,\\ldots,N)$.\nHe is going to perform $Q$ operations to create $1+Q$ sequences. **He lets $A$ be the ...",
      "is_translate": false,
      "language": "English"
    }
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