<p>You are given a string <code>s</code> and an integer <code>repeatLimit</code>. Construct a new string <code>repeatLimitedString</code> using the characters of <code>s</code> such that no letter appears <strong>more than</strong> <code>repeatLimit</code> times <strong>in a row</strong>. You do <strong>not</strong> have to use all characters from <code>s</code>.</p>

<p>Return <em>the <strong>lexicographically largest</strong> </em><code>repeatLimitedString</code> <em>possible</em>.</p>

<p>A string <code>a</code> is <strong>lexicographically larger</strong> than a string <code>b</code> if in the first position where <code>a</code> and <code>b</code> differ, string <code>a</code> has a letter that appears later in the alphabet than the corresponding letter in <code>b</code>. If the first <code>min(a.length, b.length)</code> characters do not differ, then the longer string is the lexicographically larger one.</p>

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

<pre>
<strong>Input:</strong> s = &quot;cczazcc&quot;, repeatLimit = 3
<strong>Output:</strong> &quot;zzcccac&quot;
<strong>Explanation:</strong> We use all of the characters from s to construct the repeatLimitedString &quot;zzcccac&quot;.
The letter &#39;a&#39; appears at most 1 time in a row.
The letter &#39;c&#39; appears at most 3 times in a row.
The letter &#39;z&#39; appears at most 2 times in a row.
Hence, no letter appears more than repeatLimit times in a row and the string is a valid repeatLimitedString.
The string is the lexicographically largest repeatLimitedString possible so we return &quot;zzcccac&quot;.
Note that the string &quot;zzcccca&quot; is lexicographically larger but the letter &#39;c&#39; appears more than 3 times in a row, so it is not a valid repeatLimitedString.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;aababab&quot;, repeatLimit = 2
<strong>Output:</strong> &quot;bbabaa&quot;
<strong>Explanation:</strong> We use only some of the characters from s to construct the repeatLimitedString &quot;bbabaa&quot;. 
The letter &#39;a&#39; appears at most 2 times in a row.
The letter &#39;b&#39; appears at most 2 times in a row.
Hence, no letter appears more than repeatLimit times in a row and the string is a valid repeatLimitedString.
The string is the lexicographically largest repeatLimitedString possible so we return &quot;bbabaa&quot;.
Note that the string &quot;bbabaaa&quot; is lexicographically larger but the letter &#39;a&#39; appears more than 2 times in a row, so it is not a valid repeatLimitedString.
</pre>

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

<ul>
	<li><code>1 &lt;= repeatLimit &lt;= s.length &lt;= 10<sup>5</sup></code></li>
	<li><code>s</code> consists of lowercase English letters.</li>
</ul>

class Solution:
    def repeatLimitedString(self, s: str, repeatLimit: int) -> str:
        # Use the priority queue to maintain the available characters. Each time we pop the greatest usable character and do construction. This character will be frozen for an iteration to avoid being picked up repeatedly.
        counter = collections.Counter(s)
        ac = [(-ord(ch), ch, f) for ch, f in counter.items()]
        heapq.heapify(ac)
        prev = None
        ans = []
        while ac:
            tp = heapq.heappop(ac)
            if prev is not None and prev[1] > tp[1]:
                # This means there is a larger letter being forbidden now.
                # We should populate as least letter as possible for larger lexicographical order.
                an = 1
            else:
                an = min(tp[2], repeatLimit)
            ans.append(tp[1] * an)
            if prev is not None:
                heapq.heappush(ac, prev)
            if tp[2] > an:
                prev = (tp[0], tp[1], tp[2] - an)
            else:
                prev = None
        return "".join(ans)
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