<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 {
public:
    string countOfAtoms(string formula) {
        map<string, int> aCount;
        stack<int> mStack;
        string result;
        int count = 0, multiplier = 1;
        
        for (int i = size(formula) - 1; i >= 0; i--) 
        {
            if (isalpha(formula[i]) && islower(formula[i])) 
            {
                int len = 2;
                i--;
                
                while (i >= 0 && islower(formula[i])) 
                {
                    i--;
                    len++;
                }
                
                string atom = formula.substr(i, len);
                aCount[atom] += max(count, 1) * multiplier;
                count = 0;
            } 
            else if (isalpha(formula[i]) && isupper(formula[i])) 
            {
                string atom(1, formula[i]);
                aCount[atom] += max(count, 1) * multiplier;
                count = 0;
            } 
            else if (isdigit(formula[i])) 
            {
                count = formula[i] - '0';
                int power = 10;
                
                while (i - 1 >= 0 && isdigit(formula[i - 1])) {
                    count += power * (formula[--i] - '0');
                    power *= 10;
                }
            } 
            else if (formula[i] == ')') 
            {
                mStack.push(multiplier);
                multiplier *= max(count, 1);
                count = 0;
            } 
            else {
                multiplier = mStack.top();
                mStack.pop();
            }
        }
        
        for (auto [atom, cnt]: aCount) {
            result += atom;
            
            if (cnt > 1) {
                result += to_string(cnt);
            }
        }
        
        return result;
    }
};
8500