Second Largest Query

AtCoder

IDabc343_f

Time2000ms

Memory256MB

Difficulty—

You are given a sequence $A = (A_1, A_2, \ldots, A_N)$ of length $N$. Process $Q$ queries in the order they are given. Each query is of one of the following two types: * Type $1$: Given in the form `1 p x`. Change the value of $A_p$ to $x$. * Type $2$: Given in the form `2 l r`. print the **number of occurrences** of the second largest value in $(A_l, A_{l+1}, \ldots, A_r)$. More precisely, print the number of integers $i$ satisfying $l \leq i \leq r$ such that there is exactly one distinct value greater than $A_i$ among $A_l, A_{l+1}, \ldots, A_r$. ## Constraints * $1 \leq N, Q \leq 2 \times 10^5$ * $1 \leq A_i \leq 10^9$ * For type-$1$ queries, $1 \leq p \leq N$. * For type-$1$ queries, $1 \leq x \leq 10^9$. * For type-$2$ queries, $1 \leq l \leq r \leq N$. * There is at least one type-$2$ query. * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $Q$ $A_1$ $A_2$ $\ldots$ $A_N$ $\text{query}_{1}$ $\vdots$ $\text{query}_{Q}$ Here, $\text{query}_{i}$ is the $i$\-th query and given in one of the following formats: $1$ $p$ $x$ $2$ $l$ $r$ [samples]

Samples

Input #1

Output #1

1
0
2

Initially, $A = (3, 3, 1, 4, 5)$.
For the first query, the second largest value in $(3, 3, 1)$ is $1$, which appears once in $3, 3, 1$, so print $1$.
For the second query, there is no second largest value in $(5)$, so print $0$.
The third query makes $A = (3, 3, 3, 4, 5)$.
For the fourth query, the second largest value in $(3, 3, 4)$, is $3$, which appears twice in $3, 3, 4$, so print $2$.

Input #2

1 1
1000000000
2 1 1

Output #2

Input #3

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

Output #3

API Response (JSON)

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      "content": "You are given a sequence $A = (A_1, A_2, \\ldots, A_N)$ of length $N$. Process $Q$ queries in the order they are given. Each query is of one of the following two types: *   Type $1$: Given in the form",
      "description_type": "Markdown"
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    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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    "difficulty": "None",
    "is_remote": true,
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      "statement_type": "Markdown",
      "content": "You are given a sequence $A = (A_1, A_2, \\ldots, A_N)$ of length $N$.\nProcess $Q$ queries in the order they are given. Each query is of one of the following two types:\n\n*   Type $1$: Given in the form...",
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