<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:
    unordered_map<string, int> rec(string formula, int &i) {
        unordered_map<string, int> ct;
        unordered_map<string, int> sub;
        string name = "";
        string cnt = "";
        while (i < formula.length()) {
            char c = formula[i];
            if ((c >= 'A' && c <= 'Z') || c == '(' || c == ')') {
                int currCnt = cnt == "" ? 1 : stoi(cnt);
                if (name != "") {
                    ct[name] += currCnt;
                }
                if (c >= 'A' && c <= 'Z')
                    name = c;
                else
                    name = "";
                cnt = "";
                
                if (!sub.empty()) {
                    for (auto &p : sub) {
                        ct[p.first] += p.second * currCnt;
                    }
                    sub.clear();
                }

                ++i;
                if (c == '(') {
                    sub = rec(formula, i);
                }
                if (c == ')') {
                    //for (auto &p : ct) {
                    //    cout << p.first << " " << p.second << endl;
                    //}
                    return ct;
                }
            } else if (c >= 'a' && c <= 'z') {
                name += c;
                ++i;
            } else if (c >= '0' && c <= '9') {
                cnt += c;
                ++i;
            }
        }
        return ct;
    }
    string countOfAtoms(string formula) {
        int i = 0;
        unordered_map<string, int> res = rec(formula + "(", i);
        map<string, int> r (res.begin(), res.end());
        string str = "";
        for (auto &p : r) {
            str += p.first + (p.second == 1 ? "" : to_string(p.second));
        }
        return str;
    }
};
10000