<p>You have a <strong>1-indexed</strong> binary string of length <code>n</code> where all the bits are <code>0</code> initially. We will flip all the bits of this binary string (i.e., change them from <code>0</code> to <code>1</code>) one by one. You are given a <strong>1-indexed</strong> integer array <code>flips</code> where <code>flips[i]</code> indicates that the bit at index <code>i</code> will be flipped in the <code>i<sup>th</sup></code> step.</p>

<p>A binary string is <strong>prefix-aligned</strong> if, after the <code>i<sup>th</sup></code> step, all the bits in the <strong>inclusive</strong> range <code>[1, i]</code> are ones and all the other bits are zeros.</p>

<p>Return <em>the number of times the binary string is <strong>prefix-aligned</strong> during the flipping process</em>.</p>

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

<pre>
<strong>Input:</strong> flips = [3,2,4,1,5]
<strong>Output:</strong> 2
<strong>Explanation:</strong> The binary string is initially &quot;00000&quot;.
After applying step 1: The string becomes &quot;00100&quot;, which is not prefix-aligned.
After applying step 2: The string becomes &quot;01100&quot;, which is not prefix-aligned.
After applying step 3: The string becomes &quot;01110&quot;, which is not prefix-aligned.
After applying step 4: The string becomes &quot;11110&quot;, which is prefix-aligned.
After applying step 5: The string becomes &quot;11111&quot;, which is prefix-aligned.
We can see that the string was prefix-aligned 2 times, so we return 2.
</pre>

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

<pre>
<strong>Input:</strong> flips = [4,1,2,3]
<strong>Output:</strong> 1
<strong>Explanation:</strong> The binary string is initially &quot;0000&quot;.
After applying step 1: The string becomes &quot;0001&quot;, which is not prefix-aligned.
After applying step 2: The string becomes &quot;1001&quot;, which is not prefix-aligned.
After applying step 3: The string becomes &quot;1101&quot;, which is not prefix-aligned.
After applying step 4: The string becomes &quot;1111&quot;, which is prefix-aligned.
We can see that the string was prefix-aligned 1 time, so we return 1.
</pre>

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

<ul>
	<li><code>n == flips.length</code></li>
	<li><code>1 &lt;= n &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>flips</code> is a permutation of the integers in the range <code>[1, n]</code>.</li>
</ul>

class Solution:
    def numTimesAllBlue(self, flips: List[int]) -> int:
        flips = [flip - 1 for flip in flips]

        next_bit = 0
        max_one_bit = -1
        res = 0
        bstring = 0
        seen = set()
        for i in flips:
            bstring ^= 2 ** i

            if i > max_one_bit:
                max_one_bit = i

            if i == next_bit:
                next_bit += 1
                while next_bit in seen:
                    next_bit += 1

            if max_one_bit < next_bit:
                res += 1

            seen.add(i)

        return res

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