<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:
    string minimizeResult(string expression) {
      bool plus = false;
        string a = "",b="";
        for(char ch : expression){
            if(ch == '+'){
                plus = true;
            }
            if(!plus) a+=ch;
            else b+=ch;
        }
        
        int n = a.length();
        int m = b.length();
        string ans;
        int maxi = INT_MAX;
        for(int i = 0 ; i < n ; i++){
            for(int j = 1 ; j < m ; j++){
                int left;
                if(i==0) left = 1;
                else left = stoi(a.substr(0,i));
                
                int middle = stoi(a.substr(i,n-i))+stoi(b.substr(0,j+1));
                
                int right;
                if(j==m-1)right = 1;
                else right = stoi(b.substr(j+1,m-j-1));
                
                if(left*middle*right < maxi){
                    maxi = left*middle*right;
                    ans = a.substr(0,i) + "("+ a.substr(i,n-i) + b.substr(0,j+1) + ")" + b.substr(j+1,m-j-1);
                }
            }
        }
        return ans;
    }
};
8100