<p>You are given a <strong>0-indexed</strong> string <code>expression</code> of the form <code>&quot;&lt;num1&gt;+&lt;num2&gt;&quot;</code> where <code>&lt;num1&gt;</code> and <code>&lt;num2&gt;</code> represent positive integers.</p>

<p>Add a pair of parentheses to <code>expression</code> such that after the addition of parentheses, <code>expression</code> is a <strong>valid</strong> mathematical expression and evaluates to the <strong>smallest</strong> possible value. The left parenthesis <strong>must</strong> be added to the left of <code>&#39;+&#39;</code> and the right parenthesis <strong>must</strong> be added to the right of <code>&#39;+&#39;</code>.</p>

<p>Return <code>expression</code><em> after adding a pair of parentheses such that </em><code>expression</code><em> evaluates to the <strong>smallest</strong> possible value.</em> If there are multiple answers that yield the same result, return any of them.</p>

<p>The input has been generated such that the original value of <code>expression</code>, and the value of <code>expression</code> after adding any pair of parentheses that meets the requirements fits within a signed 32-bit integer.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;247+38&quot;
<strong>Output:</strong> &quot;2(47+38)&quot;
<strong>Explanation:</strong> The <code>expression</code> evaluates to 2 * (47 + 38) = 2 * 85 = 170.
Note that &quot;2(4)7+38&quot; is invalid because the right parenthesis must be to the right of the <code>&#39;+&#39;</code>.
It can be shown that 170 is the smallest possible value.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;12+34&quot;
<strong>Output:</strong> &quot;1(2+3)4&quot;
<strong>Explanation:</strong> The expression evaluates to 1 * (2 + 3) * 4 = 1 * 5 * 4 = 20.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;999+999&quot;
<strong>Output:</strong> &quot;(999+999)&quot;
<strong>Explanation:</strong> The <code>expression</code> evaluates to 999 + 999 = 1998.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>3 &lt;= expression.length &lt;= 10</code></li>
	<li><code>expression</code> consists of digits from <code>&#39;1&#39;</code> to <code>&#39;9&#39;</code> and <code>&#39;+&#39;</code>.</li>
	<li><code>expression</code> starts and ends with digits.</li>
	<li><code>expression</code> contains exactly one <code>&#39;+&#39;</code>.</li>
	<li>The original value of <code>expression</code>, and the value of <code>expression</code> after adding any pair of parentheses that meets the requirements fits within a signed 32-bit integer.</li>
</ul>

class Solution {
public:
    int calc(string s,int a,int b){
        int num1,num2,num3,num4,i=0;

        num1=(a!=-1)?stoi(s.substr(0,a+1)):1;
        num2=stoi(s.substr(a+1,s.find('+')-a-1));
        num3=stoi(s.substr(s.find('+')+1,b-s.find('+')-1));
        num4=(b!=s.length())?stoi(s.substr(b)):1;

        return((num2+num3)*num1*num4);
    }
    string minimizeResult(string expression) {
        int x,y,val=INT_MAX,ind=expression.find('+');
        for(int a=-1;a<ind-1;a++){
            for(int b=expression.length();b>ind+1;b--){
                int num=calc(expression,a,b);
                if(num<val){
                    val=num;
                    x=a;
                    y=b;
                }
            }
        }
        return expression.substr(0,x+1)+"("+expression.substr(x+1,y-x-1)+")"+expression.substr(y);
    }
};
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