<p>There are some red and blue tiles arranged circularly. You are given an array of integers <code>colors</code> and a 2D integers array <code>queries</code>.</p>

<p>The color of tile <code>i</code> is represented by <code>colors[i]</code>:</p>

<ul>
	<li><code>colors[i] == 0</code> means that tile <code>i</code> is <strong>red</strong>.</li>
	<li><code>colors[i] == 1</code> means that tile <code>i</code> is <strong>blue</strong>.</li>
</ul>

<p>An <strong>alternating</strong> group is a contiguous subset of tiles in the circle with <strong>alternating</strong> colors (each tile in the group except the first and last one has a different color from its <b>adjacent</b> tiles in the group).</p>

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

<ul>
	<li><code>queries[i] = [1, size<sub>i</sub>]</code>, determine the count of <strong>alternating</strong> groups with size <code>size<sub>i</sub></code>.</li>
	<li><code>queries[i] = [2, index<sub>i</sub>, color<sub>i</sub>]</code>, change <code>colors[index<sub>i</sub>]</code> to <code>color<font face="monospace"><sub>i</sub></font></code>.</li>
</ul>

<p>Return an array <code>answer</code> containing the results of the queries of the first type <em>in order</em>.</p>

<p><strong>Note</strong> that since <code>colors</code> represents a <strong>circle</strong>, the <strong>first</strong> and the <strong>last</strong> tiles are considered to be next to each other.</p>

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

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

<p><strong>Output:</strong> <span class="example-io">[2]</span></p>

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

<p><strong class="example"><img alt="" data-darkreader-inline-bgcolor="" data-darkreader-inline-bgimage="" src="https://assets.leetcode.com/uploads/2024/06/03/screenshot-from-2024-06-03-20-14-44.png" style="width: 150px; height: 150px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; --darkreader-inline-bgimage: initial; --darkreader-inline-bgcolor: #181a1b;" /></strong></p>

<p>First query:</p>

<p>Change <code>colors[1]</code> to 0.</p>

<p><img alt="" data-darkreader-inline-bgcolor="" data-darkreader-inline-bgimage="" src="https://assets.leetcode.com/uploads/2024/06/03/screenshot-from-2024-06-03-20-20-25.png" style="width: 150px; height: 150px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; --darkreader-inline-bgimage: initial; --darkreader-inline-bgcolor: #181a1b;" /></p>

<p>Second query:</p>

<p>Count of the alternating groups with size 4:</p>

<p><img alt="" data-darkreader-inline-bgcolor="" data-darkreader-inline-bgimage="" src="https://assets.leetcode.com/uploads/2024/06/03/screenshot-from-2024-06-03-20-25-02-2.png" style="width: 150px; height: 150px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; --darkreader-inline-bgimage: initial; --darkreader-inline-bgcolor: #181a1b;" /><img alt="" data-darkreader-inline-bgcolor="" data-darkreader-inline-bgimage="" src="https://assets.leetcode.com/uploads/2024/06/03/screenshot-from-2024-06-03-20-24-12.png" style="width: 150px; height: 150px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; --darkreader-inline-bgimage: initial; --darkreader-inline-bgcolor: #181a1b;" /></p>
</div>

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

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

<p><strong>Output:</strong> <span class="example-io">[2,0]</span></p>

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

<p><img alt="" data-darkreader-inline-bgcolor="" data-darkreader-inline-bgimage="" src="https://assets.leetcode.com/uploads/2024/06/03/screenshot-from-2024-06-03-20-35-50.png" style="width: 150px; height: 150px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; --darkreader-inline-bgimage: initial; --darkreader-inline-bgcolor: #181a1b;" /></p>

<p>First query:</p>

<p>Count of the alternating groups with size 3:</p>

<p><img alt="" data-darkreader-inline-bgcolor="" data-darkreader-inline-bgimage="" src="https://assets.leetcode.com/uploads/2024/06/03/screenshot-from-2024-06-03-20-37-13.png" style="width: 150px; height: 150px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; --darkreader-inline-bgimage: initial; --darkreader-inline-bgcolor: #181a1b;" /><img alt="" data-darkreader-inline-bgcolor="" data-darkreader-inline-bgimage="" src="https://assets.leetcode.com/uploads/2024/06/03/screenshot-from-2024-06-03-20-36-40.png" style="width: 150px; height: 150px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; --darkreader-inline-bgimage: initial; --darkreader-inline-bgcolor: #181a1b;" /></p>

