An element in an array is called a peak if it is strictly greater than its adjacent left and right neighbors.

You are given an integer array nums and a 2D integer array queries.

Process each query in queries, which can be one of the following two types:

• $[1, l_i, r_i]$: Count the number of peak elements in the subarray nums[l_i..r_i].

• $[2, index_i, val_i]$: Update the value of nums[index_i] to val_i.

Return an array containing the results of all type 1 queries in the order they are processed.

Note: The first and last elements of any subarray are not considered peaks.

Constraints:

• $3 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^5$

• $1 \leq$ queries.length $\leq 10^5$

• queries[i][0] $= 1$ or queries[i][0] $= 2$

• For all i such that queries[i][0] $= 1$: $0 \leq$ queries[i][1] $\leq$ queries[i][2] $\leq$ nums.length $- 1$

• For all i such that queries[i][0] $= 2$: $0 \leq$ queries[i][1] $\leq$ nums.length $- 1$, $1 \leq$ queries[i][2] $\leq 10^5$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

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