<p>A <strong>peak</strong> in an array <code>arr</code> is an element that is <strong>greater</strong> than its previous and next element in <code>arr</code>.</p>

<p>You are given an integer array <code>nums</code> and a 2D integer array <code>queries</code>.</p>

<p>You have to process queries of two types:</p>

<ul>
	<li><code>queries[i] = [1, l<sub>i</sub>, r<sub>i</sub>]</code>, determine the count of <strong>peak</strong> elements in the <span data-keyword="subarray">subarray</span> <code>nums[l<sub>i</sub>..r<sub>i</sub>]</code>.<!-- notionvc: 73b20b7c-e1ab-4dac-86d0-13761094a9ae --></li>
	<li><code>queries[i] = [2, index<sub>i</sub>, val<sub>i</sub>]</code>, change <code>nums[index<sub>i</sub>]</code> to <code><font face="monospace">val<sub>i</sub></font></code>.</li>
</ul>

<p>Return an array <code>answer</code> containing the results of the queries of the first type in order.<!-- notionvc: a9ccef22-4061-4b5a-b4cc-a2b2a0e12f30 --></p>

<p><strong>Notes:</strong></p>

<ul>
	<li>The <strong>first</strong> and the <strong>last</strong> element of an array or a subarray<!-- notionvc: fcffef72-deb5-47cb-8719-3a3790102f73 --> <strong>cannot</strong> be a peak.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [3,1,4,2,5], queries = [[2,3,4],[1,0,4]]</span></p>

<p><strong>Output:</strong> <span class="example-io">[0]</span></p>

<p><strong>Explanation:</strong></p>

<p>First query: We change <code>nums[3]</code> to 4 and <code>nums</code> becomes <code>[3,1,4,4,5]</code>.</p>

<p>Second query: The number of peaks in the <code>[3,1,4,4,5]</code> is 0.</p>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [4,1,4,2,1,5], queries = [[2,2,4],[1,0,2],[1,0,4]]</span></p>

<p><strong>Output:</strong> <span class="example-io">[0,1]</span></p>

<p><strong>Explanation:</strong></p>

<p>First query: <code>nums[2]</code> should become 4, but it is already set to 4.</p>

<p>Second query: The number of peaks in the <code>[4,1,4]</code> is 0.</p>

<p>Third query: The second 4 is a peak in the <code>[4,1,4,2,1]</code>.</p>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>3 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= queries.length &lt;= 10<sup>5</sup></code></li>
	<li><code>queries[i][0] == 1</code> or <code>queries[i][0] == 2</code></li>
	<li>For all <code>i</code> that:
	<ul>
		<li><code>queries[i][0] == 1</code>: <code>0 &lt;= queries[i][1] &lt;= queries[i][2] &lt;= nums.length - 1</code></li>
		<li><code>queries[i][0] == 2</code>: <code>0 &lt;= queries[i][1] &lt;= nums.length - 1</code>, <code>1 &lt;= queries[i][2] &lt;= 10<sup>5</sup></code></li>
	</ul>
	</li>
</ul>

class SegmentTree:

    def __init__(self, arr, n):
        self.n = n
        self.segmentTree = self.build(arr)


    def merge(self, One, Two):
        return One + Two

    def build(self, arr):
        segmentTree, _merge, n = {}, self.merge, self.n

        def rec(index, l, r):
            if l == r:
                segmentTree[index] = arr[l]
                return
            
            mid = l + (r-l)//2
            rec(2*index, l, mid)
            rec(2*index+1, mid+1, r)

            segmentTree[index] = _merge(segmentTree[2*index], segmentTree[2*index+1])
        rec(1, 1, n)

        return segmentTree


    def query(self, lq, rq):
        segmentTree, _merge = self.segmentTree, self.merge
        print(lq, rq)
        def rec(index, l, r, lq, rq):
            if rq < l or r < lq:
                return 0
            
            if lq<=l and r<=rq:
                return segmentTree[index]

            mid = l + (r-l)//2
            
            return _merge(
                rec(2*index, l, mid, lq, rq), rec(2*index+1, mid+1, r, lq, rq)
            )
        
        return rec(1, 1, self.n, lq, rq)
        
    
    def update(self, updateIndex, updateVal):
        segmentTree, _merge = self.segmentTree, self.merge

        def rec(index, l, r):
            if updateIndex < l or r < updateIndex:
                return 
            
            if l == r:
                segmentTree[index] = updateVal
                return

            mid = l + (r-l)//2
            rec(2*index, l, mid)
            rec(2*index+1, mid+1, r)

            segmentTree[index] = _merge(segmentTree[2*index], segmentTree[2*index+1])
        rec(1, 1, self.n)


class Solution:
    def countOfPeaks(self, nums: List[int], queries: List[List[int]]) -> List[int]:
        
        n = len(nums)

        peaksArray = {}
        for i in range(1, n-1):
            a, b, c = nums[i-1], nums[i], nums[i+1]
            if a < b > c:
                peaksArray[i] = 1
            else:
                peaksArray[i] = 0

        tree = SegmentTree(peaksArray, n-2)

        res = []
        for _type, u, v in queries:

            if _type == 1:
                res.append(tree.query(u+1, v-1))
            else:
                nums[u] = v
                for i in u-1, u, u+1:
                    if not ( 0 < i < n-1):
                        continue
                    a, b, c = nums[i-1], nums[i], nums[i+1]
                    if a < b > c:
                        tree.update(i, 1)
                    else:
                        tree.update(i, 0)

        return res
            
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