<p>Second query: <code>colors</code> will not change.</p>

<p>Third query: There is no alternating group with size 5.</p>
</div>

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

<ul>
	<li><code>4 &lt;= colors.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>0 &lt;= colors[i] &lt;= 1</code></li>
	<li><code>1 &lt;= queries.length &lt;= 5 * 10<sup>4</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>queries[i].length == 2</code>, <code>3 &lt;= queries[i][1] &lt;= colors.length - 1</code></li>
		<li><code>queries[i][0] == 2</code>: <code>queries[i].length == 3</code>, <code>0 &lt;= queries[i][1] &lt;= colors.length - 1</code>, <code>0 &lt;= queries[i][2] &lt;= 1</code></li>
	</ul>
	</li>
</ul>

from sortedcontainers import SortedList

class Solution:
    def numberOfAlternatingGroups(self, colors: List[int], queries: List[List[int]]) -> List[int]:
        n = len(colors)
        colors += colors
        
        l, sl, base = 0, SortedList(), 1
        while base <= n:
            base <<= 1
        seg = [[0, 0] for _ in  range(2 * base)]
        
        def update(x, delta):
            node = x + base
            while node:
                seg[node][0] += delta
                seg[node][1] += delta * x
                node >>= 1
        
        def insert(l, r):
            l, r = l % n, r % n
            if r < l:
                r += n
            sl.add((l, r))
            update(r - l + 1, 1)
        
        def get_component(pos):
            pos %= n
            if pos < sl[0][0]:
                pos += n
            index = sl.bisect_right((pos, 3 * n)) - 1
            l, r = sl.pop(index)
            update(r - l + 1, -1)
            return l, r, pos
        
        for r in range(1, 2 * n):
            if colors[r] == colors[r-1]:
                if l:
                    insert(l, r-1)
                if r > n:
                    break
                l = r
        else:
            insert(0, n - 1)
        
        ret = []
        for query in queries:
            # print(colors, sl)
            # print(seg[base +1:], query)
            if query[0] == 1:
                size = query[1]
                if len(sl) == 1:
                    if n & 1:
                        ret.append(n - size + 1)
                    else:
                        ret.append(n)
                    continue
                node = size + base
                cnt, tot = seg[node]
                while node > 1:
                    if not (node & 1):
                        cnt += seg[node ^ 1][0]
                        tot += seg[node ^ 1][1]
                    node >>= 1
                ret.append(tot - (size - 1) * cnt)
            else:
                index, color = query[1:]
                if colors[index] == color:
                    continue
                colors[index] = colors[index + n] = color
                l, r, index = get_component(index)
                # print(l, r, index)
                if len(sl) == 0:
                    if not (n & 1):
                        insert(index, index)
                        insert(index + 1, index + n - 1)
                    else:
                        if index == l:
                            insert(index + 1, index)
                        elif index == r:
                            insert(index, index + n - 1)
                        else:
                            insert(l, index + n - 1)
                            insert(index, index)
                            insert(index + 1, r)
                elif l < index < r:
                    insert(l, index + n - 1)
                    insert(index, index)
                    insert(index + 1, r)
                elif l == r:
                    if len(sl) == 1:
                        get_component(l + n - 1)
                        insert(0, n - 1)
                    else:
                        ll = get_component(l + n - 1)[0]
                        rr = get_component(r + 1)[1]
                        insert(ll, rr)
                elif index == l:
                    ll = get_component(l + n - 1)[0]
                    insert(ll, l)
                    insert(l + 1, r)
                elif index == r:
                    rr = get_component(r + 1)[1]
                    insert(l, r + n - 1)
                    insert(r, rr)
                # print(sl, seg[base + 1:])
        
        # print('')
        return ret
42300