<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 f) {
        int n = f.size();
        map<string, int> mp;
        int i = 0;
        while(i<n){
            if(f[i]>='A' && f[i]<='Z'){
                string s;
                s.push_back(f[i]);
                i++;
                while(i<n && f[i]<='z' && f[i]>='a'){
                    s.push_back(f[i]);
                    i++;
                }
                string ind;
                while(i<n && f[i]<='9' && f[i]>='0'){
                    ind.push_back(f[i]);
                    i++;
                }
                int val = (ind.size()>0)?stoi(ind):1;
                mp[s]+=val;
            }
            else{
                int x = 1;
                string s;
                i++;
                while(i<n && x){
                    if(f[i]=='(') x++;
                    if(f[i]==')') x--;
                    s.push_back(f[i]);
                    i++;
                }
                s.pop_back();
                string ind;
                while(i<n && f[i]<='9' && f[i]>='0'){
                    ind.push_back(f[i]);
                    i++;
                }
                int val = (ind.size()>0)?stoi(ind):1;
                s = countOfAtoms(s);
                int j=0, m = s.size();
                while(j<m){
                    string ss;
                    ss.push_back(s[j]);
                    j++;
                    while(j<m && s[j]<='z' && s[j]>='a'){
                        ss.push_back(s[j]);
                        j++;
                    }
                    string ind;
                    while(j<m && s[j]<='9' && s[j]>='0'){
                        ind.push_back(s[j]);
                        j++;
                    }
                    int val1 = (ind.size()>0)?stoi(ind):1;
                    mp[ss]+=val1*val;
                }
            }
            
        }
        string ans;
        for(auto x:mp){
            ans+=x.first;
            if(x.second>1) ans+=to_string(x.second);
        }
        return ans;
    }
};
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