<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:
    int getInt(string s, int &i){
        int n = 0;
        while(i < s.length() && s[i] >= '0' && s[i] <= '9'){
            n *= 10;
            n += (s[i++]-'0');
        }
        if( n == 0){
            n = 1;
        }
        return n;
    }

    string getAtom(string s, int &i){
        string ans = "";
        ans += s[i++];
        while(i < s.length() && s[i] >= 'a' && s[i] <= 'z'){
            ans += s[i++];
        }
        return ans;
    }

    bool isInt(string s, int i){
        return s[i] >= '1' && s[i] <= '9';
    }

    bool isAtom(string s, int i){
        return s[i] >= 'A' && s[i] <= 'Z';
    }

    map<string, int> solve(string s, int &i){
        stack<char> st;
        map<string, int> m;
        while(i < s.length()){
            if(s[i] == '('){
                map<string, int> tempMap;
                string tempString = "";
                st.push(s[i++]);
                while(i < s.length() && !st.empty()){
                    if(s[i] == '('){
                        st.push(s[i]);
                    }
                    if(s[i] == ')'){
                        st.pop();
                        if(st.empty()){
                            i++;
                            break;
                        }
                    }
                    tempString += s[i];
                    i++;
                }
                int idx = 0;
                tempMap = solve(tempString, idx);
                int mul = getInt(s, i);
                for(auto &it:tempMap){
                    m[it.first] += it.second*mul;
                }
            }
            if(isAtom(s, i)){
                string atom = getAtom(s, i);
                int mul = getInt(s, i);
                m[atom] += mul;
            }
        }
        return m;
    }

    string countOfAtoms(string formula) {
        int i = 0;
        map<string, int> atoms = solve(formula, i);
        string ans = "";
        for(auto &it:atoms){
            ans += it.first;
            if(it.second > 1){
                ans += to_string(it.second);
            }
        }
        return ans;
    }
};
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