<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) {
        int n = formula.length();
        vector<int> mult(n, 1);
        stack<int> factors;
        int multFactor = 1;
        for(int i=n-1; i>=0; --i) {
            char ch = formula[i];
            if(ch == ')') {
                string cnt = "";
                int k = i+1;
                while(k<n && isdigit(formula[k])) {
                    cnt += formula[k++];
                }
                if(cnt == "") cnt = "1";
                int digit = stoi(cnt);
                factors.push(digit);
                multFactor *= digit;
            }
            else if(ch == '(') {
                int digit = factors.top();
                factors.pop();
                multFactor /= digit;
            }
            else if(isupper(ch)) {
                mult[i] = multFactor;
            }
            else continue;
        }
        map<string, int> res;
        for(int i=0; i<n; ++i) {
            char ch = formula[i];
            if(!isupper(ch)) continue;
            multFactor = mult[i];
            string ele = "";
            ele += ch;
            int j = i+1;
            while(j<n && islower(formula[j])) {
                ele += formula[j++];
            }
            string cnt = "";
            int k = j;
            while(k<n && isdigit(formula[k])) {
                cnt += formula[k++];
            }
            if(cnt == "") cnt = "1";
            int digit = stoi(cnt);
            res[ele] += digit * multFactor;
            i = k-1;
        }
        string ans = "";
        for(auto &[ele, digit] :res) {
            string cnt = to_string(digit);
            if(cnt == "1") cnt = "";
            ans += ele + cnt;
        }
        return ans;
    }
};
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