<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:
        stack = [defaultdict(int)]
        i = 0 
        while i < len(formula):
            if formula[i] == "(":
                stack.append(defaultdict(int))
            elif formula[i] == ")":
                cur_map = stack.pop()
                count = ""
                while i + 1 < len(formula) and formula[i + 1].isdigit():
                    count += formula[i + 1]
                    i += 1
                count = 1 if not count else int(count)
                prev_map = stack[-1]
                for elem in cur_map:
                    prev_map[elem] += cur_map[elem] * count
            else:
                element = formula[i]
                count = ""
                """
                if i + 1 < len(formula) and formula[i + 1].islower():
                    element = formula[i:i+2]
                    i += 1
                """
                while i + 1 < len(formula) and formula[i + 1].islower():
                    element += formula[i + 1]
                    i += 1
                while i + 1 < len(formula) and formula[i + 1].isdigit():
                    count += formula[i + 1]
                    i += 1
                count = 1 if not count else int(count)
                cur_map = stack[-1]
                cur_map[element] += count
            i += 1

        cnt_map = stack[-1]
        res = ""
        for elem in sorted(cnt_map.keys()):
            count = "" if cnt_map[elem] == 1 else cnt_map[elem]
            res += elem + str(count)
        return res
16600