<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 s) {
        stack<pair<string, int>> st; 
        stack<int> fact;
        int n = s.length(), m = 1, val = 1;

        for(int i = n - 1; i >= 0; i--){
            char ch = s[i];
            // ch --> lowercase letter
            if(ch >= 'a' && ch <= 'z'){
                string element = "";
                while(!(s[i] >= 'A' && s[i] <= 'Z')){
                    element = s[i] + element;
                    i--;
                }
                element = s[i] + element;
                int freq = m*val;
                st.push({element, freq});
                val = 1;
            }
            // ch --> uppercase letter
            else if(s[i] >= 'A' && s[i] <= 'Z'){
                string element = "";
                element += s[i];
                int freq = m*val;
                st.push({element, freq});
                val = 1;
            }
            else if(ch == ')'){
                fact.push(val);
                m *= val;
                val = 1;
            }
            else if(ch == '('){
                m /= fact.top();
                fact.pop();
            }
            else{
                string num = "";
                while(s[i] <= '9' && s[i] >= '0'){
                    num = s[i] + num;
                    i--;
                }
                i++; 
                val = stoi(num);
            }
        }
        
        map<string, int> mp;
        while(! st.empty()){
            auto it = st.top(); st.pop();
            string str = it.first;
            int freq = it.second;
            mp[str] += freq;
        }
        string res = "";
        for(auto it : mp){
            string ele = it.first;
            string freq = "";
            if(it.second != 1) freq += to_string(it.second);
            res += ele + freq;
        }
        return res;
    }
};
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