<p>Given a string <code>formula</code> representing a chemical formula, return <em>the count of each atom</em>.</p>

<p>The atomic element always starts with an uppercase character, then zero or more lowercase letters, representing the name.</p>

<p>One or more digits representing that element&#39;s count may follow if the count is greater than <code>1</code>. If the count is <code>1</code>, no digits will follow.</p>

<ul>
	<li>For example, <code>&quot;H2O&quot;</code> and <code>&quot;H2O2&quot;</code> are possible, but <code>&quot;H1O2&quot;</code> is impossible.</li>
</ul>

<p>Two formulas are concatenated together to produce another formula.</p>

<ul>
	<li>For example, <code>&quot;H2O2He3Mg4&quot;</code> is also a formula.</li>
</ul>

<p>A formula placed in parentheses, and a count (optionally added) is also a formula.</p>

<ul>
	<li>For example, <code>&quot;(H2O2)&quot;</code> and <code>&quot;(H2O2)3&quot;</code> are formulas.</li>
</ul>

<p>Return the count of all elements as a string in the following form: the first name (in sorted order), followed by its count (if that count is more than <code>1</code>), followed by the second name (in sorted order), followed by its count (if that count is more than <code>1</code>), and so on.</p>

<p>The test cases are generated so that all the values in the output fit in a <strong>32-bit</strong> integer.</p>

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

<pre>
<strong>Input:</strong> formula = &quot;H2O&quot;
<strong>Output:</strong> &quot;H2O&quot;
<strong>Explanation:</strong> The count of elements are {&#39;H&#39;: 2, &#39;O&#39;: 1}.
</pre>

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

<pre>
<strong>Input:</strong> formula = &quot;Mg(OH)2&quot;
<strong>Output:</strong> &quot;H2MgO2&quot;
<strong>Explanation:</strong> The count of elements are {&#39;H&#39;: 2, &#39;Mg&#39;: 1, &#39;O&#39;: 2}.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> formula = &quot;K4(ON(SO3)2)2&quot;
<strong>Output:</strong> &quot;K4N2O14S4&quot;
<strong>Explanation:</strong> The count of elements are {&#39;K&#39;: 4, &#39;N&#39;: 2, &#39;O&#39;: 14, &#39;S&#39;: 4}.
</pre>

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

<ul>
	<li><code>1 &lt;= formula.length &lt;= 1000</code></li>
	<li><code>formula</code> consists of English letters, digits, <code>&#39;(&#39;</code>, and <code>&#39;)&#39;</code>.</li>
	<li><code>formula</code> is always valid.</li>
</ul>

class Solution:
    def countOfAtoms(self, formula: str) -> str:
        import collections
        import re

        def parse():
            stack = [collections.Counter()]
            i, n = 0, len(formula)
            while i < n:
                if formula[i] == '(':  # Opening parenthesis
                    stack.append(collections.Counter())
                    i += 1
                elif formula[i] == ')':  # Closing parenthesis
                    i += 1
                    i_start = i
                    while i < n and formula[i].isdigit():
                        i += 1
                    multiplier = int(formula[i_start:i] or 1)
                    top = stack.pop()
                    for elem, count in top.items():
                        stack[-1][elem] += count * multiplier
                else:  # Element name
                    i_start = i
                    i += 1
                    while i < n and formula[i].islower():
                        i += 1
                    elem = formula[i_start:i]
                    i_start = i
                    while i < n and formula[i].isdigit():
                        i += 1
                    multiplier = int(formula[i_start:i] or 1)
                    stack[-1][elem] += multiplier
            return stack.pop()

        count = parse()
        return ''.join(f'{elem}{count[elem] > 1 and count[elem] or ""}' for elem in sorted(count))

# Example usage:
# sol = Solution()
# print(sol.countOfAtoms("H2O"))  # Output: "H2O"
# print(sol.countOfAtoms("Mg(OH)2"))  # Output: "H2MgO2"
# print(sol.countOfAtoms("K4(ON(SO3)2)2"))  # Output: "K4N2O14S4"
16500