<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:
    def countOfAtoms(self, formula: str) -> str:

        stack=[]
        l=0
        while l<len(formula):
            n=formula[l]
            if n=='(':
                stack.append(n)
            elif n==')':
                digit=''
                r=l
                while r+1< len(formula) and formula[r+1].isdigit():
                    r+=1
                    digit+=formula[r]
                digit=int(digit) if digit else 1
                tmp=[]
                while stack[-1]!='(':
                    e=stack.pop()
                    if digit==1:
                        e[1] =e[1]*digit
                    else:
                        e[1] =e[1]*digit if e[1]!=0 else digit
                    tmp.append(e)
                stack.pop()
                stack.extend(tmp[::-1])
                l=r
            elif n.isalpha() and n.islower():
                stack[-1][0]+=n
            elif n.isalpha() and n.isupper():
                stack.append([n,0] )
            else:
                stack[-1][1]= stack[-1][1]*10+int(n)         
            l+=1
        
        d=defaultdict(int)
        for k,n in stack:
            d[k]+=n if n!=0 else 1
        res=''
        for k,v in sorted(d.items(),key=lambda x:x[0]):
            if v==1:
                res+=k
            else:
                res+=k+str(v)
        return res



            

        
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