<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 SGT:
    def __init__(self, n):
        self.seg = [0] * (4 * n + 1)

    def build(self, ind, low, high, arr):
        if low == high:
            self.seg[ind] = arr[low]
            return

        mid = (low + high) // 2

        self.build(2 * ind + 1, low, mid, arr)
        self.build(2 * ind + 2, mid + 1, high, arr)

        self.seg[ind] = self.seg[2 * ind + 1] + self.seg[2 * ind + 2]

    def query(self, ind, low, high, l, r):
        if r < low or high < l:
            return 0

        if low >= l and high <= r:
            return self.seg[ind]

        mid = (low + high) // 2
        left = self.query(2 * ind + 1, low, mid, l, r)
        right = self.query(2 * ind + 2, mid + 1, high, l, r)

        return left + right

    def update(self, ind, low, high, i, val):
        if low == high:
            self.seg[ind] = val
            return

        mid = (low + high) // 2

        if i <= mid:
            self.update(2 * ind + 1, low, mid, i, val)
        else:
            self.update(2 * ind + 2, mid + 1, high, i, val)

        self.seg[ind] = self.seg[2 * ind + 1] + self.seg[2 * ind + 2]


class Solution:
    def countOfPeaks(self, nums, queries):
        n = len(nums)
        peak = [0] * n

        for i in range(1, n - 1):
            if nums[i] > nums[i - 1] and nums[i] > nums[i + 1]:
                peak[i] = 1

        result = []
        st = SGT(n)
        st.build(0, 0, n - 1, peak)

        for q in queries:
            type = q[0]

            if type == 1:
                l = q[1]
                r = q[2]

                if r - l < 2:
                    result.append(0)
                else:
                    res = st.query(0, 0, n - 1, l + 1, r - 1)
                    result.append(res)
            elif type == 2:
                p = q[1]
                x = q[2]
                nums[p] = x

                def update_peak(idx):
                    nonlocal peak
                    if 0 < idx < n - 1:
                        if nums[idx] > nums[idx - 1] and nums[idx] > nums[idx + 1]:
                            if peak[idx] == 0:
                                peak[idx] = 1
                                st.update(0, 0, n - 1, idx, 1)
                        else:
                            if peak[idx] == 1:
                                peak[idx] = 0
                                st.update(0, 0, n - 1, idx, 0)

                update_peak(p)
                if p > 0:
                    update_peak(p - 1)
                if p < n - 1:
                    update_peak(p + 1)

        return result
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