<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:
     map<string, int> countHelper(string formula) {
        map<string, int> freq;
        while(i < formula.size() && formula[i] != ')') {
            if(formula[i] == '(') {
                i += 1;
                map<string, int> nestedFreq = countHelper(formula);
                for(auto pair: nestedFreq) {
                    freq[pair.first] += pair.second;
                }
            } else {
                string currAtom;
                currAtom += formula[i];
                i += 1;
                while(i < formula.size() && islower(formula[i])) {
                    currAtom += formula[i];
                    i += 1;
                }

                string currCount;
                while(i < formula.size() && isdigit(formula[i])) {
                    currCount += formula[i];
                    i += 1;
                }

                if(currCount.size() == 0) {
                    freq[currAtom] += 1;
                } else {
                    freq[currAtom] += stoi(currCount);
                }
            }
        }
        
        i += 1;
        string multiplier;
        while(i < formula.size() && isdigit(formula[i])) {
            multiplier += formula[i];
            i += 1;
        }
        if(multiplier.size() != 0){
            for(auto pair: freq) {
                freq[pair.first] = pair.second * stoi(multiplier);
            }
        }
        return freq;
    }
    string countOfAtoms(string formula) {
        map<string, int> freq = countHelper(formula);
        string ans;
        for(auto iter : freq) {
            ans += iter.first;
            if(iter.second > 1) {
                ans += to_string(iter.second);
            }
        }
        return ans;
    }
private:
    int i = 0;
};
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